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Scientific publications on "Light & Color in Nature"

Many scientific papers have been published on subjects related to "Meteorological Optics" or "Atmospheric Optics". A significant proportion of these papers have been triggered by a series of international meetings on "Light & Color in Nature" which attracts scientists from around the world who love to observe and explain optical phenomena in their natural environment. The meetings began (and continue) because these people enjoy getting together to learn from and share with each other.

1) Meteorological Optics, August 28-29, 1978, Keystone, Colorado (coordinated by David Lynch)

2) Atmospheric Optics, January 3-5, 1983, Incline Village, Nevada (coordinated by William Mach & Alistair Fraser)

3) Meteorological Optics, April 2-3, 1986, Honolulu, Hawaii (coordinated by David Lynch)

4) Light & Color in the Open Air, July 11-13, 1990, Washington, D.C.(coordinated by Robert Greenler)

5) Light & Color in the Open Air, June 16-18, 1993, State College, Pennsylvania (coordinated by Craig Bohren)

6) Light & Color in the Open Air, February 10-12, 1997, Santa Fe, New Mexico (coordinated by Ken Sassen)

7) Meteorological Optics, June 6-8, 2001, Boulder, Colorado (coordinated by Stanley Gedzelman)

8) Atmospheric/Meteorological Optics, June 13-17, 2004, Bad Honnef, Germany (coordinated by Michael Vollmer)

9) Light & Color in Nature, June 25-29, 2007, Bozeman, Montana (coordinated by Joseph Shaw)

10) Light & Color in Nature, June 16-20, 2010, St. Mary's City, Maryland (coordinated by Chuck Adler)

11) Light & Color in Nature, August 4-8, 2013, University of Alaska at Fairbanks, Alaska (coordinated by Ken Sassen)

12) Light & Color in Nature, May 31 - June 3, 2016, University of Granada, Spain (coordinated by Javier Hernández-Andrés)

13) Light & Color in Nature, July 15-18, 2019, College of the Atlantic, Bar Harbor, Maine (coordinated by Raymond Lee)

A paper entitled "Light and Color in Nature: A Return to Optics' Roots" by Robert Greenler and David Lynch (Optics and Photonics News, 22, 30-37, September 2011) explores the history of these meetings and offers some magnificent illustrations. Free download

Following each of these meetings, the Optical Society of America (OSA) has generously published a Feature Issue of one of its peer-reviewed journals. These Feature Issues draw heavily (but not exclusively) on contributions made at these meetings.

Journal of Optical Society of America: August 1979

Journal of Optical Society of America: December 1983

Journal of Optical Society of America A: March 1987

Applied Optics: August 1991

Applied Optics: July 1994

Applied Optics: March 1998

Applied Optics: January 2003

Applied Optics: September 2005

Applied Optics: December 2008

Applied Optics: October 2011

Applied Optics: February 2015

Applied Optics: July 2017

Applied Optics: July 2020

The following very long list shows relevant papers published by the OSA (with the feature issues identified by a yellow background color). This list is in reverse chronological order, but you can easily search for key words (e.g "halo" or "rainbow") or for the name of a particular author using the "Find" feature of your web browser.

If you have a subscription to the relevant OSA Journal, you can download a PDF version of each paper by clicking on the link marked OSA Optics InfoBase and then clicking on "View Full Text: PDF". If you do not have such a subscription, you can purchase a PDF version (currently at a price of $15 per paper if you are an OSA member or $35 if you are not an OSA member) by following the same link.

However, the following authors have made their papers freely available via their non-commercial web sites - as indicated by the Free download links.
John Adam
Pat Arnott
Michael Berry
Javier Hernández-Andrés
Gábor Horváth
Günther Können
Philip Laven
James A. Lock
Raymond L. Lee Jr
Waldemar H. Lehn
David K. Lynch
Markus Selmke
Joachim Schlichting
Joe Shaw
Walter Tape

Please note that OSA's Copyright Policy states that "Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law".

Generalized Airy theory and its region of quantitative validity Free download
James A. Lock, Gunther P. Können and Philip Laven
Journal of Quantitative Spectroscopy & Radiative Transfer 312 (2024) 108794
Airy theory has long proved to be a remarkably simple analytical model that describes the various features of the atmospheric rainbow. But the stringent assumptions upon which its derivation is based, prevent it from being quantitatively accurate in practical situations. We derive an analytical generalization of Airy theory for both the transverse electric and magnetic polarizations and for an arbitrary number of internal reflections. This generalized analytical model contains both the Airy integral and its first derivative, multiplied by constants of proportionality that are independent of the scattering angle. We find that, for the primary rainbow, it provides a quantitatively accurate approximation to the exact Lorenz-Mie-Debye theory of the rainbow for a much wider range of sizes of spherical water drops than does the original version of Airy theory, but still has stringent limitations for the second-order rainbow and beyond.

Bubble optics: upward emerging ray paths
Markus Selmke and James Lock
Applied Optics, 60, 29, 9188-9199 (2021) OSA Optics InfoBase
Light scattered by floating bubbles is a fascinating everyday phenomenon and a relevant issue for climate science and remote sensing. Here, we discuss light scattering in the upward hemisphere in the geometrical optics (GO) approximation for plane wave incidence with various inclinations on isolated floating bubbles of various sizes, using numerical and analytical caustic theory methods. We identify and discuss the relevant ray paths and explain the caustic evolution observed on a screen placed close to and above a large bubble.

Bubble Optics: Leonardo’s cross revisited: Part 1, numerical methods
Markus Selmke and James Lock
Applied Optics, 60, 21, 6213-6225 (2021) OSA Optics InfoBase
Likely around 1508, Leonardo DaVinci observed a curious image of the sun formed by a floating bubble. Now, some 500 years later, we give a full picture of the surprisingly rich phenomenology of the light pattern formed below surface bubbles. Under shallow illumination, and for shallow depths of water, the caustic deviates from the symmetrical astroid shape obtained for larger depths and/or near-vertical illu- mination. Whereas the astroid caustic involves refraction through the outer meniscus only, more complex ray paths explain the asymmetric, multi-component (composite) light pattern.

Bubble Optics: Leonardo’s cross revisited: Part 2, paraxial analytical methods
James Lock and Markus Selmke
Applied Optics, 60, 21, 6226-6234 (2021) OSA Optics InfoBase
In about 1508, Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the meniscus surrounding a bubble on the surface of a water-filled container. This caustic was analyzed in a companion paper using a numerical ray theory spot diagram approach, and is analyzed here using analytic ray theory approaches appropriate to the paraxial regime. We demonstrate that the caustic assumes the standard astroid form when the maximum meniscus slope is small, and the shape starts to distort as the maximum meniscus slope increases. We show that competition between generalized coma and generalized astigmatism, with generalized coma dominating, is responsible for the cusp points of the astroid in the plane of the incident light being reversed with respect to their images in the exit plane of the optical system. We also show that Leonardo’s cross is the result of the two-fold symmetry of the astigmatic focusing of the diagonally incident plane wave by the circularly symmetric meniscus.

Bubble Optics: Leonardo’s cross revisited: Part 3, non-paraxial analytical methods
James Lock and Markus Selmke
Applied Optics, 60, 21, 6235-6242 (2021) OSA Optics InfoBase
In about 1508 Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the circularly symmetric meniscus surrounding a bubble on the surface of a water-filled container. This caustic was analyzed in two companion papers using a numerical ray theory spot diagram approach, and paraxial analytical methods. In this study we employ non-paraxial analytical methods which are necessary when the outer bubble meniscus rises high above the ambient water surface. We also use a simple exactly soluble approximation to the outer meniscus shape, and obtain a distorted astroid caustic. We show that one of the refraction astroid cusp points is blocked by an aperture effect for steeply diagonally incident light, and the missing cusp is approximately replaced by a new cusp due to light transmitted through the bubble into the water, and reflecting from the underside of the outer meniscus.


Optical caustics of multiple objects in water: two vertical rods and normally incident light
Markus Selmke and James A. Lock
Applied Optics 59, 26, 7981-7993 (2020) OSA Optics InfoBase
The optical caustics of the combined water menisci raised by two objects with identical circular cross sections show peculiar caustic metamorphoses known from binary gravitational lenses. We highlight their genericity and analyze the connection of the refracting interface topography and curvature landscape with the caustics’ (and their images’) topology.

Feature issue: Applied Optics, July 2020

Subsuns and rainbows during solar eclipses Free download
Gunther P. Können, Glenn Schneider, Evan H. Zucker, and Panu Lahtinen
Applied Optics 59, 21, F1-F10 (July 2020) OSA Optics InfoBase
A photographic observation sequence was obtained of a subsun before, during, and after the total phase of the 2016 solar eclipse. The time-resolved images were obtained from a high-altitude jet aircraft. The image sequence was searched for the possible presence of a solar corona-generated subsun during totality. Although the subsun-creating conditions apparently persisted during totality, the drop in signal intensity compared to the local background prevented its detection. Separately,we document a visual observation from the 1977 total solar eclipse of a rainbow that faded, in the last a few seconds before totality, from being normally multicolored to monochromatic red from water drops then predominantly illuminated by light from the solar chromosphere. A similar transition in the final seconds before, and after, totality is expected to occur for parhelia. The posited short-living monochromatic red parhelion resulting from the momentary illumination of ice crystals by the solar chromosphere is still waiting to be observed.

Below the horizon—the physics of extreme visual ranges
Michael Vollmer
Applied Optics 59, 21, F11-F19 (2020) OSA Optics InfoBase
Visual ranges of up to 440 km have recently been documented by photographs of ground-based observers. A report from 1948 claimed a record visual range from a plane of more than 530 km and a similar recent observation from 2017 was documented by a photo. Such extreme visual ranges can in principle be explained by the interplay of refraction and light scattering. However, they require optimal atmospheric conditions, and cleverly chosen locations and times.

Dislocated spots and triple splittings of natural rainbows generated by large drop distortions, oscillations, and tilts
Alexander Haußmann
Applied Optics 59, 21, F20-F31 (2020) OSA Optics InfoBase
For an accurate modeling of natural rainbows, it is necessary to take into account the flattened shape of falling raindrops. Larger drops do also oscillate, and their axes exhibit tilt angles with respect to the vertical. In this paper, I will discuss two rare rainbow phenomena that are influenced by these effects: bright spots belonging to various rainbow orders, but appearing at remarkable angular distances from their traditional locations, as well as triple-split primary rainbows. While the former have not been observed in nature so far, the latter have been documented in a few photographs. This paper presents simulations based on natural drop size distributions using both a geometric optical model, as well as numerically calculated Möbius shifts applied to Debye series data.

Near-zone transmission caustic of a hanging water drop
James A. Lock
Applied Optics 59, 21, F32-F40 (2020) OSA Optics InfoBase
A water drop hanging from a house siding board after a rain shower is near-normally illuminated by sunlight either shortly after sunrise or before sunset. A focusing caustic consisting of a bright V-shape or U-shape with a small bright elliptical shape immediately above it is frequently seen on the next lower siding board. In addition, there are two broad regions of illumination immediately above the caustic, fanning out to the upper left and upper right. This complicated pattern, composed of a bright V-shape or U-shape, and the bottom half of the small bright elliptical-shape immediately above it, is caused by the hyperbolic umbilic diffraction caustic near the condition of maximum focus. This can be observed because, by a stroke of good fortune, the distance between the lower edge of a siding board and the flat portion of the next siding board beneath it is nearly equal to the paraxial focal distance of the caustic. Blocking off the light incident on the top, bottom, left side, and right side of the drop was used to determine the portion of the drop responsible for different parts of the caustic. The results were found to match the predictions for the hyperbolic umbilic caustic.

Digital all-sky polarization imaging of the total solar eclipse on 21 August 2017 in Rexburg, Idaho, USA
Laura M. Eshelman, Martin Jan Tauc, Taiga Hashimoto, Kendra Gillis, William Weiss, Bryan Stanley, Preston Hooser, Glenn E. Shaw, and Joseph A. Shaw
Applied Optics 59, 21, F41-F52 (2020) OSA Optics InfoBase
All-sky polarization images were measured from sunrise to sunset and during a cloud-free totality on 21 August 2017 in Rexburg, Idaho using two digital three-camera all-sky polarimeters and a time-sequential liquid-crystalbased all-sky polarimeter. Twenty-five polarimetric images were recorded during totality, revealing a highly dynamic evolution of the distribution of skylight polarization, with the degree of linear polarization becoming nearly zenith-symmetric by the end of totality. The surrounding environment was characterized with an infrared cloud imager that confirmed the complete absence of clouds during totality, an AERONET solar radiometer that measured aerosol properties, a portable weather station, and a hand-held spectrometer with satellite images that measured surface reflectance at and near the observation site. These observations confirmthat previously observed totality patterns are general and not unique to those specific eclipses. The high temporal image resolution revealed a transition of a neutral point from the zenith in totality to the normal Babinet point just above the Sun after third contact, providing the first indication that the transition between totality and normal daytime polarization patterns occurs over of a time period of approximately 13 s.

Imaging through a homogeneous circular cylinder: the role of virtual caustics, rainbow glare points, and image fragmentation
James A. Lock
Applied Optics 59, 21, F53-F62 (2020) OSA Optics InfoBase
Small air bubbles on the rear inside surface of a water-filled cylinder, near its edges, appear horizontally elongated, joined in pairs, and take on color. Similarly, if an extended object is sufficiently close to the water-filled cylinder, three images of the object are seen when looking through the cylinder. The center image joins onto the left or right image as the observermoves his or her head back and forth in front of the cylinder. The first observation is explained in terms of glare points of light, and the real and virtual parts of the external caustic of the light transmitted through the water-filled cylinder. The second observation is explained as an example of Berry’s caustic touching theorem which describes the topological method of fragmentation of an object’s image into multiple images. For the situation studied here, an imaginary cylindrical aberration caustic of the water-filled cylinder decomposes object space into a three-ray region sandwiched between two one-ray regions. As an extended object crosses the caustic boundary from one of the one-ray regions into the three-ray region, an image-pair creation event occurs, which is followed by an image-pair disconnection event producing the three images. Similarly, when the extended object crosses the caustic boundary fromthe three-ray region into one of the one-ray regions, an image-pair merging event occurs, which is followed by an image-pair annihilation event producing the one remaining image.

Analyzing colors and spectra of natural rainbows with hyperspectral imaging Free download
Raymond L. Lee, Jr.
Applied Optics 59, 21, F63-F70 (2020) OSA Optics InfoBase
Few colorimetric analyses of natural rainbows (i.e., bows seen in rain showers) have been published, and these are limited either to approximate techniques (colorimetrically calibrated red–green–blue (RGB) cameras) or to rainbow proxies (bows seen in sunlit water-drop sprays). Furthermore, no research papers provide angularly detailed spectra of natural rainbows in the visible and near-IR. Thus some uncertainty exists about whether the published spectra and colors differ perceptibly fromthose in natural rainbows.However, battery-powered imaging spectrometers now make possible direct field measurements of the observed chromaticities and spectra in such bows. These data (1) show consistent spectral and colorimetric patterns along rainbow radii and (2) let one subtract additively mixed background light to reveal the intrinsic colors and spectra produced by rainbow scattering in nature.

Detection of polarization neutral points in observations of the combined corona and sky during the 21 August 2017 total solar eclipse Free download
Frans Snik, Steven P. Bos, Stefanie A. Brackenhoff, David S. Doelman, Emiel H. Por, Felix Bettonvil, Michiel Rodenhuis, Dmitry Vorobiev, Laura M. Eshelman, and Joseph A. Shaw
Applied Optics 59, 21, F71-F77 (2020) OSA Optics InfoBase
We report the results of polarimetric observations of the total solar eclipse of 21 August 2017 from Rexburg, Idaho (USA). We use three synchronized DSLR cameras with polarization filters oriented at 0°, 60°, and 120° to provide high-dynamic-range RGB polarization images of the corona and surrounding sky. We measure tangential coronal polarization and vertical sky polarization, both as expected. These observations provide detailed detections of polarization neutral points above and below the eclipsed Sun where the coronal polarization is canceled by the sky polarization. We name these special polarization neutral points after Minnaert and Van de Hulst.

Solar eclipse skies and limb reddening
Stanley David Gedzelman
Applied Optics 59, 21, F78-F84 (2020) OSA Optics InfoBase
During solar eclipses the sunlit tops of cloud layers and arctic sea ice near the umbra appear salmon–brown when viewed from airplanes or satellites. Under these conditions, the clouds and atmosphere are illuminated by light restricted to the solar limb, which has effective radiating temperatures as low as 4000 K. The resulting limb reddening largely accounts for the color. A second-order scattering model is used to simulate the color of photographs of cloud tops taken from a flight during the 21 August 2017 eclipse and MODIS Aqua and Terra satellite “true color” images during the 2 July 2019 eclipse. These observed color changes provide data that has potential value in determining the vertical temperature profile of the solar photosphere.

Mueller matrix characterizations of circularly polarized reflections from golden scarab beetles
Laura E. Bagge, Arthur C. Kenton, Bridget A. Lyons, Martin F. Wehling, and Dennis H. Goldstein
Applied Optics 59, 21, F85-F93 (2020) OSA Optics InfoBase
Circularly polarized light (CPL) reflections are rare in nature. Only a few animal groups — most notably certain stomatopod crustaceans and certain beetles in the family Scarabaeidae — are known to reflect CPL from incident unpolarized light. Here, we examine five species ofmetallic scarabs in the genus Chrysinathat, to the naked human eye, look remarkably similar. Using aspectropolarimetric reflectometer to characterize the complete Mueller matrix elements of the beetles’ elytral surfaces, we found that four of the five species were strongly left-handed circularly polarized(LHCP), and only one scarab species, Chrysinaresplendens, had an overall lower degree of polarization and switched from LHCP to right-handed circularly polarized reflectance depending on wavelength.

Was Dürer 500  years ahead of science?
David Pye
Applied Optics 59, 21, F94-F97 (2020) OSA Optics InfoBase
Brewster’s dark patch is a simple optical effect in the environment. It is easily seen, but apparently it has not been formally noticed or explained until quite recently. Nevertheless, some artists appear to have represented it in paintings without, of course, knowing its optical origins. A case can be made that a watercolor by Albrecht Dürer from around 1497 illustrates the phenomenon.

Clear sky blinks
David K. Lynch and Steven C. Richtsmeier
Applied Optics 59, 21, F98-F104 (2020) OSA Optics InfoBase
Ice blinks and water skies are brightness variations on the undersides of overcasts that allow ground-based observers to judge the nature of distant surfaces such as water (dark) or ice (bright). The clear sky should also scatter light from distant surfaces that might be visually detectable. We demonstrate that clear sky blinks do occur, can be visually discerned, and can be successfully photographed. We also model them theoretically using Monte Carlo simulations. The presence of atmospheric aerosols significantly enhances clear sky blinks.

Sunrise on the pines
John Hardwick
Applied Optics 59, 25, 7560-7566 (2020) OSA Optics InfoBase
As the sun rises above a mountain ridge populated with pine trees, a short-lived but spectacular light scattering effect off the pine needles is visible. It was noted by the Victorian physicist and mountaineer John Tyndall in his two mountaineering books, and this paper describes Tyndall’s observations, discusses his and Professor Necker’s descriptions, and illustrates the effect with a modern photographic image, as well as commenting on possible explanations of the phenomenon. A rarely cited reference to a memorandum of Babinet has been found that gave Necker’s description as a spectacular example to illustrate his theorem “Babinet’s Principle.”

Bubble optics
Markus Selmke
Applied Optics, 59, 1, 45-58 (January 2020) OSA Optics InfoBase
Starting from a peculiar image observed below a bubble that is floating at a water–air interface, this paper analyzes several optical properties of these special types of refracting objects (termed bubble axicons). Using mainly geometrical optics, their relation to common axicons, the shadow-sausage effect, and elementary optical catastrophes (caustics) are discussed.


Halo in the box: a macroscopic crystal arrangement to project mosaic halos
Markus Selmke and Sarah Selmke
Applied Optics 57, 29, 8614-8623 (October 2018) OSA Optics InfoBase
We describe a three-dimensional halo demonstration experiment. A volumetric arrangement of crystals is used to project a mosaic halo display upon illumination. The demonstration can be used to convey the collective scattering aspect of the natural halo mechanism and at the same time vividly portray the concept of orientation classes in the context of halo theory.

Wine glass caustic and halo analogies
Markus Selmke
Applied Optics 57, 19, 5259-5267 (July 2018) OSA Optics InfoBase
This paper aims to develop an understanding of a peculiar hourglass-shaped caustic that can be observed if a partially filled wine glass is illuminated by parallel light. The light pattern is first described in terms of an idealized model of the liquid volume only: the sum of the parametric projection curves obtained by light refraction through liquid cones of varying wall inclinations in the framework of geometrical optics. Within this analysis, analogues to two specific refraction ice halos, the circumzenithal and the Parry arc, will prove to be helpful. The analysis is supplemented by ray tracing simulations that further elucidate the origin of the hourglass caustic when the glass is added to the refraction scenario.

The rainbow in the box
Markus Selmke and Sarah Selmke
American Journal of Physics, 86, 4, 316-318 (2018). American Journal of Physics
We describe a three-dimensional (3D) rainbow demonstration experiment. Its key idea is to convey a particular aspect of the natural phenomenon, namely, the origin of the perceived rainbow being multiple individual glints from within a rainshower. Raindrops in this demonstration are represented by acrylic spheres arranged on pillars within a cubic volume. Defocused imaging with a camera or the eye reveals a mosaic rainbow (segment) when viewed and illuminated in the appropriate fashion.

Revisiting the round bottom flask rainbow experiment
Markus Selmke and Sarah Selmke
American Journal of Physics, 86, 1, 14-21 (2018) American Journal of Physics
A popular demonstration experiment in optics uses a round-bottom flask filled with water to project a circular rainbow on a screen with a hole through which the flask is illuminated. We show how the vessel's wall shifts the first- and second-order bows towards each other and consequently reduces the width of Alexander's dark band. We address the challenge this introduces in observing Alexander's dark band, and explain the importance of a sufficient distance between the flask and the screen. The wall-effect also introduces a splitting of the bows that can easily be misinterpreted.

Refraction near the horizon—an empirical approach. Part 1: terrestrial refraction of the dip: erratum
Marcel E. Tschudin
Applied Optics 57, 13, 3479-3480 (May 2018) OSA Optics InfoBase
This erratum corrects Eq. (13a) in Applied Optics 55, 3104(2016) and shows its effecton the proposed dip estimate functions Eqs. (21a)–(21d2). The differences are small, maximal up to a few percent and well within the original error limits. A new figure shows how the variability of the terrestrial refraction of the dip — as estimated with the proposed estimate functions — decreases with increasing observer heights.

Extended visual range during solar eclipses
Michael Vollmer and Joseph A. Shaw
Applied Optics 57, 12, 3250-3259 (April 2018) OSA Optics InfoBase
During the solar eclipse on 21 August 2017, observed from Rexburg, Idaho, the eastern horizon for a short time period close to totality showed the contours of the Grand Teton mountain range from distances between about 80 and 90 km. In most of the partial phase before and after the eclipse, the visual range was below 80 km and the mountains could not be seen by the naked eye because of wildfire smoke in the air. We present photographic evidence of extension of the visual range during the eclipse and explain it in terms of a simple model for the daytime visual range. In this model, contrast between a black object and the sky increases whenever the ratio of nearby to distant air light reduces. As a consequence, we predict asymmetries with regard to totality and also that similar phenomena may be observed if part of the line of sight close to the observer is in deep shade of a thick cloud cover.


Polarization optics of the Brewster’s dark patch visible on water surfaces versus solar height and sky conditions: theory, computer modeling, photography, and painting
Péter Takács, András Barta, David Pye, and Gábor Horváth
Applied Optics 56, 30, 8353-8361 (2017) OSA Optics InfoBase
When the sun is near the horizon, a circular band with approximately vertically polarized skylight is formed at 90° from the sun, and this skylight is only weakly reflected from the region of the water surface around the Brewster’s angle (53° from the nadir). Thus, at low solar heights under a clear sky, an extended dark patch is visible on the water surface when one looks toward the north or south quarter perpendicular to the solar vertical. In this work, we study the radiance distribution of this so-called Brewster’s dark patch (BDP) in still water as functions of the solar height and sky conditions. We calculate the pattern of reflectivity 𝑅 R of a water surface for a clear sky and obtain from this idealized situation the shape of the BDP. From three full-sky polarimetric pictures taken about a clear, a partly cloudy, and an overcast sky, we determine the 𝑅 R pattern and compose from that synthetic color pictures showing how the radiance distribution of skylight reflected at the water surface and the BDPs would look under these sky conditions. We also present photographs taken without a linearly polarizing filter about the BDP. Finally, we show a 19th century painting on which a river is seen with a dark region of the water surface, which can be interpreted as an artistic illustration of the BDP.

Artificial circumzenithal and circumhorizontal arcs
Markus Selmke and Sarah Selmke
American Journal of Physics, 85, 8, 575-581 (2017) American Journal of Physics
A glass of water, with white light incident upon it, is typically used to demonstrate a rainbow. On a closer look, this system turns out to be a rather close analogy of a different kind of atmospheric optics phenomenon altogether: circumzenithal and the circumhorizontal halos. The work we present here should provide a missing practical demonstration for these beautiful and common natural ice halo displays.

Feature issue: Applied Optics, July 2017

Light and color in the open air—introduction to the feature issue Free download
Philip Laven, Joseph A. Shaw, and Raymond L. Lee
Applied Optics, Vol. 56, Issue 19, pp. LC1-LC2 (July 2017) OSA Optics InfoBase
This feature issue reports recent progress in scientific understanding of optical phenomena in the natural world, visible to the naked eye. The issue contains papers largely arising from presentations given at the 12th International Conference on Light and Color in Nature, held at the University of Granada from 31 May to 3 June 2016.

Icebows Free download
David K. Lynch and David S. P. Dearborn
Applied Optics, Vol. 56, Issue 19, pp. G1-G4 (July 2017) OSA Optics InfoBase
Theoretical and experimental studies show that water ice spheres can produce a rainbow in which the primary and secondary bows overlap. To our knowledge, no such natural “icebow” has ever been reported.

Simultaneous observation of a glory and in-situ microphysical cloud properties Free download
Mahen Konwar, Philip Laven, and T. V. Prabha
Applied Optics, Vol. 56, Issue 19, pp. G5-G8 (July 2017) OSA Optics InfoBase
While making airborne measurements of cloud particles, a bright glory was observed on a thin layer cloud. By deliberately flying through this glory-producing cloud on several occasions, cloud particle size distributions were obtained. We found that warm liquid clouds with narrow cloud droplet size distributions are responsible for producing the observed glory. This paper presents these results and compares the results of Mie theory simulations with an image of the glory.

Transmission bows of radially inhomogeneous spheres Free download
James A. Lock and Philip Laven
Applied Optics, Vol. 56, Issue 19, pp. G9-G19 (July 2017) OSA Optics InfoBase
We consider transmission scattering of a plane wave by a radially inhomogeneous sphere containing a localized region of refractive index decrease. In ray theory, the boundary conditions on the deflection angle at axial and grazing incidence determine that transmission scattering gives rise to an even number of bows, half of them being relative maximum bows and half being relative minimum bows. For a model refractive index profile, we determine the conditions under which different numbers of bows occur, and we suggest physical mechanisms responsible for producing them. We also verify that these bows occur in wave scattering in the short wavelength limit, both in the frequency domain and time domain.

Iridescent clouds and distorted coronas Free download
Philip Laven
Applied Optics, Vol. 56, Issue 19, pp. G20-G25 (July 2017) OSA Optics InfoBase
Near-forward scattering of sunlight generates coronas and iridescence on clouds. Coronas are caused by diffraction, whereas iridescence is less easily explained. Iridescence often appears as bands of color aligned with the edges of clouds or as apparently random patches of color on clouds. This paper suggests that iridescence is due to interference between light that has been diffracted by a spherical droplet of water and light that has been transmitted through the same droplet.

Mountain shadows revisited
John A. Adam
Applied Optics, Vol. 56, Issue 19, pp. G26-G35 (July 2017) OSA Optics InfoBase
Using purely geometric considerations, a sequence of mountain shadow models is considered. The observer is located at the summit of idealized mountains with several different cross-sectional profiles. The result for a triangular profile is generalized to the case of an off-summit observer. We also examine the case of a conical mountain. In addition, a simple geometric model is formulated for mountain “spikes” in terms of the differences in shadow length and contrast for an off-summit observer within the shadow. The first appendix is devoted to the notion of “umbral volume” and the second to the geometry of sunlit areas on a conical mountain.

Blue sun glints on water viewed through a polarizer
Joseph A. Shaw and Michael Vollmer
Applied Optics, Vol. 56, Issue 19, pp. G36-41 (July 2017) OSA Optics InfoBase
Sun glints are formed by specular reflections of the sun from capillary waves formed by wind blowing over water. These glints are normally colorless for a high sun or take on the color of the light source, such as orange–red during sunset or sunrise. However, when the glints are highly polarized by reflection near the Brewster angle, i.e., with relatively high sun they can change from colorless to a blue appearance caused by blue light leakage through a polarizing filter oriented orthogonal to the plane of polarization of the reflected light. Measurements are shown of crossed-polarizer transmission spectra exhibiting blue and near infrared light leakage for photographic polarizing filters and polarized sunglasses. A variety of photographs is shown to confirm blue light leakage as the source of the blue glint color.

Spectral measurement and modeling of natural rainbows Free download
Raymond L. Lee
Applied Optics, Vol. 56, Issue 19, pp. G42-G50 (July 2017) OSA Optics InfoBase
Although quantitative observations of rainbow spectra, colors, and luminances are needed for any comprehensive analysis of rainbow scattering theory, very little such data has been published. But new remote sensing tools now make possible the detailed spectral and colorimetric measurement of natural rainbows, which here are defined as bows seen in sunlit rain or water-drop sprays. To measure these often short-lived phenomena, both multispectral tools (colorimetrically calibrated RGB cameras) and hyperspectral tools (imaging spectrometers) are used to examine the spectral and angular fine structure of natural rainbows. Airy theory for aerodynamically flattened drops helps to explain some of these bows’ observed features, such as the reduced color gamuts caused by smaller drop sizes and low sun elevations h0. However, other features such as the distinct blues seen in rainbows at higher h0 are not well explained.

Hafgerðingar and giant waves
Siebren van der Werf
Applied Optics, Vol. 56, Issue 19, pp. G51-G58 (July 2017) OSA Optics InfoBase
A 13th-century text in Old Norse, Konungs Skuggsjá (translated as The King’s Mirror), tells about a phenomenon that may be encountered in the Greenland Sea. It is called hafgerðingar (sea fences). The horizon is raised, and from there three giant waves come rolling in. Recently Lehn and Schroeder have explained the phenomenon as a superior mirage. I extend their analysis by introducing a periodic time dependence in the properties of the inversion layer, and show that also the illusion of incoming waves and an immediate danger may so be explained.

Mirages at Lake Geneva: the Fata Morgana
Andrew T. Young and Eric Frappa
Applied Optics, Vol. 56, Issue 19, pp. G59-G68 (July 2017) OSA Optics InfoBase
Fata Morgana mirages are frequently seen at Lake Geneva. We show the first photographs of them, including a real-time video, and explain their main features, which are due to the very turbulent entrainment zones of capping inversions, especially in valley circulations.

Teaching rainbows with simulations: revisiting Minnaert’s lab experiment
Francisco L. Naranjo-Correa, Guadalupe Martinez-Borreguero, Angel Luis Pérez-Rodriguez, Pedro J. Pardo-Fernandez, and Maria Isabel Suero-Lopez
Applied Optics, Vol. 56, Issue 19, pp. G69-G74 (July 2017) OSA Optics InfoBase
This work presents an educational simulation to support students’ learning about the formation of the rainbow. The main aim of the simulation is to provide our students with a didactic tool in addition to their traditional laboratory practice, which can be easily implemented in e-learning teaching platforms. A system consisting of a flask filled with water and a screen with a rounded aperture placed between the sun and the flask was simulated; this way a faint rainbow was seen on the simulated screen. The interactive nature of the simulation allowed the students to perform some alterations that would be impossible to do in the real world; thus, the observed rainbow deviated from the simplest model. Additionally, all these modifications could be rendered into an animation, in order to observe changes in real time.

High-order rainbows of a spherical particle produced by near-grazing incident light
James A. Lock
Applied Optics, Vol. 56, Issue 19, pp. G75-G87 (July 2017) OSA Optics InfoBase
This study is concerned with the formation of high-order rainbows by near-grazing light incident on a spherical particle. As the number of internal reflections involved increases, the incident Descartes ray strikes the sphere surface increasingly closer to its edge, where the predictions of ray theory and Airy theory become invalid. The deflection angle of the confluence of the stationary points of the phase of the partial wave scattering amplitudes is studied as a function of rainbow order and sphere radius. It is found that as the rainbow order increases, the angular interval over which the upper supernumerary ray stationary point occurs shrinks to zero. In addition, for deflection angles beyond the confluence of the upper supernumerary ray with the tunneling ray, intensity oscillations are due to interference of the field of the lower supernumerary ray with that of the edge region Fock transition, rather than interference between the upper and lower supernumerary rays.

Rainbows by elliptically deformed drops. I. Möbius shift for high-order rainbows Free download
James A. Lock and Günther P. Können
Applied Optics, Vol. 56, Issue 19, pp. G88-G97 (July 2017) OSA Optics InfoBase
Using ray theory, the Möbius shift of the (p−1)-order rainbow angle for a particle having an elliptical cross section is obtained to first order in the ellipticity as a function of the tilt of the ellipse with respect to the propagation direction of the incoming rays. The result is then adapted to the geometry of scattering of light rays from the sun by a falling water drop as a function of sun height angle. The variation in the angular spacing between the supernumeraries is determined as a function of location along the rainbow arc, the conditions under which the rainbow angle is insensitive to drop flattening were determined, and the dependence of the Möbius shift on the drop refractive index is shown for rainbows up to fourth order (p=5).

Rainbows by elliptically deformed drops. II. The appearance of supernumeraries of high-order rainbows in rain showers Free download
James A. Lock and Günther P. Können
Applied Optics, Vol. 56, Issue 19, pp. G98-G103 (July 2017) OSA Optics InfoBase
The appearance of supernumeraries of high-order rainbows in heavy rain showers is explored for rainbows up to order five (p=6). This is done by using a combination of the ray-theory-based first-order Möbius approximation for high-order rainbows with the Airy approximation of the rainbow radiance distribution. We conclude that supernumerary formation of rainbows of order three, four, and five is possible in natural rain showers. Supernumeraries of the third-order and fourth-order rainbows are preferentially formed near the bottom of these rainbows. A strategy for observing supernumeraries of high-order rainbows is proposed.

Supernumerary arcs of rainbows: Young’s theory of interference Free download
Philip Laven
Applied Optics, Vol. 56, Issue 19, pp. G104-G112 (July 2017) OSA Optics InfoBase
Supernumerary arcs on rainbows are historically important because in the early 1800s they provided evidence in favor of the wave theory of light. The success of Airy’s rainbow integral has overshadowed the earlier contribution from Young, who proposed that supernumerary arcs were caused by interference between two geometrical rays that emerge from the raindrop at the same scattering angle. Airy dismissed Young’s idea as “the imperfect theory of interference” because it predicted supernumerary arcs at the wrong angles. Young was unaware that a light ray encountering a focal line can suffer a phase shift of 90°. If these phase shifts are taken into account, the theory of interference becomes surprisingly accurate.

Inflight observation of Bottlinger’s rings
Joseph A. Shaw
Applied Optics, Vol. 56, Issue 19, pp. G113-G119 (July 2017) OSA Optics InfoBase
On the morning of 5 November 2013, a bright subsun was consistently visible during a flight from Bozeman, Montana, to Salt Lake City, Utah. Just after passing over the Wasatch Mountains and beginning to descend into the Salt Lake Valley, the subsun expanded to a rare display of Bottlinger’s rings—an elliptical halo surrounding the subsun. The rings remained visible for 1 to 2 min. This paper shows photographs of the sequence, along with meteorological data from a nearby radiosonde. The display occurred in virga below clouds at an air temperature in the approximate range from −8°C to −12°C, in air saturated with respect to ice, at an altitude of approximately 2600–3600 m above mean sea level.

How daylight influences high-order chromatic descriptors in natural images Free download
Juan Ojeda, Juan Luis Nieves, and Javier Romero
Applied Optics, Vol. 56, Issue 19, pp. G120-G127 (July 2017) OSA Optics InfoBase
Despite the global and local daylight changes naturally occurring in natural scenes, the human visual system usually adapts quite well to those changes, developing a stable color perception. Nevertheless, the influence of daylight in modeling natural image statistics is not fully understood and has received little attention. The aim of this work was to analyze the influence of daylight changes in different high-order chromatic descriptors (i.e., color volume, color gamut, and number of discernible colors) derived from 350 color images, which were rendered under 108 natural illuminants with Correlated Color Temperatures (CCT) from 2735 to 25,889 K. Results suggest that chromatic and luminance information is almost constant and does not depend on the CCT of the illuminant for values above 14,000 K. Nevertheless, differences between the red-green and blue-yellow image components were found below that CCT, with most of the statistical descriptors analyzed showing local extremes in the range 2950 K–6300 K. Uniform regions and areas of the images attracting observers’ attention were also considered in this analysis and were characterized by their patchiness index and their saliency maps. Meanwhile, the results of the patchiness index do not show a clear dependence on CCT, and it is remarkable that a significant reduction in the number of discernible colors (58% on average) was found when the images were masked with their corresponding saliency maps. Our results suggest that chromatic diversity, as defined in terms of the discernible colors, can be strongly reduced when an observer scans a natural scene. These findings support the idea that a reduction in the number of discernible colors will guide visual saliency and attention. Whatever the modeling is mediating the neural representation of natural images, natural image statistics, it is clear that natural image statistics should take into account those local maxima and minima depending on the daylight illumination and the reduction of the number of discernible colors when salient regions are considered.

Colored thunderstorms
Stanley David Gedzelman
Applied Optics, Vol. 56, Issue 19, pp. G128-G135 (July 2017) OSA Optics InfoBase
Three scenarios that produce colored thunderstorms are simulated. In Scenario #1, the thunderstorm’s sunlit face exhibits a color gradient from white or yellow at top to red at base when the sun is near the horizon. It is simulated with a second-order scattering model as a combination of sunlight and skylight reflected from the cloud face that is attenuated and reddened by Rayleigh and Mie scattering over the long optical path near sunset that increases from cloud top to base. In Scenario #2, the base of the precipitation shaft appears luminous green–blue when surrounded by a much darker arcus cloud. It is simulated as multiply scattered light transmitted through the precipitation shaft using a Monte Carlo model that includes absorption by liquid water and ice. The color occurs over a wide range of solar zenith angles with large liquid water content, but the precipitation shaft is only bright when hydrometeors are large. Attenuation of the light by Rayleigh and Mie scattering outside the precipitation shaft shifts the spectrum to green when viewed from a distance of several kilometers. In Scenario #3, the shaded cloud face exhibits a “sickly” yellow–green color. It is simulated with a second-order scattering model as the result of distant skylight that originates in the sunlit region beyond an opaque anvil of order 40 km wide but is attenuated by Rayleigh and Mie scattering in its path to the cloud and observer.

Light scattering from sessile water drops and raindrop-shaped glass beads as a validation tool for rainbow simulations
Alexander Haußmann
Applied Optics, Vol. 56, Issue 19, pp. G136-G144 (July 2017) OSA Optics InfoBase
The shape deviation of falling raindrops from exact spheres is known to affect the appearance of natural rainbows, e.g., by enhancing the visibility of supernumerary arcs around the top or by creating branching effects known as “twinned rainbows.” To check the accuracy of numerical optical models for rainbow scattering from such nonspherical drops, two simple and low-cost experiments are presented in this paper: (1) sessile, i.e., sitting, drops on ultrahydrophobic surfaces, and (2) glass beads in the shape of falling raindrops. The experimental results are compared to polarization-resolved Monte Carlo ray-tracing simulations, with special emphasis on circular polarization, which results from total internal reflections in these nonspherical scatterers.

Atmospheric optics in the near infrared
Michael Vollmer and Joseph A. Shaw
Applied Optics, Vol. 56, Issue 19, pp. G145-G155 (July 2017) OSA Optics InfoBase
Digital near-infrared photography opens up new observation possibilities and applications for atmospheric optics. We discuss necessary conditions and requirements for observing a variety of atmospheric optical phenomena in the infrared spectral range and report for the first time near-infrared photographs of 22° ring halos and inferior mirages. Our emphasis is on optical phenomena observable in the troposphere, excluding the large body of work addressing near-infrared airglow and aurora.

Antitwilight I: structure and optics Free download
David K. Lynch, David S. P. Dearborn, and Steven C. Richtsmeier
Applied Optics, Vol. 56, Issue 19, pp. G156-G168 (July 2017) OSA Optics InfoBase
Time-lapse videos, still photos, visual observations, and theoretical studies were used to investigate the antitwilight, i.e., twilight opposite the Sun. Colors, brightnesses, and antitwilight features as a function of solar altitude were measured. Four roughly horizontal bands were identified and explained physically in terms of atmospheric geometry, the observer’s line-of-sight, optical depth, refraction, and multiple scattering. Particular emphasis is placed on (1) the origin of the dark segment, (2) the rapid rising of the Belt of Venus with solar altitude, and (3) ray tracing light through the low atmosphere to understand refractive effects. New names are suggested for three of the four bands, and the new terminology is reconciled with earlier papers.

Antitwilight II: Monte Carlo simulations Free download
Steven C. Richtsmeier, David K. Lynch, and David S. P. Dearborn
Applied Optics, Vol. 56, Issue 19, pp. G169-G178 (July 2017) OSA Optics InfoBase
For this paper, we employ the Monte Carlo scene (MCScene) radiative transfer code to elucidate the underlying physics giving rise to the structure and colors of the antitwilight, i.e., twilight opposite the Sun. MCScene calculations successfully reproduce colors and spatial features observed in videos and still photos of the antitwilight taken under clear, aerosol-free sky conditions. Through simulations, we examine the effects of solar elevation angle, Rayleigh scattering, molecular absorption, aerosol scattering, multiple scattering, and surface reflectance on the appearance of the antitwilight. We also compare MCScene calculations with predictions made by the MODTRAN radiative transfer code for a solar elevation angle of +1°.

Tropospheric haze and colors of the clear twilight sky Free download
Raymond L. Lee and Duncan C. Mollner
Applied Optics, Vol. 56, Issue 19, pp. G179-G187 (July 2017) OSA Optics InfoBase
At the earth’s surface, clear-sky colors during civil twilights depend on the combined spectral effects of molecular scattering, extinction by tropospheric aerosols, and absorption by ozone. Molecular scattering alone cannot produce the most vivid twilight colors near the solar horizon, for which aerosol scattering and absorption are also required. However, less well known are haze aerosols’ effects on twilight sky colors at larger scattering angles, including near the antisolar horizon. To analyze this range of colors, we compare 3D Monte Carlo simulations of skylight spectra with hyperspectral measurements of clear twilight skies over a wide range of aerosol optical depths. Our combined measurements and simulations indicate that (a) the purest antisolar twilight colors would occur in a purely molecular, multiple-scattering atmosphere, whereas (b) the most vivid solar-sky colors require at least some turbidity. Taken together, these results suggest that multiple scattering plays an important role in determining the redness of the antitwilight arch.

Characterizing ice particles using two-dimensional reflections of a lidar beam
M. Goerke, Z. Ulanowski, G. Ritter, E. Hesse, R. R. Neely, L. Taylor, R. A. Stillwell, and P. H. Kaye
Applied Optics, Vol. 56, Issue 19, pp. G188-G196 (July 2017) OSA Optics InfoBase
We report a phenomenon manifesting itself as brief flashes of light on the snow’s surface near a lidar beam. The flashes are imaged and interpreted as specular reflection patterns from individual ice particles. Such patterns have a two-dimensional structure and are similar to those previously observed in forward scattering. Patterns are easiest to capture from particles with well-defined horizontal facets, such as near-horizontally aligned plates. The patterns and their position can be used to determine properties such as ice particle shape, size, roughness, alignment, and altitude. Data obtained at Summit in Greenland show the presence of regular hexagonal and scalene plates, columns, and rounded plates of various sizes, among others.

Bow-shaped caustics from conical prisms: a 13th-century account of rainbow formation from Robert Grosseteste’s De iride Free download
Joshua S. Harvey, Hannah E. Smithson, Clive R. Siviour, Giles E. M. Gasper, Sigbjørn O. Sønnesyn, Brian K. Tanner, and Tom C. B. McLeish
Applied Optics, Vol. 56, Issue 19, pp. G197-G204 (July 2017) OSA Optics InfoBase
The rainbow has been the subject of discussion across a variety of historical periods and cultures, and numerous optical explanations have been suggested. Here, we further explore the scientific treatise De iride [On the Rainbow] written by Robert Grosseteste in the 13th century. Attempting to account for the shape of the rainbow, Grosseteste bases his explanation on the optical properties of transparent cones, which he claims can give rise to arc-shaped projections through refraction. By stating that atmospheric phenomena are reducible to the geometric optics of a conical prism, the De iride lays out a coherent and testable hypothesis. Through both physical experiment and physics-based simulation, we present a novel characterization of cone–light interactions, demonstrating that transparent cones do indeed give rise to bow-shaped caustics—a nonintuitive phenomenon that suggests Grosseteste’s theory of the rainbow is likely to have been grounded in observation.

Numerical reproduction and explanation of road surface mirages under grazing-angle scattering
Jia Lu and Huaichun Zhou
Applied Optics, Vol. 56, Issue 19, pp. 5550-5558 (July 2017) OSA Optics InfoBase
The mirror-like reflection image of the road surface under grazing-angle scattering can be easily observed in daily life. It was suggested that road surface mirages may occur due to a light-enhancing effect of the rough surface under grazing-angle scattering. The main purpose of this work is to explain the light-enhancing mechanism of rough surfaces under grazing-angle scattering. The off-specular reflection from a random rough magnesium oxide ceramic surface is analyzed by using the geometric optics approximation method. Then, the geometric optics approximation method is employed to develop a theoretical model to predict the observation effect of the grazing-angle scattering phenomenon of the road surface. The rough surface is assumed to consist of small-scale rough surface facets. The road surface mirage is reproduced from a large number of small-scale rough surface facets within the eye’s resolution limit at grazing scattering angles, as the average bidirectional reflectance distribution function value at the bright location is about twice that of the surface in front of the mirage. It is suggested that the light-enhancing effect of the rough surface under grazing-angle scattering is not proper to be termed as “off-specular reflection,” since it has nothing to do with the “specular” direction with respect to the incident direction.


Refraction near the horizon—an empirical approach. Part 1: terrestrial refraction of the dip
Marcel E. Tschudin
Applied Optics 55, 12, 3104-3115 (April 2016) OSA Optics InfoBase
This study aims at providing improved closed-form refraction estimates for observations near the horizon. In this first part, over 1800 previously published direct measurements of the horizon’s depression (dip) over the sea are reanalyzed using a nonconventional robust procedure for coping with numerous real, large, and asymmetric outliers from abnormal dips. The derived 1-parameter function agrees with those proposed in modern almanacs and for land surveying. It is found that the dips of warmer and colder sea surfaces vs. air are best described with two different functions. The two proposed 3-parameter functions, also using temperature difference between air and sea and wind speed, reduce the estimated error of the 1-parameter function by ~⅓ and the number of outliers by ∼⅔.
N.B. See erratum published in Applied Optics 57, 13, 3479-3480 (May 2018)

Complex artificial halos for the classroom
Markus Selmke and Sarah Selmke
American Journal of Physics, 84, 7, 561-564 (2016) American Journal of Physics
Halos represent a common and imposing atmospheric optics phenomenon whose displays are caused by tiny air-borne ice crystals. Their variety stems from a certain set of orientation classes to which these crystals belong. We present a robust and inexpensive device, made of modular components, that allows for the replication of most of these orientation classes in the laboratory. Under the illumination of light, the corresponding artificial halo counterparts emerge. The mechanical realization of this device allows a thorough understanding and demonstration of these beautiful atmospheric optics phenomena.


Application of vector ray tracing to the computation of Möbius shifts for the primary and secondary rainbows
Haitao Yu, Jianqi Shen and Cameron Tropea
Applied Optics Vol. 54, Issue 31, pp. 9093-9101 (November 2015) OSA Optics InfoBase
The Möbius approximation for the primary rainbow and the Können approximation for the secondary rainbow have been modified to yield consistent predictions of the Möbius shift of the top and bottom rainbows, respectively. The applicability ranges of the Möbius and Können approximations are investigated by comparison to vector ray tracing (VRT) simulations. For the primary rainbow, these results indicate that the Möbius approximation is valid for spheroidal water droplets (m=1.333) in the range of aspect ratios 0.98 ≤ a/c ≤ 1.02. For the secondary rainbow, the Können approximation predicts the Möbius shift well for spheroidal water droplets within the range 0.99 ≤ a/c ≤ 1.01. For a spheroidal droplet with side-on incidence, the difference between the approximations and VRT simulations are discussed. Furthermore, the dependence of Möbius shifts on the relative refractive index of droplet is discussed.

Interference phenomena at backscattering by ice crystals of cirrus clouds
Anatoli Borovoi, Natalia Kustova, and Alexander Konoshonkin
Opt. Express 23, 24557-24571 (September 2015) OSA Optics InfoBase
It is shown that light backscattering by hexagonal ice crystals of cirrus clouds is formed within the physical-optics approximation by both diffraction and interference phenomena. Diffraction determines the angular width of the backscattering peak and interference produces the interference rings inside the peak. By use of a simple model for distortion of the pristine hexagonal shape, we show that the shape distortion leads to both oscillations of the scattering (Mueller) matrix within the backscattering peak and to a strong increase of the depolarization, color, and lidar ratios needed for interpretation of lidar signals.

Intensity distribution of the parhelic circle and embedded parhelia at zero solar elevation: theory and experiments
Sarah Borchardt and Markus Selmke
Applied Optics, Vol. 54, No. 22, pp. 6608-6615 (August 2015) OSA Optics InfoBase
We describe the individual contributions to the intensity distribution of the parhelic circle for plate-oriented hexagonal crystals at exactly zero solar elevation using geometrical optics. An experimental as well as theoretical study of in-plane ray paths provides details on the mechanism for several halos, including the parhelia, the 120° and 90° parhelia, a blue edge, and the Liljequist parhelia. Azimuthal coordinates for associated characteristic features in the intensity distribution are compared with experimental data obtained using a spinning hexagonal glass prism.

Three-dimensional graphic physically based simulator of rainbows together with the background scene
Moon-Ryul Jung
Applied Optics, Vol. 54, Issue 8, pp. 1926-1935 (March 2015) OSA Optics InfoBase
This paper presents a single scattering 3D graphics simulator of rainbows that includes the thickness of the rain shaft and the background scenery. The simulator is devised so that we can find a good configuration of the sun, the viewers, and the volume of water drops in a complicated geometric setting. The background-scene geometry and light-reflecting properties are modelled using 3D graphics tools. The simulator allows both the light reflected from the background surface and the light scattered by water drops to contribute to the final image by taking the depth to the background surface into account. The simulator generates an image of the rainbow by using the radiative transfer equation (RTE). We use ray optics to compute the average scattering cross section and the average phase function of particles that are the main parameters of the RTE. Depending on the density distribution of the water drops, the rainbow is perceived to be translucent, and the background scene is visible through the rainbow. We simulate other effects of the variation of the water-dropdensity and the location of the viewer, e.g., the visibility of the secondary rainbow, the brightness of the sky around the rainbow, the close-up view of the rainbow, and the full-circle rainbow. We explain these effects partly by computing the luminance contrasts of the primary and secondary bows against their local backgrounds.

Feature issue: Applied Optics, February 2015

Light and Color in the Open Air: introduction to the feature issue Free download
Joseph A. Shaw, Raymond L. Lee, Jr., and Philip Laven
Applied Optics, Vol. 54, Issue 4, pp. LC1-LC2 (February 2015) OSA Optics InfoBase
This is a feature issue devoted to optical phenomena in nature. Many of the papers published in this feature issue are based on presentations given at the “Light & Color in Nature” conference held in August 2013 at the University of Alaska—Fairbanks.

Naked eye visibility of Sirius in broad daylight Free download
Günther P. Können, Jaap Tinbergen, and Piet Stammes
Applied Optics, Vol. 54, Issue 4, pp. B1-B7 (February 2015) OSA Optics InfoBase
Sirius was spotted with the naked eye at broad daylight by looking along the finder of a 1 m telescope on La Palma Observatory at a 2370 m height. Sun elevation was 73°; Sirius was nearly straight under the Sun at 37° elevation. The sky radiance, although not recorded directly, could be determined from the simultaneously obtained high-precision wavelength-dependent sky polarization data near Sirius. This was done by fitting the polarization data with the doubling-adding KNMI (DAK) radiative transfer model, which provided the values of the surface albedo and of the aerosol optical thickness required for determining the absolute sky radiance. Our analysis implies that Sirius, when positioned overhead, can be a daytime naked eye object from sea level even if its culmination occurs at solar noon. It also suggests that the second-brightest star (Canopus), if positioned overhead, could be perceptible even at solar noon.

Snell’s window in wavy water Free download
David K. Lynch
Applied Optics, Vol. 54, Issue 4, pp. B8-B11 (February 2015) OSA Optics InfoBase
The angular diameter of Snell’s window as a function of maximum wave slope is calculated. For flat water the diameter is 97° and increases up to about 122° when the wave slope is about 16°. Steeper waves break and disrupt the smooth surface used in the analysis. Breaking waves produce a window almost 180° wide. The brightness of the dark area around Snell’s window is heavily influenced by turbidity and upwelling radiation, especially in shallow water.

Photographic observation and optical simulation of a pollen corona display in Japan
Souichiro Hioki and Hironobu Iwabuchi
Applied Optics, Vol. 54, Issue 4, pp. B12-B21 (February 2015) OSA Optics InfoBase
Brightness and chromaticity profiles were extracted from a vivid solar corona image taken with a digital camera in Sendai, Japan, to compare with a radiative transfer simulation applying Lorenz–Mie theory and single-scattering approximation. The comparison revealed suspended particles having a narrow particle size distribution peaking at radius 14.5 μm. Presumably, pollen of an indigenous coniferous tree, the cryptomeria (Cryptomeria japonica), is responsible for the corona display. The extracted brightness and chromaticity profiles are reproduced well by assuming the presence of a water soluble aerosol and dust in addition to the pollen. We find that photographic analysis of corona displays, similar to that used to measure cloud particle size, is applicable to estimating pollen particle size distribution and column number density.

Influence of scattering surface inclination on the opposition effect Free download
David K. Lynch
Applied Optics, Vol. 54, Issue 4, pp. B22-B25 (February 2015) OSA Optics InfoBase
New observations and analyses are presented of the opposition effect on mud cracks (mud polygons) on desert playas. The enhanced brightness of the surface near the antisolar point has been previously and correctly ascribed to two sources: shadow-hiding and coherent backscatter. The observations reported here suggest that a third optical mechanism influences the OE: some parts of the mud polygon are more strongly illuminated than others, depending on the angle of incidence of sunlight. This causes the areas facing the observer and the sun to be brighter than the rest of the polygon field. This mechanism, called “dilution,” also should occur in all OEs.

Photographic observation of a natural fifth-order rainbow
Harald E. Edens
Applied Optics, Vol. 54, Issue 4, pp. B26-B34 (February 2015) OSA Optics InfoBase
A photograph has been obtained of a natural fifth-order (quinary) rainbow. The photograph was acquired on 8 August 2012 with a digital camera and a polarization filter to maximize contrast of the rainbows with the background. The quinary rainbow, together with its first supernumerary, appears in a contrast-enhanced version of the photograph as broad green and blue-violet color bands within Alexander’s dark band between the primary and secondary rainbows. The red band of the quinary rainbow is obscured by the much brighter secondary rainbow. A comparison with a numerical simulation using the Debye series confirms that the color bands of the quinary rainbow appear at the expected location. The numerical simulation produces a good match with the photograph for a droplet radius of 0.46 mm. The green band of the quinary rainbow is even faintly discernible in the unprocessed photograph, suggesting that under exceptional viewing conditions the green band of the quinary rainbow may be observed visually with the aid of a polarization filter.

Polarization and visibility of higher-order rainbows Free download
Günther P. Können
Applied Optics, Vol. 54, Issue 4, pp. B35-B40 (February 2015) OSA Optics InfoBase
The degree of polarization of rainbows of order k with k ≥ 3 is bounded in the interval [75%, 78%], where 75% is the limit for k→∞. A polarization filter can improve the signal-to-background ratio of the third and fourth rainbows by a factor of 2, which may lift their visibilities in natural circumstances above the threshold of human visual perception. Under optimal circumstances, the latter may be true for the recently photographed green fingerprint of the fifth rainbow, even without the aid of a polarization filter. The prospects for observing the sixth rainbow are unclear. There exists a possibility that the signal of the natural seventh rainbow (appearing at 64° from the Sun) may be separated from its background if photographed under perfect conditions through a polarization filter.

Role of dust in landscape brightness and color Free download
David K. Lynch
Applied Optics, Vol. 54, Issue 4, pp. B41-B45 (February 2015) OSA Optics InfoBase
Scattering by microscopic particles renders virtually all dusty surfaces brighter than dust-free surfaces. Examples of surface brightening are demonstrated in the landscape and laboratory and explained theoretically using Mie theory calculations. The implications for landscape photography and remote sensing are discussed.

Re-visiting the atmospheric corona Free download
Philip Laven
Applied Optics, Vol. 54, Issue 4, pp. B46-B53 (February 2015) OSA Optics InfoBase
The atmospheric corona is a well-known diffraction phenomenon, typically seen as colored rings surrounding the Sun or Moon. In many respects, Fraunhofer diffraction provides a good explanation of the corona. As the angular sizes of the corona’s rings are inversely proportional to the radius, r, of the spherical particles causing the corona, it should be easy to estimate the particle size from observations and photographs. Noting that some of the techniques commonly used for particle sizing based on diffraction theory can give misleading results for coronas caused by the scattering of sunlight, this paper uses Mie theory simulations to demonstrate that the inner 3 red rings of the corona have angular radii of θ ≈ 16/r, 31/r, and 47/r, when θ is measured in degrees and r is measured in μm.

35 minute green flash observed at Little America on 16 October 1929: a retrospective study
James A. Lock
Applied Optics, Vol. 54, Issue 4, pp. B54-B63 (February 2015) OSA Optics InfoBase
On 16 October 1929 five members of the Byrd Expedition 1 observed an intermittent 35 min green flash at the Little America station (latitude −78.57°) in Antarctica. The flash was the result of strong atmospheric refraction, likely associated with a subcritical Novaya Zemlya mirage. This paper examines the constraints placed on the observation by the Earth–Sun orbital kinematics. It is found that the length of the observation cannot be explained solely by the slowness of the setting rate of the Sun, nor the time required just before the beginning of the Antarctic summer for the top of the Sun to set, reach its relative minimum position at the horizon, and then rise back up again. The observed length of the effect, however, is consistent with the Sun effectively setting twice and rising twice during the observation, with the first effective rising being the result of the observers climbing up the radio towers at the Little America station in order to keep the top of the Sun in view.

Infrared Moon imaging for remote sensing of atmospheric smoke layers Free download
Joseph A. Shaw, Paul W. Nugent, and Michael Vollmer
Applied Optics, Vol. 54, Issue 4, pp. B64-B75 (February 2015) OSA Optics InfoBase
Simultaneous visible and long-wave infrared (IR) images of the Moon were used with a simple energy-balance model to study the spatial pattern of lunar surface temperatures. The thermal images were obtained with a radiometrically calibrated, compact, low-cost, commercial IR camera mounted on a small telescope. Differences between the predicted and measured maximum Moon temperatures were used to determine the infrared optical depth (OD), which represents the path-integrated extinction of an elevated layer of wildfire smoke in the atmosphere. The OD values retrieved from the IR Moon images were combined with simultaneous OD measurements from a ground-based, zenith-pointing lidar operating at a wavelength of 532 nm to determine an IR-to-visible OD ratio of 0.50 ± 0.18 for moderately aged wildfire smoke aerosol.

Visible and invisible mirages: comparing inferior mirages in the visible and thermal infrared Free download
Michael Vollmer, Joseph A. Shaw, and Paul W. Nugent
Applied Optics, Vol. 54, Issue 4, pp. B76-B84 (February 2015) OSA Optics InfoBase
Visible (VIS)-light and thermal infrared (IR) inferior mirages in the 8–14 μm waveband have been observed simultaneously for the takeoff and landing of various airplanes at distances of several kilometers. Similarities as well as differences between the VIS and IR mirages are discussed

Downwelling spectral irradiance during evening twilight as a function of the lunar phase Free download
Glenn Palmer and Sönke Johnsen
Applied Optics, Vol. 54, Issue 4, pp. B85-B92 (February 2015) OSA Optics InfoBase
We measured downwelling spectral vector irradiance (from 350 to 800 nm) during evening civil and nautical twilight (solar elevation down to −12°). Nine sets of measurements were taken to cover the first half of the lunar cycle (from the new to full moon) and were also used to calculate chromaticity (CIE 1976 u′v′). The lunar phase had no consistent effect on downwelling irradiance until solar elevation was less than −8°. For lower solar elevations, the effect of the moon increased with the fraction of the illuminated lunar disk until the fraction was approximately 50%. For fractions greater than 50%, the brightness and chromaticity of the downwelling irradiance were approximately independent of the fraction illuminated, likely because the greater brightness of a fuller moon was offset by its lower elevation during twilight. Given the importance of crepuscular periods to animal activity, including predation, reproductive cycles, and color vision in dim light, these results may have significant implications for animal ecology.

Probable photographic detection of the natural seventh-order rainbow Free download
Harald E. Edens and Günther P. Können
Applied Optics, Vol. 54, Issue 4, pp. B93-B96 (February 2015) OSA Optics InfoBase
We present a stacked and contrast-enhanced image comprised of 12 digital photographs that shows a series of color hues in the correct order and location to be part of the seventh-order rainbow. The observation was made on September 22, 2013, near Magdalena in New Mexico (USA). The seventh-order rainbow is located at 64° from the Sun in a region of the sky with little interference from the zero-order glow. The color hues in the image range from red to blue-violet, spanning about 12° in total extent; their locations generally agree with a numerical Debye-series simulation of the seventh-order rainbow. Despite the low color contrast of the seventh-order rainbow, the current observation indicates that it is feasible with current digital-imaging technology to detect this higher-order rainbow in near-ideal atmospheric conditions.

Artificially generated halos: rotating sample crystals around various axes
Michael Großmann, Klaus-Peter Möllmann, and Michael Vollmer
Applied Optics, Vol. 54, Issue 4, pp. B97-B106 (February 2015) OSA Optics InfoBase
So far experiments with artificial halos from single transparent crystals have suffered from the lack of apparatus that allows simultaneous rotation around two and three axes. A new setup is presented which overcomes these restrictions by combining electrical as well as pneumatic concepts. This enables reproducible experiments of the most common halos observed in nature and for the first time artificial ring halos from single hexagons rotating around three axes simultaneously. In addition, an old qualitative halo demonstration based on perceived colors of rotating colored areas whose contours represent scattering plots has been reinvestigated and the usually nonsaturated color of artificial parhelia was visualized using a crossed prism method. These new experiments are discussed in the context of all known artificial halo experiments.

Seeing, adapting to, and reproducing the appearance of nature
Mark D. Fairchild
Applied Optics, Vol. 54, Issue 4, pp. B107-B116 (February 2015) OSA Optics InfoBase
The perception of color in nature is a complex multidimensional phenomenon. The vast range and high dimensionality of the light stimulus in a natural scene is reduced in range and dimension by the human visual system. The color experience is reduced to the appearance attributes of brightness, lightness, colorfulness, chroma, saturation, and hue from spectral energy distributions in the scene, while the vast range of light levels present in the world is reduced to a more manageable perceptual range through local adaptation. These processes set the stage for our efforts to capture, process, and reproduce the colors of nature as well as make artistic interpretations of them. This paper reviews the challenges involved in accurately capturing and reproducing optical phenomena observed in nature.

Observation, analysis, and reconstruction of a twinned rainbow
Alexander Haußmann
Applied Optics, Vol. 54, Issue 4, pp. B117-B127 (February 2015) OSA Optics InfoBase
A photograph of a twinned rainbow, obtained on 11 May, 2012, in Dresden, Germany, is precisely calibrated with respect to lens projection and camera orientation. Since the twinning was only located in a part of the picture, it was possible to read out the red–green–blue intensity data from both a twinned and nontwinned position of the rainbow. These data were fitted with modeled spectra for polydisperse drop distributions, which were calculated with a Debye series algorithm and shifted in the scattering angle to account for the nonspherical shape of natural raindrops. The shift data were acquired from raytracing through realistic raindrop shapes modeled by two conjoined half-spheroids of different oblateness. Effective drop size distributions along the line of sight are derived from the fit for the two sampling positions and used to generate a true-color simulation of the original photograph. By this, the optical determination of physical rainfall properties is demonstrated.

Colors of thermal pools at Yellowstone National Park Free download
Paul W. Nugent, Joseph A. Shaw, and Michael Vollmer
Applied Optics, Vol. 54, Issue 4, pp. B128-B139 (February 2015) OSA Optics InfoBase
The brilliant visible colors of various hot springs and pools in Yellowstone National Park are explained with a combination of scattering from the water and from microbial mats that coat the bottoms of these thermal features. A simple 1D radiative transfer model was used to simulate the colors recorded in visible photographs and the spectrum of light making up these colors. The model includes attenuation in water by absorption and molecular scattering as well as reflection characteristics of the microbial mats and surface reflection of the water. Pool geometries are simulated as simple rough cones scaled to have depths and widths that match published data. Thermal images are also used to record the spatial distribution of water skin temperature. The measurements and simulations confirm that colors observed from shallow-water features arise primarily from the spectral properties of the microbial mat, which is related to the water temperature, while colors observed from deeper water arise primarily from the wavelength-dependent absorption and scattering in the water.

Mother-of-pearl cloud particle size and composition from aircraft-based photography of coloration and lidar measurements
Jens Reichardt, Susanne Reichardt, Chris A. Hostetler, Patricia L. Lucker, Thomas J. McGee, Laurence W. Twigg, Andreas Dörnbrack, Mark R. Schoeberl, and Ping Yang
Applied Optics, Vol. 54, Issue 4, pp. B140-B153 (February 2015) OSA Optics InfoBase
During a Stratospheric Aerosol and Gas (SAGE)-III Ozone Loss and Validation Experiment (SOLVE)-II science flight on 4 February 2003, a mother-of-pearl cloud over Iceland was underflown by the NASA DC-8 and measured with the lidars onboard. In addition, color photos were taken during the approach. Aided by extensive modeling of cloud coloration, the main results of the analysis of this unique data set are: (1) the polar stratospheric cloud was mountain wave-induced and of type II; (2) the spectacular color display was caused by ice particles with sizes around 2 μm.

Shadows Free download
David K. Lynch
Applied Optics, Vol. 54, Issue 4, pp. B154-B164 (February 2015) OSA Optics InfoBase
We investigate the brightness distribution in and around outdoor shadows (for a variety of sky conditions) using modeling and field measurements. The dominant factor influencing the brightness of a shadow is the solid angle subtended by the object blocking the Sun. Occulters at the zenith that subtend a small solid angle cast shadows that are bright and possess a nearly uniform brightness across their extent. Shadows from large occulters are much darker and their brightness varies considerably, being darkest at their centers. For nonzenith occulters, the proximal (nearest the Sun) side of the shadow is darker than the distal side and the shadow will be darkest beneath the center of the occulter. Occulters (e.g., tree or cloud) influence the brightness of sunlit portions near the shadow because they block part of the sky and reflect light into the shadow. The aureole has a significant influence on the brightness of shadow edges. Semi-analytic formulations for the brightness in shadows are presented, and analytic expressions in wells and tunnels are derived.

Red-based cumulus
Stanley David Gedzelman
Applied Optics, Vol. 54, Issue 4, pp. B165-B169 (February 2015) OSA Optics InfoBase
Observations and model simulations of cumulus clouds whose bases are tinted red when the Sun is well above the horizon are presented. Conditions for seeing red bases include (1) a red underlying surface (which may consist of dust clouds, as from haboobs) with high albedo, (2) small fractional cloud cover when the Sun is far enough below the zenith for direct sunlight to illuminate much of the surface directly below and around cloud base, (3) optically thick clouds so that the bases are dark, and (4) clouds with bases that are near enough to the observer to appear high in the sky so that the admixture of scattered light from the intervening atmosphere is minimized.

Inferior mirages: an improved model
Andrew T. Young
Applied Optics, Vol. 54, Issue 4, pp. B170-B176 (February 2015) OSA Optics InfoBase
A quantitative model of the inferior mirage is presented, based on a realistic temperature profile in the convective boundary layer, using Monin–Obukhov similarity theory. The top of the inverted image is determined by the logarithmic part of the profile; the bottom is the apparent horizon, which depends on optical obstruction by roughness elements. These effects of surface roughness are included in the model, which is illustrated with a simulation. The vertical magnification varies throughout the mirage, becoming infinite at Minnaert’s ill-named “vanishing line”—which makes green flashes apparent to the naked eye.

A note on the radiance distributions of halos due to scattering by randomly orientated crystals Free download
Günther P. Können
Applied Optics, Vol. 54, Issue 4, pp. B177-B184 (February 2015) OSA Optics InfoBase
The radiance distribution of light scattered by randomly oriented ice crystals differs fundamentally from the radiance distribution of light scattered by spherical raindrops or by preferentially oriented ice crystals. A formalism for light scattering by randomly oriented crystals is given and applied to four examples, among them the circular 22° halo and the antisolar halospot, the latter being the glory analogue for ice crystals. A long-standing misconception about the nature of the radiance distribution of circular halos is quantified and discussed.

The prodigious halo of the other Huygens Free download
Günther P. Können
Applied Optics, Vol. 54, Issue 4, pp. B185-B193 (February 2015) OSA Optics InfoBase
At the height of the ceremony in the Principality of Orange of the restoration of the sovereignty of the House of Nassau in 1665, a ceremony led by Christiaan’s father, Constantijn Huygens, a “solar crown” appeared in the sky, apparently a divine sign of approval. A nearly forgotten contemporary color engraving of this miraculous event has survived. Constantijn seized the opportunity by using to his advantage the general euphoria among the citizens caused by the appearance. We argue that Constantijn knew exactly what was going on in the sky because of his son’s work on halo theory. Given its brightness and its time of appearance, it seems plausible that the most prominent halo in the Orange halo display was a circumscribed halo rather than the more familiar but bleaker circular 22° halo. The same probably holds for most of the other high-sun halos that caused general consternation, dating from the Octavian halo of 44 BC, to the Chernobyl halo of 1986, and indeed up to bright high-sun halos of the present.

Measuring and modeling twilight’s Belt of Venus Free download
Raymond L. Lee
Applied Optics, Vol. 54, Issue 4, pp. B194-B203 (February 2015) OSA Optics InfoBase
The Belt of Venus (or antitwilight arch) is a reddish band often seen above the antisolar horizon during clear civil twilights, and immediately beneath it is the bluish-gray earth’s shadow (or dark segment) cast on the atmosphere. Although both skylight phenomena have prompted decades of scientific research, surprisingly few measurements exist of their spectral, colorimetric, and photometric structure. Hyperspectral imaging of several clear twilights supplies these missing radiometric details and reveals some common spectral features of the antisolar sky at twilight: (1) color differences between the dark segment and the sunlit sky above the antitwilight arch are small or nil; (2) antisolar color and luminance extremes usually occur at different elevation angles; and (3) the two twilight phenomena are most vivid for modest aerosol optical depths. A second-order scattering model that includes extinction by aerosols and ozone provides some preliminary radiative transfer explanations of these twilight features’ color and brightness.

Some elementary but surprising facts about the Sun’s path at sunset
A. James Mallmann and Steven P. Mayer
Applied Optics, Vol. 54, Issue 4, pp. B204-B206 (February 2015) OSA Optics InfoBase
For temperate latitudes, the assumed path of the Sun across the sky would suggest that the angle between the horizon and the Sun’s path at sunset would be much greater on the first day of summer when the Sun is high in the sky at noon than on the first day of winter when the Sun’s noon elevation is 47° lower. The angle that the Sun’s path makes with the horizon at sunset is, however, exactly the same on the first day of summer and the first day of winter—for any latitude. For 43° north latitude, although the range of angles over a year for the Sun’s noon elevation is 47°, the range of angles between the horizon and the Sun’s path at sunset is only 5°.

Caustics due to complex water menisci
Charles L. Adler and James A. Lock
Applied Optics, Vol. 54, Issue 4, pp. B207-B221 (February 2015) OSA Optics InfoBase
Shadows of leaves and other objects that can float on the surface of still or slowly flowing water such as a pond or a gently flowing stream have shapes that frequently look nothing like their boundaries because of meniscus effects. Menisci can either refract light into the shadow region making it brighter, or away from it extending the area of darkness. Generally speaking one will find both effects in the shadows of leaves with complicated outlines. In this paper we present an approximate theoretical model for the light intensity in these shadow regions with results of laboratory experiments and computer simulations matching our calculations. The calculations indicate a minimum depth for the water of ∼10  cm for typical floating leaves at which caustic structures form in the shadows. For depths significantly less than this, the shadows will more or less match the outline of the leaf. But for depths much greater the shadows will be significantly different, often not looking anything like the leaf itself.

Recovering of weather degraded images based on RGB response ratio constancy
Raúl Luzón-González, Juan L. Nieves, and Javier Romero
Applied Optics, Vol. 54, Issue 4, pp. B222-B231 (February 2015) OSA Optics InfoBase
Images captured under bad weather conditions suffer from poor contrast and visibility. These effects are noticeable for haze, mist, fog, or dust storms. We have proposed a recovering method for images captured for several adverse weather conditions based on the RGB response ratio constancy under illuminant changes. This algorithm improves the visibility, contrast, and color in degraded images with low computational times. We obtain results similar to those from previously published deweathering methods but with no prior information about the image content or atmospheric parameters needed.

Tropospheric haze and colors of the clear daytime sky Free download
Raymond L. Lee
Applied Optics, Vol. 54, Issue 4, pp. B232-B240 (February 2015) OSA Optics InfoBase
To casual observers, haze’s visible effects on clear daytime skies may seem mundane: significant scattering by tropospheric aerosols visibly (1) reduces the luminance contrast of distant objects and (2) desaturates sky blueness. However, few published measurements of hazy-sky spectra and chromaticities exist to compare with these naked-eye observations. Hyperspectral imaging along sky meridians of clear and hazy skies at one inland and two coastal sites shows that they have characteristic colorimetric signatures of scattering and absorption by haze aerosols. In addition, a simple spectral transfer function and a second-order scattering model of skylight reveal the net spectral and colorimetric effects of haze.

Adaptive exposure estimation for high dynamic range imaging applied to natural scenes and daylight skies Free download
Miguel A. Martínez, Eva M. Valero, and Javier Hernández-Andrés
Applied Optics, Vol. 54, Issue 4, pp. B241-B250 (February 2015) OSA Optics InfoBase
Digital imaging of natural scenes and optical phenomena present on them (such as shadows, twilights, and crepuscular rays) can be a very challenging task because of the range spanned by the radiances impinging on the capture system. We propose a novel method for estimating the set of exposure times (bracketing set) needed to capture the full dynamic range of a scene with high dynamic range (HDR) content. The proposed method is adaptive to scene content and to any camera response and configuration, and it works on-line since the exposure times are estimated as the capturing process is ongoing. Besides, it requires no a priori information about scene content or radiance values. The resulting bracketing sets are minimal in the default method settings, but the user can set a tolerance for the maximum percentage of pixel population that is underexposed or saturated, which allows for a higher number of shots if a better signal-to-noise ratio (SNR) in the HDR scene is desired. This method is based on the use of the camera response function that is needed for building the HDR radiance map by stitching together several differently exposed low dynamic range images of the scene. The use of HDR imaging techniques converts our digital camera into a tool for measuring the relative radiance outgoing from each point of the scene, and for each color channel. This is important for accurate characterization of optical phenomena present in the atmosphere while not suffering any loss of information due to its HDR. We have compared our method with the most similar one developed so far [IEEE Trans. Image Process. 17, 1864 (2008)]. Results of the experiments carried out for 30 natural scenes show that our proposed method equals or outperforms the previously developed best approach, with less shots and shorter exposure times, thereby asserting the advantage of being adaptive to scene content for exposure time estimation. As we can also tune the balance between capturing time and the SNR in our method, we have compared its SNR performance against that of Barakat’s method as well as against a ground-truth HDR image of maximum SNR. Results confirm the success of the proposed method in exploiting its tunability to achieve the desired balance of total Δt and SNR.

Optical transmission properties of Pentelic and Paros marble
Rosa Weigand, Pablo A. García, Joaquín Campos Acosta, and Jacobo Storch de Gracia
Applied Optics, Vol. 54, Issue 4, pp. B251-B255 (February 2015) OSA Optics InfoBase
Ancient Greek and Roman sources report that the statue of Zeus in Olympia had a head, and in particular eyes, similar to the description of Zeus by Homer, so we think that the statue was visible to the human eye. Since the temple was 12 m high, and had a small door and no windows, the illumination of the statue by conventional media is questionable. The aim of this paper is to characterize the optical transmission of Paros and Pentelic marble to demonstrate that it was possible to have the Zeus temple illuminated through the roof marble tiles. Spectral absolute transmittance measurements were taken in samples with different thicknesses using a calibrated spectrophotometer, as well as total transmittance measurements using a luxmeter. The results show that both types of marble transmit light and that Pentelic marble has a higher transmittance in the visible range than Paros marble in some cases and hence could have been one reason, among others, to change the type of marble in the roof in antiquity.

Measurements of skylight polarization: a case study in urban region with high-loading aerosol
Lianghai Wu, Jun Gao, Zhiguo Fan, and Jun Zhang
Applied Optics, Vol. 54, Issue 4, pp. B256-B265 (February 2015) OSA Optics InfoBase
We investigate skylight polarization patterns in an urban region using our developed full-Stokes imaging polarimeter. A detailed description of our imaging polarimeter and its calibration are given, then, we measure skylight polarization patterns at wavelength λ = 488 nm and at solar elevation between −05°10′ and +35°42′ in the city of Hefei, China. We show that in an urban region with high-loading aerosols: (1) the measured degree of linear polarization reaches the maximum near sunset, and large areas of unpolarized sky exist in the forward sunlight direction close to the Sun; (2) the position of neural points shifts from the local meridian plane and, if compared with a clear sky, alters the symmetrical characteristics of celestial polarization pattern; and (3) the observed circular polarization component is negligible.


Polarization transition between sunlit and moonlit skies with possible implications for animal orientation and Viking navigation: anomalous celestial twilight polarization at partial moon Free download
András Barta, Alexandra Farkas, Dénes Száz, Ádám Egri, Pál Barta, József Kovács, Balázs Csák, István Jankovics, Gyula Szabó, and Gábor Horváth
Applied Optics, Vol. 53, Issue 23, pp. 5193-5204 (August 2014). OSA Optics InfoBase
Using full-sky imaging polarimetry, we measured the celestial distribution of polarization during sunset and sunrise at partial (78% and 72%) and full (100%) moon in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum. We investigated the temporal change of the patterns of degree p and angle α of linear polarization of sunlit and moonlit skies at dusk and dawn. We describe here the position change of the neutral points of sky polarization, and present video clips about the celestial polarization transition at moonlit twilight. We found that at partial moon and at a medium latitude (47° 15.481′ N) during this transition there is a relatively short (10–20 min) period when (i) the maximum of p of skylight decreases, and (ii) from the celestial α pattern neither the solar–antisolar nor the lunar–antilunar meridian can be unambiguously determined. These meridians can serve as reference directions of animal orientation and Viking navigation based on sky polarization. The possible influence of these atmospheric optical phenomena during the polarization transition between sunlit and moonlit skies on the orientation of polarization-sensitive crepuscular/nocturnal animals and the hypothesized navigation of sunstone-aided Viking seafarers is discussed.

Accuracy of sun localization in the second step of sky-polarimetric Viking navigation for north determination: a planetarium experiment Free download
Alexandra Farkas, Dénes Száz, Ádám Egri, Miklós Blahó, András Barta, Dóra Nehéz, Balázs Bernáth, and Gábor Horváth
Journal of Optical Society of America A, Vol. 31, Issue 7, pp. 1645-1656 (July 2014) OSA Optics InfoBase
It is a widely discussed hypothesis that Viking seafarers might have been able to locate the position of the occluded sun by means of dichroic or birefringent crystals, the mysterious sunstones, with which they could analyze skylight polarization. Although the atmospheric optical prerequisites and certain aspects of the efficiency of this sky-polarimetric Viking navigation have been investigated, the accuracy of the main steps of this method has not been quantitatively examined. To fill in this gap, we present here the results of a planetarium experiment in which we measured the azimuth and elevation errors of localization of the invisible sun. In the planetarium sun localization was performed in two selected celestial points on the basis of the alignments of two small sections of two celestial great circles passing through the sun. In the second step of sky-polarimetric Viking navigation the navigator needed to determine the intersection of two such celestial circles. We found that the position of the sun (solar elevation θS, solar azimuth φs) was estimated with an average error of +0.6° ≤ Δθ ≤ +8.8° and −3.9° Δφ ≤ +2.0°. We also calculated the compass direction error when the estimated sun position is used for orienting with a Viking sun-compass. The northern direction (ωNorth) was determined with an error of −3.34° ≤ ΔωNorth ≤ +6.29°. The inaccuracy of the second step of this navigation method was high (ΔωNorth = −16.3°) when the solar elevation was 5° ≤ θS ≤ 25°, and the two selected celestial points were far from the sun (at angular distances 95° ≤ γ1, γ2 ≤ 115°) and each other (125° ≤ δ ≤ 145°). Considering only this second step, the sky-polarimetric navigation could be more accurate in the mid-summer period (June and July), when in the daytime the sun is high above the horizon for long periods. In the spring (and autumn) equinoctial period, alternative methods (using a twilight board, for example) might be more appropriate. Since Viking navigators surely also committed further errors in the first and third steps, the orientation errors presented here underestimate the net error of the whole sky-polarimetric navigation.

Blue moons and Martian sunsets
Kurt Ehlers, Rajan Chakrabarty and Hans Moosmüller
Applied Optics, Vol. 53, Issue 9, pp. 1808-1819 (March 2014) OSA Optics InfoBase
The familiar yellow or orange disks of the moon and sun, especially when they are low in the sky, and brilliant red sunsets are a result of the selective extinction (scattering plus absorption) of blue light by atmospheric gas molecules and small aerosols, a phenomenon explainable using the Rayleigh scattering approximation. On rare occasions, dust or smoke aerosols can cause the extinction of red light to exceed that for blue, resulting in the disks of the sun and moon to appear as blue. Unlike Earth, the atmosphere of Mars is dominated by micron-size dust aerosols, and the sky during sunset takes on a bluish glow. Here we investigate the role of dust aerosols in the blue Martian sunsets and the occasional blue moons and suns on Earth.We use the Mie theory and the Debye series to calculate the wavelength-dependent optical properties of dust aerosols most commonly found on Mars. Our findings show that while wavelength selective extinction can cause the sun’s disk to appear blue, the color of the glow surrounding the sun as observed from Mars is due to the dominance of near-forward scattering of blue light by dust particles and cannot be explained by a simple, Rayleigh-like selective extinction explanation.

Color-coordinate system from a 13th-century account of rainbows Free download
Hannah E. Smithson, Philip S. Anderson, Greti Dinkova-Bruun, Robert A. E. Fosbury, Giles E. M. Gasper, Philip Laven, Tom C. B. McLeish, Cecilia Panti and Brian K. Tanner
Journal of Optical Society of America A, Vol. 31, Issue 4, pp. A341-349 (2014) OSA Optics InfoBase
We present a new analysis of Robert Grosseteste’s account of color in his treatise De iride (On the Rainbow), dating from the early 13th century. The work explores color within the 3D framework set out in Grosseteste’s De colore [see J. Opt. Soc. Am. A 29, A346 (2012)], but now links the axes of variation to observable properties of rainbows. We combine a modern understanding of the physics of rainbows and of human color perception to resolve the linguistic ambiguities of the medieval text and to interpret Grosseteste’s key terms.


Orientation with a Viking sun-compass, a shadow-stick, and two calcite sunstones under various weather conditions Free download
Balázs Bernáth, Miklós Blahó, Ádám Egri, András Barta, György Kriska, and Gábor Horváth
Applied Optics, Vol. 52, Issue 25, pp. 6185-6194 (August 2013). OSA Optics InfoBase
It is widely accepted that Vikings used sun-compasses to derive true directions from the cast shadow of a gnomon. It has been hypothesized that when a cast shadow was not formed, Viking navigators relied on crude skylight polarimetry with the aid of dichroic or birefringent crystals, called “sunstones.” We demonstrate here that a simple tool, that we call “shadow-stick,” could have allowed orientation by a sun-compass with satisfying accuracy when shadows were not formed, but the sun position could have reliably been estimated. In field tests, we performed orientation trials with a set composed of a sun-compass, two calcite sunstones, and a shadow-stick. We show here that such a set could have been an effective orientation tool for Vikings only when clear, blue patches of the sky were visible.


Spectral polarization of clear and hazy coastal skies Free download
Raymond L. Lee and Orlando R. Samudio
Applied Optics, Vol. 51, Issue 31, pp. 7499-7508 (November 2012). OSA Optics InfoBase
Linear polarization of the clear daytime sky has often been measured as a spectrally integrated or quasi-monochromatic variable, but seldom as a spectral one. So we use a hyperspectral imaging system to measure skylight polarization at high spectral and angular resolutions for clear and hazy skies at our coastal site. The resulting polarization maps and spectra exhibit both commonalities and differences that seem unexplained by an existing polarized radiative transfer model. Comparing the measured polarization spectra with those predicted by aerosol single scattering suggests some basic verisimilitude tests for improving such models.

Spectral recovery of outdoor illumination by an extension of the Bayesian inverse approach to the Gaussian mixture model Free download
Shahram Peyvandi, Seyed Hossein Amirshahi, Javier Hernández-Andrés, Juan Luis Nieves, and Javier Romero
Journal of Optical Society of America A, Vol. 29, Issue 10, pp. 2181-2189 (October 2012). OSA Optics InfoBase
The Bayesian inference approach to the inverse problem of spectral signal recovery has been extended to mixtures of Gaussian probability distributions of a training dataset in order to increase the efficiency of estimating the spectral signal from the response of a transformation system. Bayesian (BIC) and Akaike (AIC) information criteria were assessed in order to provide the Gaussian mixture model (GMM) with the optimum number of clusters within the spectral space. The spectra of 2600 solar illuminations measured in Granada (Spain) were recovered over the range of 360–830 nm from their corresponding tristimulus values using a linear model of basis functions, the Wiener inverse (WI) method, and the Bayesian inverse approach extended to the GMM (BGMM). A model of Gaussian mixtures for solar irradiance was deemed to be more appropriate than a single Gaussian distribution for representing the probability distribution of the solar spectral data. The results showed that the estimation performance of the BGMM method was better than either the linear model or the WI method for the spectral approximation of daylight from the three-dimensional tristimulus values.

Understanding Light Scattering by a Coated Sphere. Part 1: Theoretical Considerations Free download
James A. Lock and Philip Laven
Journal of Optical Society of America A, Vol. 29, Issue 8, pp. 1489-1497 (August 2012). OSA Optics InfoBase
Although scattering of light by a coated sphere is much more complicated than scattering by a homogeneous sphere, each of the partial wave amplitudes for scattering of a plane wave by a coated sphere can be expanded in a Debye series. The Debye series can then be rearranged in terms of the various reflections that each partial wave undergoes inside the coated sphere. For a given number of internal reflections, it is found that many different Debye terms produce the same scattered intensity as a function of scattering angle. This is called path degeneracy. In addition, some of the ray trajectories are repeats of those occurring for a smaller number of internal reflections in the sense that they produce identical time delays as a function of scattering angle. These repeated paths, however, have a different intensity as a function of scattering angle than their predecessors. The degenerate paths and repeated paths considerably simplify the interpretation of scattering within the coated sphere, thus making it possible to catalog the contributions of the various paths.

Understanding Light Scattering by a Coated Sphere. Part 2: Time Domain Analysis Free download
Philip Laven and James A. Lock
Journal of Optical Society of America A, Vol. 29, Issue 8, pp. 1498-1507 (August 2012) OSA Optics InfoBase
Numerical computations were made of scattering of an incident electromagnetic pulse by a coated sphere that is large compared to the dominant wavelength of the incident light. The scattered intensity was plotted as a function of the scattering angle and delay time of the scattered pulse. For fixed core and coating radii, the Debye series terms that most strongly contribute to the scattered intensity in different regions of scattering angle-delay time space were identified and analyzed. For a fixed overall radius and an increasing core radius, the first-order rainbow was observed to evolve into three separate components. The original component faded away, while the two new components eventually merged together. The behavior of surface waves generated by grazing incidence at the core/coating and coating/exterior interfaces was also examined and discussed.

A three-dimensional color space from the 13th century Free download
Hannah E. Smithson, Greti Dinkova-Bruun, Giles E. M. Gasper, Mike Huxtable, Tom C. B. McLeish and Cecilia Panti
Journal of Optical Society of America A, Vol. 29, Issue 2, A346-A352 (February 2012) OSA Optics InfoBase
We present a new commentary on Robert Grosseteste’s De colore, a short treatise that dates from the early 13th century, in which Grosseteste constructs a linguistic combinatorial account of color. In contrast to other commentaries(e.g., Kuehni & Schwarz, Color Ordered: A Survey of Color Order Systems from Antiquity to the Present, 2007, p. 36), we argue that the color space described by Grosseteste is explicitly three-dimensional. We seek the appropriate translation of Grosseteste’s key terms, making reference both to Grosseteste’s other works and the broader intellectual context of the 13th century, and to modern color spaces.


Feature issue: Applied Optics, October 2011

Light and Color in the Open Air: introduction to the feature issue Free download
Joseph A. Shaw, Raymond L. Lee, Jr., and Philip Laven
Applied Optics, Vol. 50, Issue 28, pp. LC1-LC2 (October 2011) OSA Optics InfoBase
This is a feature issue devoted to optical phenomena that can be observed in nature, primarily with the naked eye. Many of the papers published in this feature issue are based on presentations given at the “Light & Color in Nature” conference held in June 2010 at St. Mary’s College of Maryland.

Visibility of natural tertiary rainbows Free download
Raymond L. Lee, Jr. and Philip Laven
Applied Optics, Vol. 50, Issue 28, pp. F152-F161 (October 2011) OSA Optics InfoBase
Naturally occurring tertiary rainbows are extraordinarily rare and only a handful of reliable sightings and photographs have been published. Indeed, tertiaries are sometimes assumed to be inherently invisible because of sun glare and strong forward scattering by raindrops. To analyze the natural tertiary’s visibility, we use Lorenz–Mie theory, the Debye series, and a modified geometrical optics model (including both interference and nonspherical drops) to calculate the tertiary’s (1) chromaticity gamuts, (2) luminance contrasts, and (3) color contrasts as seen against dark cloud backgrounds. Results from each model show that natural tertiaries are just visible for some unusual combinations of lighting conditions and raindrop size distributions.

Photographic evidence for the third-order rainbow Free download
Michael Großmann, Elmar Schmidt, and Alexander Haußmann
Applied Optics, Vol. 50, Issue 28, pp. F134-F141 (October 2011) OSA Optics InfoBase
The first likely photographic observation of the tertiary rainbow caused by sunlight in the open air is reported and analyzed. Whereas primary and secondary rainbows are rather common and easily seen phenomena in atmospheric optics, the tertiary rainbow appears in the sunward side of the sky and is thus largely masked by forward scattered light. Up to now, only a few visual reports and no reliable photographs of the tertiary rainbow are known. Evidence of a third-order rainbow has been obtained by using image processing techniques on a digital photograph that contains no obvious indication of such a rainbow. To rule out any misinterpretation of artifacts, we carefully calibrated the image in order to compare the observed bow’s angular position and dispersion with those predicted by theory.

Photographic observation of a natural fourth-order rainbow Free download
Michael Theusner
Applied Optics, Vol. 50, Issue 28, pp. F129-F133 (October 2011) OSA Optics InfoBase
We report what is believed to be the first photographic recording of a quaternary rainbow in nature. It appears on the Sun side of the sky with its red arc at a radius of about 45° from the Sun. The original pictures have been subjected to various forms of image processing to reveal the tertiary rainbow as well as the quaternary rainbow, which are separated by only a few degrees with their colors reversed and their red arcs adjacent to each other.

Rainbows, water droplets, and seeing—slow motion analysis of experiments in atmospheric optics
Michael Vollmer and Klaus-Peter Möllmann
Applied Optics, Vol. 50, Issue 28, pp. F21-F28 (October 2011) OSA Optics InfoBase
Many physics processes underlying phenomena in atmospheric optics happen on a rather short time scale such that neither the human eye nor video cameras are able to analyze the details. We report applications of high-speed imaging of laboratory experiments in atmospheric optics with subsequent slow motion analysis. The potential to study respective transient effects is investigated in general and for a few phenomena in detail, in particular for rainbow scattering due to single oscillating droplets during free fall, and for light propagation effects through atmospheric paths with turbulences, leading, e.g., to scintillation of stars or shimmering of mirage images.

Zero-order bows in radially inhomogeneous spheres: direct and inverse problems Free download
John A. Adam
Applied Optics, Vol. 50, Issue 28, pp. F50-F59 (October 2011) OSA Optics InfoBase
Zero-order ray paths are examined in radially inhomogeneous spheres with differentiable refractive index profiles. It is demonstrated that zero-order and sometimes twin zero-order bows can exist when the gradient of refractive index is sufficiently negative. Abel inversion is used to “recover” the refractive index profiles; it is therefore possible in principle to specify the nature and type of bows and determine the refractive index profile that induces them. This may be of interest in the field of rainbow refractometry and optical fiber studies. This ray-theoretic analysis has direct similarities with the phenomenon of “orbiting” and other phenomena in scattering theory and also in seismological, surface gravity wave, and gravitational “lensing” studies. For completeness these topics are briefly discussed in the appendixes; they may also be of pedagogic interest.

Imaging polarimetry of the fogbow: polarization characteristics of white rainbows measured in the high Arctic Free download
Gábor Horváth, Ramón Hegedüs, András Barta, Alexandra Farkas, and Susanne Åkesson
Applied Optics, Vol. 50, Issue 28, pp. F64-F71 (October 2011) OSA Optics InfoBase
The knowledge on the optics of fogbows is scarce, and their polarization characteristics have never been measured to our knowledge. To fill this gap we measured the polarization features of 16 fogbows during the Beringia 2005 Arctic polar research expedition by imaging polarimetry in the red, green and blue spectral ranges. We present here the first polarization patterns of the fogbow. In the patterns of the degree of linear polarization p, fogbows and their supernumerary bows are best visible in the red spectral range due to the least dilution of fogbow light by light scattered in air. In the patterns of the angle of polarization α fogbows are practically not discernible because their α-pattern is the same as that of the sky: the direction of polarization is perpendicular to the plane of scattering and is parallel to the arc of the bow, independently of the wavelength. Fogbows and their supernumeraries were best seen in the patterns of the polarized radiance. In these patterns the angular distance δ between the peaks of the primary and the first supernumerary and the angular width σ of the primary bow were determined along different radii from the center of the bow. δ ranged between 6.08° and 13.41°, while σ changed from 5.25° to 19.47°. Certain fogbows were relatively homogeneous, meaning small variations of δ and σ along their bows. Other fogbows were heterogeneous, possessing quite variable δ- and σ-values along their bows. This variability could be a consequence of the characteristics of the high Arctic with open waters within the ice shield resulting in the spatiotemporal change of the droplet size within the fog.

Time domain analysis of scattering by a water droplet Free download
Philip Laven
Applied Optics, Vol. 50, Issue 28, pp. F29-F38 (October 2011) OSA Optics InfoBase
Rainbows, coronas and glories are caused by the scattering of sunlight from water droplets in the atmosphere. Although these optical phenomena are seen fairly frequently, even scientifically minded people sometimes struggle to provide explanations for their formation. This paper offers explanations of these phenomena based on numerical computations of the scattering of a 5 fs pulse of red light by a spherical droplet of water. The results reveal the intricate details of the various scattering mechanisms, some of which are essentially undetectable except in the time domain..

Glitter and glints on water Free download
David K. Lynch, David S. P. Dearborn, and James A. Lock
Applied Optics, Vol. 50, Issue 28, pp. F39-F49 (October 2011) OSA Optics InfoBase
We present new observations of glitter and glints using short and long time exposure photographs and high frame rate videos. Using the sun and moon as light sources to illuminate the ocean and laboratory water basins, we found that (1) most glitter takes place on capillary waves rather than on gravity waves, (2) certain aspects of glitter morphology depend on the presence or absence of thin clouds between the light source and the water, and (3) bent glitter paths are caused by asymmetric wave slope distributions We present computer simulations that are able to reproduce the observations and make predictions about the brightness, polarization, and morphology of glitter and glints. We demonstrate that the optical catastrophe represented by creation and annihilation of a glint can be understood using both ray optics and diffraction theory.

Approach to photorealistic halo simulations
Stanley David Gedzelman
Applied Optics, Vol. 50, Issue 28, pp. F102-F111 (October 2011) OSA Optics InfoBase
A multiple-scattering Monte Carlo model that can produce near-photographic quality images is developed and used to simulate several dramatic halo displays. The model atmosphere contains an absorbing ozone layer plus two clear, molecular air layers with Rayleigh scattering surrounding a cloud layer and an atmospheric boundary layer with aerosol particles subject to Lorentz–Mie scattering. Halos are produced by right hexagonal or pyramidal crystals that reflect and refract according to geometric optics without diffraction, although “junk” crystals with a pronounced forward-scattering peak but no halo peaks may be included to simulate typical, faint halos. Model parameters include ozone height and content, surface and cloud pressure, cloud optical thickness, crystal shapes, orientations and abundances, atmospheric turbidity, aerosol radius, and albedo. Beams for each wavelength are sorted into small bins as halo beams if they have been scattered once only by a single crystal and otherwise as sky beams, which are smoothed and combined with the halo beams to produce images. Multiple scattering generally vitiates halos, but extremely rare halos, such as Kern’s arc, can be produced if a significant fraction of crystals in optically thick clouds have identical shapes and are highly oriented. Albedo is a model by-product with potential value in climate studies.

Color changes in objects in natural scenes as a function of observation distance and weather conditions Free download
Javier Romero, Raúl Luzón-González, Juan L. Nieves, and Javier Hernández-Andrés
Applied Optics, Vol. 50, Issue 28, pp. F112-F120 (October 2011) OSA Optics InfoBase
We have analyzed the changes in the color of objects in natural scenes due to atmospheric scattering according to changes in the distance of observation. Hook-shaped curves were found in the chromaticity diagram when the object moved from zero distance to long distances, where the object chromaticity coordinates approached the color coordinates of the horizon. This trend is the result of the combined effect of attenuation in the direct light arriving to the observer from the object and the airlight added during its trajectory. Atmospheric scattering leads to a fall in the object’s visibility, which is measurable as a difference in color between the object and the background (taken here to be the horizon). Focusing on color difference instead of luminance difference could produce different visibility values depending on the color tolerance used. We assessed the cone-excitation ratio constancy for several objects at different distances. Affine relationships were obtained when an object’s cone excitations were represented both at zero distance and increasing distances. These results could help to explain color constancy in natural scenes for objects at different distances, a phenomenon that has been pointed out by different authors.

Atmospheric ozone and colors of the Antarctic twilight sky Free download
Raymond L. Lee, Jr., Wolfgang Meyer, and Götz Hoeppe
Applied Optics, Vol. 50, Issue 28, pp. F162-F171 (October 2011) OSA Optics InfoBase
Zenith skylight is often distinctly blue during clear civil twilights, and much of this color is due to preferential absorption at longer wavelengths by ozone’s Chappuis bands. Because stratospheric ozone is greatly depleted in the austral spring, such decreases could plausibly make Antarctic twilight colors less blue then, including at the zenith. So for several months in 2005, we took digital images of twilight zenith and antisolar skies at Antarctica’s Georg von Neumayer Station. Our colorimetric analysis of these images shows only weak correlations between ozone concentration and twilight colors. We also used a spectroradiometer at a midlatitude site to measure zenith twilight spectra and colors. At both locations, spectral extinction by aerosols seems as important as ozone absorption in explaining colors seen throughout the twilight sky.

CauStereo: Range from light in nature
Yohay Swirski, Yoav Y. Schechner, Ben Herzberg, and Shahriar Negahdaripour
Applied Optics, Vol. 50, Issue 28, pp. F89-F101 (October 2011) OSA Optics InfoBase
Underwater, natural illumination typically varies strongly temporally and spatially. The reason is that waves on the water surface refract light into the water in a spatiotemporally varying manner. The resulting underwater illumination field forms a caustic network and is known as flicker. This work shows that caustics can be useful for stereoscopic vision, naturally leading to range mapping of the scene. Range triangulation by stereoscopic vision requires the determination of correspondence between image points in different viewpoints, which is often a difficult problem. We show that the spatiotemporal caustic pattern very effectively establishes stereo correspondences. Thus, we term the use of this effect as CauStereo. The temporal radiance variations due to flicker are unique to each object point, thus disambiguating the correspondence, with very simple calculations. Theoretical limitations of the method are analyzed using ray-tracing simulations. The method is demonstrated by underwater in situ experiments.

Elliptical pollen corona from North American boreal paper birch trees (Betula papyrifera): strong fall orientations for near-spherical particles
Kenneth Sassen
Applied Optics, Vol. 50, Issue 28, pp. F1-F5 (October 2011) OSA Optics InfoBase
It has only recently been realized that solar corona can be generated by dispersions of tree pollen grains suspended in the atmosphere, and these studies have come almost exclusively from Scandinavia. Using corona photographic and surface pollen analyses, it is shown here that paper birch trees in the interior of Alaska regularly generate solar corona during the boreal green-out in mid-May. Although near-spherical in shape, these ∼27 μm average diameter particles have three surface protrusions involved in germination that are indicated to aid in the generation of elliptical corona, for which a strong preferential particle orientation is needed. For observations at solar elevation angles of ∼35°–40°, an axis ratio of about 1.2 and average radius of 2.5° (for the second-order red band) are found. Because oriented particles of a particular shape tend to fall slower than randomly oriented ones, this microdesign promotes the lateral spread of pollen and enhances tree reproductive opportunities, an especially important trait for pioneering species.

Icy wave-cloud lunar corona and cirrus iridescence Free download
Joseph A. Shaw and Nathan J. Pust
Applied Optics, Vol. 50, Issue 28, pp. F6-F11 (October 2011) OSA Optics InfoBase
Dual-polarization lidar data and radiosonde data are used to determine that iridescence in cirrus and a lunar corona in a thin wave cloud were caused by tiny ice crystals, not droplets of liquid water. The size of the corona diffraction rings recorded in photographs is used to estimate the mean diameter of the diffracting particles to be 14.6 μm, much smaller than conventional ice crystals. The iridescent cloud was located at the tropopause [∼11–13.6 km above mean sea level (ASL)] with temperature near −70 °C, while the more optically pure corona was located at approximately 9.5 km ASL with temperature nearing −60 °C. Lidar cross-polarization ratios of 0.5 and 0.4 confirm that ice formed both the iridescence and the corona, respectively.

Crepuscular rays: laboratory experiments and simulations
Stanley David Gedzelman and Michael Vollmer
Applied Optics, Vol. 50, Issue 28, pp. F142-F151 (October 2011) OSA Optics InfoBase
Model simulations of laboratory-generated and natural crepuscular rays are presented. Rays are created in the laboratory with parallel light beams that pass through artificial fogs and milk–water solutions. Light scattered by 90° in a dilute mixture of whole milk first increases in intensity with distance from the source to a maximum as a result of multiple scattering by mainly small angles before decreasing exponentially due to extinction as distance continues to increase. Crepuscular rays are simulated for three cloud configurations. In case 1, the Sun at the zenith is blocked by a cloud with an overhanging anvil. The rays appear white against blue sky and are brightest when atmospheric turbidity, β ≈ 11. Shading by the anvil separates maximum brightness from apparent cloud edge. In case 2, a ray passes through a rectangular gap in a cloud layer. The ray is faint blue in a molecular atmosphere but turns pale yellow as β and solar zenith angle, φsun, increase. At φsun = 60° it appears most striking when the cloud is optically thick, β ∼ 5, and the beam width Δx ≈1000 m. In these cases, increasing aerosol radius, raer, to about 1000 nm brightens, narrows, and shortens rays. In case 3, the twilight Sun is shaded by a towering cloud or mountain. The shaded rays are deeper blue than the sunlit sky because the light originates higher in the atmosphere, where short waves have suffered less depletion from scattering. The long optical path taken by sunlight at twilight makes color and lighting contrasts of the rays greatest when the air is quite clean, i.e., for β - 1≪1. In all cases, the brightest rays occur when sunlight passes through an optical thickness of atmosphere, τ ≈ O(1).

Reflection halo twins: subsun and supersun Free download
Günther P. Können and Siebren Y. van der Werf
Applied Optics, Vol. 50, Issue 28, pp. F80-F88 (October 2011) OSA Optics InfoBase
From an aircraft, a short distinct vertical structure is sometimes seen above the setting sun. Such a feature can be understood as a halo, which is the counterpart of the well-known subsun. Whereas the latter arises from reflections off basal faces of plate-oriented ice crystals illuminated from above, what we call the supersun emerges when these crystals are illuminated from below. The supersun occurs when the sun is below the true horizon and is only visible from elevated positions. The curvature of the Earth causes the ensemble of reflecting crystal faces to act as a hollow mirror and the supersun appears as a vertical band of uniform width, extending from the sun upwards to its supersolar point. We discuss the geometrical properties of the phenomenon and simulate its shape and radiance distribution with an extended version of an atmospheric ray-tracing program.

Crystals of hexagonal ice with (2 0 2 3) Miller index faces explain exotic arcs in the Lascar halo display
Nicolas A. Lefaudeux
Applied Optics, Vol. 50, Issue 28, pp. F121-F128 (October 2011) OSA Optics InfoBase
This article focuses on the 1997 Lascar halo display, during which very unusual arcs and halos were documented. Photographs have been analyzed with the aid of a specific image processing method developed by us. Using crystals of hexagonal ice with exotic (2 0 2 3) Miller index faces, it is possible to simulate all the features of the display with constant crystal populations and oriented crystals in plate orientation. The simulations perform better than the cubic ice explanation. The existence of (2 0 2 3) crystal faces is supported by a 1998 South Pole halo display

Found: a diagram of the 1630 Rome halo display Free download
Eva Seidenfaden
Applied Optics, Vol. 50, Issue 28, pp. F60-F63 (October 2011) OSA Optics InfoBase
Christoph Scheiner’s diagram of the 1630 Rome halo display, thought to be lost already in 1658, may have been found.

Lava lamp optics
Thomas Alan Clark
Applied Optics, Vol. 50, Issue 28, pp. F16-F20 (October 2011) OSA Optics InfoBase
An interesting optical focusing effect occurred in the early heating phases of a simple model of a lava lamp that was constructed to demonstrate convection effects. During this early heating phase, the interface between the two immiscible liquids was found to form a surface of rotation with a conic cross section that acted as a mirror to produce an excellent image of the filament of the bulb within the lower liquid. The relevant features of the lamp construction are discussed briefly, and photographs of this focusing effect are shown. A simple analysis is presented that transforms the photographed cross section of the liquid interface into the true cross section by removing the effect of the cylindrical lens formed by the fluid-filled bottle, and the resulting cross section is then fitted to the shape of an ellipse. The possible cause for the shape of this liquid interface is discussed and compared and contrasted with the somewhat analogous situation of a stretched circular membrane that is subjected to different gas pressures on either side of the membrane.

Noninverted images in inferior mirages
Siebren Y. van der Werf
Applied Optics, Vol. 50, Issue 28, pp. F12-F15 (October 2011) OSA Optics InfoBase
Inferior mirages over sun-exposed roads often appear in isolated strips at their near sides and the reflected scenery exhibits multiple images. This effect is explained as due to slight undulations of the road’s surface. At the same time, some of these images, although they are reflections, are not inverted. Photographic material illustrates this phenomenon and a ray tracing study is presented that confirms these conclusions.

Noctilucent clouds: modern ground-based photographic observations by a digital camera network
Audrius Dubietis, Peter Dalin, Ričardas Balčiūnas, Kazimieras Černis, Nikolay Pertsev, Vladimir Sukhodoev, Vladimir Perminov, Mark Zalcik, Alexander Zadorozhny, Martin Connors, Ian Schofield, Tom McEwan, Iain McEachran, Soeren Frandsen, Ole Hansen, Holger Andersen, Jesper Grønne, Dmitry Melnikov, Alexander Manevich, and Vitaly Romejko
Applied Optics, Vol. 50, Issue 28, pp. F72-F79 (October 2011) OSA Optics InfoBase
Noctilucent, or “night-shining,” clouds (NLCs) are a spectacular optical nighttime phenomenon that is very often neglected in the context of atmospheric optics. This paper gives a brief overview of current understanding of NLCs by providing a simple physical picture of their formation, relevant observational characteristics, and scientific challenges of NLC research. Modern ground-based photographic NLC observations, carried out in the framework of automated digital camera networks around the globe, are outlined. In particular, the obtained results refer to studies of single quasi-stationary waves in the NLC field. These waves exhibit specific propagation properties—high localization, robustness, and long lifetime—that are the essential requisites of solitary wave.

Mie scattering in the time domain. Part 1. The role of surface waves Free download
James A. Lock and Philip Laven
Journal of Optical Society of America A, Vol. 28, Issue 6, pp. 1086-1095 (June 2011) OSA Optics InfoBase
We computed the Debye series p = 1 and p = 2 terms of the Mie scattered intensity as a function of scattering angle and delay time for a linearly polarized plane wave pulse incident on a spherical dielectric particle and physically interpreted the resulting numerical data. Radiation shed by electromagnetic surface waves plays a prominent role in the scattered intensity. We determined the surface wave phase and damping rate and studied the structure of the p = 1, 2 surface wave glory in the time domain.

Mie scattering in the time domain. Part II. The role of diffraction Free download
James A. Lock and Philip Laven
Journal of Optical Society of America A, Vol. 28, Issue 6, pp. 1096-1106 (June 2011) OSA Optics InfoBase
The p = 0 term of the Mie–Debye scattering amplitude contains the effects of external reflection and diffraction. We computed the reflected intensity in the time domain as a function of the scattering angle and delay time for a short electromagnetic pulse incident on a spherical particle and compared it to the predicted behavior in the forward-focusing region, the specular reflection region, and the glory region. We examined the physical consequences of three different approaches to the exact diffraction amplitude, and determined the signature of diffraction in the time domain. The external reflection surface wave amplitude gradually replaces the diffraction amplitude in the angular transition region between forward-focusing and the region of specular reflection. The details of this replacement were studied in the time domain.

Illuminant spectrum estimation at a pixel Free download
Sivalogeswaran Ratnasingam and Javier Hernández-Andrés
Journal of Optical Society of America A, Vol. 28, Issue 4, pp. 696-703 (March 2011). OSA Optics InfoBase
In this paper, an algorithm is proposed to estimate the spectral power distribution of a light source at a pixel. The first step of the algorithm is forming a two-dimensional illuminant invariant chromaticity space. In estimating the illuminant spectrum, generalized inverse estimation and Wiener estimation methods were applied. The chromaticity space was divided into small grids and a weight matrix was used to estimate the illuminant spectrum illuminating the pixels that fall within a grid. The algorithm was tested using a different number of sensor responses to determine the optimum number of sensors for accurate colorimetric and spectral reproduction. To investigate the performance of the algorithm realistically, the responses were multiplied with Gaussian noise and then quantized to 10 bits. The algorithm was tested with standard and measured data. Based on the results presented, the algorithm can be used with six sensors to obtain a colorimetrically good estimate of the illuminant spectrum at a pixel.

Extending “color constancy” outside the visible region Free download
Sivalogeswaran Ratnasingam and Javier Hernández-Andrés
Journal of Optical Society of America A, Vol. 28, Issue 4, pp. 541-547 (March 2011). OSA Optics InfoBase
In this paper, the results of an investigation of the possibility of extending “color constancy” to obtain illuminant-invariant reflectance features from data in the near-ultraviolet (UV) and near-infrared (IR) wavelength regions are reported. These features are obtained by extending a blackbody-model-based color constancy algorithm proposed by Ratnasingam and Collins [J. Opt. Soc. Am. A 27, 286 (2010)] to these additional wavelengths. Ratnasingam and Collins applied the model-based algorithm in the visible region to extract two illuminant-invariant features related to the wavelength-dependent reflectance of a surface from the responses of four sensors. In this paper, this model-based algorithm is extended to extract two illuminant-invariant reflectance features from the responses of sensors that cover the visible and either the near-UV or near-IR wavelength. In this investigation, test reflectance data sets are generated using the goodness–fitness coefficient (GFC). The appropriateness of the GFC for generating the test data sets is demonstrated by comparing the results obtained with these data with those obtained from data sets generated using the CIELab distance. Results based upon the GFC are then presented that suggest that the model-based algorithm can extract useful features from data from the visible and near-IR wavelengths. Finally, results are presented that show that, although the spectrum of daylight in the near UV is very different from a blackbody spectrum, the algorithm can be modified to extract useful features from visible and near-UV wavelengths.


Phase matrix for light scattering by concentrically stratified spheres: comparison of geometric optics and the “exact” theory
Yoshihide Takano and Kuo-Nan Liou
Applied Optics, Vol. 49, Issue 20, pp. 3990-3996 (July 2010) OSA Optics InfoBase
We have developed a hit-and-miss Monte Carlo geometric ray-tracing program to compute the scattering phase matrix for concentrically stratified spheres. Using typical refractive indices for water and aerosols in the calculations, numerous rainbow features appear in the phase matrix that deviate from the results calculated from homogeneous spheres. In the context of geometric ray tracing, rainbows and glory are identified by means of their ray paths, which provide physical explanation for the features produced by the “exact” Lorenz–Mie theory. The computed results for the phase matrix, the single-scattering albedo, and the asymmetry factor for a size parameter of ∼600 compared closely with those evaluated from the “exact” theory.

Horizontal magnification of finite-sized celestial objects
Sergey N. Kivalov and Andrew T. Young
Applied Optics, Vol. 49, Issue 14, pp. 2720-2727 (2010) OSA Optics InfoBase
We investigate the magnification due to refraction of the apparent horizontal sizes of finite celestial bodies, such as the Sun or Moon. Two models are discussed and compared with the earlier works of Biot and Chauvenet. It is shown that the apparent horizontal size of the object varies with respect to its true horizontal size as a function of altitude or zenith distance, from a reduction of about 0.0276% at the zenith, to an amplification of about 0.0045% when the object appears just at the horizon (namely, when the true altitude γ is negative and related to the corresponding refraction R by γ = −R ). It is also shown that the apparent horizontal size is equal to the true size when the true altitude γ is related to the corresponding refraction R by γ = −R/2 . Thus, the total magnification (and reduction) range for differently sized objects is about 0.032%–0.033% and depends on the refraction.

Calculation of Debye series expansion of light scattering
Jianqi Shen and Huarui Wang
Applied Optics, Vol. 49, Issue 13, pp. 2422-2428 (May 2010) OSA Optics InfoBase
The Debye series expansion (DSE) is of importance for understanding light scattering features and for testing the validity of geometric optics approach to light scattering. We recast the partial-wave reflection and transmission coefficients so that all the related complex functions can be calculated with stability in all necessary orders. Numerical tests are performed for both the full scattering intensities and the components in a wide range of particle sizes and refractive indices. The results are compared with those from Mie calculation and from MiePlot v4.1, showing that the algorithm is stable, reliable, and robust in a wide range of particle sizes and refractive indices. The developed algorithm may also apply to the DSE calculation of light scattering by multilayered spheres or cylinders.

Debye series for light scattering by a spheroid Free download
Feng Xu, James A. Lock, and Cameron Tropea
J. Opt. Soc. Am. A, Vol. 27, Issue 4, pp. 671-686 (April 2010) OSA Optics InfoBase
The Debye series is developed for electromagnetic scattering by a spheroid in order to decompose the far-zone fields into various physical processes. The geometrical rainbow angle and supernumerary spacing parameter are determined from the Debye intensity by fitting the results to an Airy function and comparing them to their assumed values in ray optics and Airy theory, respectively. Eccentricity-related scattering phenomena including the rainbow's angular shift, the disappearance of the rainbow, and the rainbow-enhanced glory are quantitatively demonstrated and analyzed.

Optical caustics observed in light scattered by an oblate spheroid Free download
James A. Lock and Feng Xu
Applied Optics, Vol. 49, Issue 8, pp. 1288-1304 (March 2010) OSA Optics InfoBase
The electromagnetic fields scattered when a plane wave is incident on an oblate spheroid in the side-on orientation may be calculated using a generalization of Mie theory, and the results may be decomposed in a Debye series expansion. A number of optical caustics are observed in the computed scattered intensity for the one internal reflection portion of the Debye series for scattering angles in the vicinity of the first-order rainbow, and are analyzed in terms of the rainbow, transverse cusp, and hyperbolic umbilic caustics of catastrophe optics. The specific features of these three caustics are described, as is their assembly into the global structure of the observed caustics for spheroid scattering. It is found that, for a spheroid whose radius is an order of magnitude larger than the wavelength of the incident light, the interference structure accompanying the transverse cusp and hyperbolic umbilic caustics is only partially formed.

Debye series analysis of radiation pressure force exerted on a multilayered sphere
Renxian Li, Xiang'e Han, and Kuan Fang Ren
Applied Optics, Vol 49, Issue 6, pp. 955-963 (February 2010) OSA Optics InfoBase
On the basis of generalized Lorenz-Mie theory, the Debye series expansion (DSE) for radiation pressure forces (RPF) exerted on a multilayered sphere induced by focused beams is introduced. The DSE can isolate the contribution of each scattering process to RPF, and give a physical explanation of RPF. Typically, the RPF induced by a Gaussian beam is studied. The DSE is employed to the simulation of RPF corresponding to different scattering processes (diffraction, reflection, refraction, etc.) in detail, and gives the physical mechanism of RPF. The effects of various parameters, such as scattering mode p, beam position, and radius of core for coated spheres, to RPF is researched.


Quételet's fringes due to scattering by small spheres just above a reflecting surface Free download
Wilfried Suhr and H. Joachim Schlichting
Applied Optics, Vol. 48, Issue 26, pp. 4978-4984 (September 2009) OSA Optics InfoBase
In various everyday situations, a characteristic interference pattern can be observed on water surfaces. This pattern can be divided into two overlapping components: a corona and a system of Quételet's rings, often with only a section of these visible in the form of fringes. We attribute this phenomenon to thin films of small spheres located just above the reflecting water surface. Due to differences in the optical arrangement, explanatory models applicable for conventionally produced Quételet's rings are not transferable. We present a compatible mathematical model and some obvious analogies in order to explain the occurrence and properties of this phenomenon.

Detailed electromagnetic simulation for the structural color of butterfly wings
R. Todd Lee and Glenn S. Smith
Applied Optics, Vol. 48, Issue 21, pp. 4177-4190 (July 2009) OSA Optics InfoBase
Many species of butterflies exhibit interesting optical phenomena due to structural color. The physical reason for this color is subwavelength features on the surface of a single scale. The exposed surface of a scale is covered with a ridge structure. The fully three-dimensional, periodic, finite-difference time-domain method is used to create a detailed electromagnetic model of a generic ridge. A novel method for presenting the three-dimensional observed color pattern is developed. Using these tools, the change in color that is a result of varying individual features of the scale is explored. Computational models are developed that are similar to three butterflies: Morpho rhetenor, Troides magellanus, and Ancyluris meliboeus.

Specular scattering by preferentially oriented ice crystals
Anatoli Borovoi and Natalia Kustova
Applied Optics, Vol. 48, Issue 19, pp. 3878-3885 (July 2009) OSA Optics InfoBase
Scattered light for preferentially oriented ice crystals is divided into specular and diffuse components, where the specular scattering is created by horizontally oriented facets of fluttering crystals. The specular component for a fluttering thin plate modeling these crystals is found analytically. The solution obtained is a two-dimensional (2D) convolution of a geometric optics pattern depending only on flutter and an independent diffraction function. The geometric optics pattern is explicitly expressed through the probability density for particle tilts, and the diffraction function is taken in the Fraunhofer diffraction approximation. The 2D convolution calculated numerically reveals a cumulative enhancement of scattered light in the scattering domain center. Certain possibilities to retrieve both flutter parameters and particle sizes from the specular patterns are discussed.

Scattering database for spheroidal particles
Karsten Schmidt, Jochen Wauer, Tom Rother, and Thomas Trautmann
Applied Optics, Vol. 48, Issue 11, pp. 2154-2164 (April 2009) OSA Optics InfoBase
We present a database containing light scattering quantities of randomly oriented dielectric spheroidal particles in the resonance region. The database has been generated by using a thoroughly tested T-matrix method implementation. The data possess a defined accuracy so that they can be used as benchmarks for electromagnetic and light scattering computations of spheroids. Within its parameter range the database may also be applied as a fast tool to investigate the scattering properties of nonspherical particles and to verify assumptions or statements concerning their scattering behavior. A user interface has been developed to facilitate the data access. It also provides some additional functionalities such as interpolations between data or the computation of size-averaged scattering quantities. A detailed description of the database and the user interface is given, followed by examples illustrating their capabilities and handling. On request, the database including the documentation is available, free of charge, on a CD-ROM.

Flashes of light below the dripping faucet: an optical signal from capillary oscillations of water drops
Thomas Timusk
Applied Optics, Vol. 48, issue 6, pp.1212-1217 (February 2009) OSA Optics InfoBase
Falling water drops from a dripping faucet, illuminated from above, exhibit a row of bright strips of light, a few centimeters apart at a fixed distance below the faucet. Flash photographs of the drops show that they are oblate in shape when the flashes occur, and the bright flashes of light originate from the edge of the drop that is on the opposite of the overhead light source. Here we show that the spots result from the same internal reflection that gives rise to the rainbow in a cloud of spherical drops. The periodic flashes reflect the capillary oscillations of the liquid drop between alternating prolate and oblate shapes, and the dramatic enhancement in the oblate phase results from a combination of several optical effects. Ray tracing analysis shows that the flashes occur when the rainbow angle is 42° in spherical drops but sweeps over a wide range between 35° and 65° for typical ellipsoidal drops, and the intensity of the caustic is strongly enhanced in the oblate phase. This phenomenon can be seen in all brightly lit water sprays with millimeter size drops and is responsible for their white color.

All-sky imaging: a simple, versatile system for atmospheric research
Axel Kreuter, Matthias Zangerl, Michael Schwarzmann, and Mario Blumthaler
Applied Optics, Vol. 48, issue 6, pp. 1091-1097 (February 2009) OSA Optics InfoBase
A simple and inexpensive fully automated all-sky imaging system based on a commercial digital camera with a fish-eye lens and a rotating polarizer is presented. The system is characterized and two examples of applications in atmospheric physics are given: polarization maps and cloud detection. All-sky polarization maps are obtained by acquiring images at different polarizer angles and computing Stokes vectors. The polarization in the principal plane, a vertical cut through the sky containing the Sun, is compared to measurements of a well-characterized spectroradiometer with polarized radiance optics to validate the method. The images are further used for automated cloud detection using a simple color-ratio algorithm. The resulting cloud cover is validated against synoptic cloud observations. A Sun coverage parameter is introduced that shows, in combination with the total cloud cover, useful correlation with UV irradiance.


Feature issue: Applied Optics, December 2008

Light and Color in the Open Air: introduction to the feature issue Free download
Joseph A. Shaw, Raymond L. Lee, Jr., and Charles L. Adler
Applied Optics, Vol. 47, Issue 34, pp. LC1-LC2 (December 2008) OSA Optics InfoBase
This feature issue is a celebration of the joy and scientific richness of observing optical phenomena in nature. The majority of papers are adapted from presentations given at the Ninth International Meeting on Light and Color in Nature, held in Bozeman, Montana, from 25 to 29 June 2007.

Spatiotemporal change of sky polarization during the total solar eclipse on 29 March 2006 in Turkey: polarization patterns of the eclipsed sky observed by full-sky imaging polarimetry Free download
Brigitta Sipocz, Ramón Hegedüs, György Kriska and Gábor Horváth
Applied Optics, Vol. 47, No. 34, p H1-H10 (December 2008) OSA Optics InfoBase
Using 180° field-of-view (full-sky) imaging polarimetry, we measured the spatiotemporal change of the polarization of skylight during the total solar eclipse on 29 March 2006 in Turkey. We present our observations here on the temporal variation of the celestial patterns of the degree p and angle α of linear polarization of the eclipsed sky measured in the red (650 nm), green (550 nm), and blue (450 nm) parts of the spectrum. We also report on the temporal and spectral change of the positions of neutral (unpolarized, p = 0) points, and points with local minima or maxima of p of the eclipsed sky. Our results are compared with the observations performed by the same polarimetric technique during the total solar eclipse on 11 August 1999 in Hungary. Practically the same characteristics of celestial polarization were encountered during both eclipses. This shows that the observed polarization phenomena of the eclipsed sky may be general.

Geometric optics and rainbows: generalization of a result by Huygens Free download
John A. Adam
Applied Optics, Vol. 47, Issue 34, pp. H11-H13 (December 2008) OSA Optics InfoBase
In 1652 Huygens derived a formula specifying the rainbow angle for the primary bow (k = 1) in terms of the refractive index only. A generalization of this result for any k ≥ 1 is outlined, along with an alternative representation. The details of the derivation can be found in (Adam, Mathematics Magazine, 2008, under review), but the results as stated may be of interest to the atmospheric optics community.

Visibility of stars, halos, and rainbows during solar eclipses Free download
Günther P. Können and Claudia Hinz
Applied Optics, Vol. 47, Issue 34, pp. H14-H24 (December 2008) OSA Optics InfoBase
The visibility of stars, planets, diffraction coronas, halos, and rainbows during the partial and total phases of a solar eclipse is studied. The limiting magnitude during various stages of the partial phase is presented. The sky radiance during totality with respect to noneclipse conditions is revisited and found to be typically 1/4000. The corresponding limiting magnitude is +3.5. At totality, the signal-to-background ratio of diffraction coronas, halos, and rainbows has dropped by a factor of 250. It is found that diffraction coronas around the totally eclipsed Sun may nevertheless occur. Analyses of lunar halo observations during twilight indicate that bright halo displays may also persist during totality. Rainbows during totality seem impossible.

Noncircular glories and their relationship to cloud droplet size Free download
Philip Laven
Applied Optics, Vol. 47, Issue 34, pp. H25-H30 (December 2008) OSA Optics InfoBase
The atmospheric glory caused by backscattering of sunlight from clouds usually has circular colored rings. However, glories with noncircular rings are frequently observed, especially along the edges of clouds. Noting that the angular radius of the rings of glories is a sensitive indicator of the size of the water droplets in clouds, several images of glories have been examined in an attempt to explain the formation of noncircular glories.

Using a trichromatic CCD camera for spectral skylight estimation Free download
Miguel A. López-Álvarez, Javier Hernández-Andrés, Javier Romero, F. J. Olmo, A. Cazorla, and L. Alados-Arboledas
Applied Optics, Vol. 47, Issue 34, pp. H31-H38 (December 2008) OSA Optics InfoBase
In a previous work [J. Opt. Soc. Am. A 24, 942-956 (2007)] we showed how to design an optimum multispectral system aimed at spectral recovery of skylight. Since high-resolution multispectral images of skylight could be interesting for many scientific disciplines, here we also propose a nonoptimum but much cheaper and faster approach to achieve this goal by using a trichromatic RGB charge-coupled device (CCD) digital camera. The camera is attached to a fish-eye lens, hence permitting us to obtain a spectrum of every point of the skydome corresponding to each pixel of the image. In this work we show how to apply multispectral techniques to the sensors' responses of a common trichromatic camera in order to obtain skylight spectra from them. This spectral information is accurate enough to estimate experimental values of some climate parameters or to be used in algorithms for automatic cloud detection, among many other possible scientific applications.

Visually discerning the curvature of the Earth Free download
David K. Lynch
Applied Optics, Vol. 47, Issue 34, pp. H39-H43 (December 2008) OSA Optics InfoBase
Reports and photographs claiming that visual observers can detect the curvature of the Earth from high mountains or high-flying commercial aircraft are investigated. Visual daytime observations show that the minimum altitude at which curvature of the horizon can be detected is at or slightly below 35,000 ft, providing that the field of view is wide (60°) and nearly cloud free. The high-elevation horizon is almost as sharp as the sea-level horizon, but its contrast is less than 10% that of the sea-level horizon. Photographs purporting to show the curvature of the Earth are always suspect because virtually all camera lenses project an image that suffers from barrel distortion. To accurately assess curvature from a photograph, the horizon must be placed precisely in the center of the image, i.e., on the optical axis.

Maximum deviation of light in a transparent wedge Free download
Walter Tape
Applied Optics, Vol. 47, Issue 34, pp. H44-H51 (December 2008) OSA Optics InfoBase
The maximum is found for the deviation of light passing through a transparent wedge of refractive index n and wedge angle α. The methods are conceptual and geometric, and they require very little calculation. There turn out to be two qualitatively different ray path candidates for maximum deviation, and the geometric approach leads naturally to a criterion involving n and α that decides between the two candidates. Finding the maximum deviation is equivalent to finding the outer radius of a circular halo.

Simulating irradiance during lunar eclipses: the spherically symmetric case
Michael Vollmer and Stanley David Gedzelman
Applied Optics, Vol. 47, Issue 34, pp. H52-H61 (December 2008) OSA Optics InfoBase
Irradiance during total lunar eclipses is simulated using a pinhole model. The Moon is illuminated by direct sunlight that is refracted into the Earth's shadow as it passes through the atmosphere at the terminator but is depleted by scattering by molecules, extinction by aerosol particles, absorption by ozone, and obstruction by clouds and elevated land. On a spherical, sea-level Earth, and a cloudless, molecular atmosphere with no ozone, the eclipsed Moon appears red and calculated irradiance at the center of the umbra is reduced by a factor of about 2400 from direct moonlight. Selective absorption mainly of light around 600 nm by stratospheric ozone turns the periphery of the umbra pale blue. Typical distributions of aerosol particles, ozone, mountains, and clouds around the terminator reduce irradiance by an additional factor of the order of 100.

Lunar eclipse photometry: absolute luminance measurements and modeling
Nina Hernitschek, Elmar Schmidt, and Michael Vollmer
Applied Optics, Vol. 47, Issue 34, pp. H62-H71 (December 2008) OSA Optics InfoBase
The Moon's time-dependent luminance was determined during the 9 February 1990 and 3 March 2007 total lunar eclipses by using calibrated, industry standard photometers. After the results were corrected to unit air mass and to standard distances for both Moon and Sun, an absolute calibration was accomplished by using the Sun's known luminance and a pre-eclipse lunar albedo of approximately 13.5%. The measured minimum level of brightness in the total phase of both eclipses was relatively high, namely −3.32 mvis and −1.7 mvis, which hints at the absence of pronounced stratospheric aerosol. The light curves were modeled in such a way as to let the Moon move through an artificial Earth shadow composed of a multitude of disk and ring zones, containing a relative luminance data set from an atmospheric radiative transfer calculation.

The legendary Rome halo displays Free download
Walter Tape, Eva Seidenfaden, and Günther P. Können
Applied Optics, Vol. 47, Issue 34, pp. H72-H84 (December 2008) OSA Optics InfoBase
The two Rome halo displays of 1629 and 1630 are prominent in the early halo literature, and the 1629 display is still cited today for having contained a 28° circular halo. We have examined seventeenth century correspondence and publications in order to learn as much as possible about the existing documentation of the two displays. We find the documentation to be too weak to support a definitive interpretation of either display, and we see little evidence for a 28° halo or for other rare halos. The two displays remain important for their role in initiating modern halo science.

When Huygens and Mariotte agree Free download
Walter Tape
Applied Optics, Vol. 47, Issue 34, pp. H85-H90 (December 2008) OSA Optics InfoBase
Edme Mariotte in the seventeenth century attributed halos to tiny ice prisms in the atmosphere. Christiaan Huygens attributed them to tiny spheres or cylinders. The two seemingly incompatible theories largely agree in their predictions for the common halos. This article explains why.

Variability in low altitude astronomical refraction as a function of altitude
Russell D. Sampson, Edward P. Lozowski, and Arsha Fathi-Nejad
Applied Optics, Vol. 47, Issue 34, pp. H91-H94 (December 2008) OSA Optics InfoBase
Low altitude astronomical refraction (LAAR) of the setting Sun was measured over a sea horizon from a coastal location in Barbados, West Indies. The altitude of the upper limb of the Sun and the apparent horizon were determined using a digital video camera (Canon XL2) and a digital SLR camera (Canon EOS 5D). A total of 14 sunsets were measured between 2005 and 2007. From these measurements LAAR variability was estimated at 14 standard altitudes of the refracted Sun between 0°.01 and 4°.5. The relative variability decreases with increasing altitude from ± 0.0195 of mean refraction at an altitude of 0°.01 to ± 0.0142 at 4°.5. If extrapolated to an altitude of 15°, a linear fit to the data produces a relative variability of ± 0.0038 and an absolute variability of ± 0".45. Statistical analysis of the relative variability in LAAR appears to support the decreasing trend. However, error propagation analysis further suggests that the observed values of refraction may exceed the accuracy of the measurement system at altitudes higher than 2°.

Isaac Newton and the astronomical refraction Free download
Waldemar H. Lehn
Applied Optics, Vol. 47, Issue 34, pp. H95-H105 (December 2008) OSA Optics InfoBase
In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.

Measuring overcast colors with all-sky imaging Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 47, Issue 34, pp. H106-H115 (December 2008) OSA Optics InfoBase
Digital images of overcast skies as seen from the earth's surface open new windows onto the angular details of overcast colors and visible-wavelength spectra. After calibration with a spectroradiometer, a commercial CCD camera equipped with a fisheye lens can produce colorimetrically accurate all-sky maps of overcast spectra. Histograms and azimuthally averaged curves of the resulting chromaticities show consistent, but unexpected, patterns in time-averaged overcast colors. Although widely used models such as LOWTRAN7 and MODTRAN4 cannot explain these characteristic patterns, a simple semiempirical model based on the radiative transfer equation does, and it provides insights into the visible consequences of absorption and scattering both within and beneath overcasts.

Observed brightness distributions in overcast skies Free download
Raymond L. Lee, Jr., and David E. Devan
Applied Optics, Vol. 47, Issue 34, pp. H116-H127 (December 2008) OSA Optics InfoBase
Beneath most overcasts, clouds' motions and rapidly changing optical depths complicate mapping their angular distributions of luminance Lv and visible-wavelength radiance L. Fisheye images of overcast skies taken with a radiometer-calibrated digital camera provide a useful new approach to solving this problem. Maps calculated from time-averaged images of individual overcasts not only show their brightness distributions in unprecedented detail, but they also help solve a long-standing puzzle about where brightness maxima of overcasts are actually located. When combined with simulated radiance distributions from MODTRAN4, our measured radiances also let us estimate the gradients of cloud thickness observed in some overcasts.

Quantifying the “milky sky” experiment Free download
Stanley David Gedzelman, Miguel Ángel López-Álvarez, Javier Hernandez-Andrés, and Robert Greenler
Applied Optics, Vol. 47, Issue 34, pp. H128-H132 (December 2008) OSA Optics InfoBase
Spectra of direct and scattered light that passed through a tank of water mixed with up to 25 ml of homogenized skim milk were measured with a spectroradiometer in a classic experiment used to illustrate why the sky is blue and why the Sun turns red near the horizon. The direct light penetrating the tank was reddened by preferential scattering of short waves by the milk particles (protein casein micelles and fat globules). Scattered light was blue near the light source when the optical thickness was small and red far from the source when the optical thickness was large. The measured radiance spectra and Mie theory were used to estimate that the optically effective mean diameters of protein casein micelles and fat globules were 170 and 610 nm.

Effects of refractive index on glories Free download
Philip Laven
Applied Optics, Vol. 47, Issue 34, pp. H133-H142 (December 2008) OSA Optics InfoBase
Atmospheric glories are caused by backscattering of sunlight from spherical droplets of water (e.g., from fog or clouds). But what would glories look like if they were caused by scattering from more exotic substances, such as clouds of ethane as found on Titan? Examining backscattering as a function of the refractive index n of spherical droplets leads to the surprising conclusion that a glory's appearance is almost independent of n (at least for 1.03 < n < 1.7) - unlike the colors of rainbows, which are critically dependent on the variation of n across the visible spectrum.

Color of smoke from brush fires Free download
David K. Lynch and Lawrence S. Bernstein
Applied Optics, Vol. 47, Issue 34, pp. H143-H148 (December 2008) OSA Optics InfoBase
Smoke clouds from brush fires usually appear reddish or brownish when viewed from below in transmission, while a thin smoke cloud or part of a thick cloud near its periphery is noticeably bluish. Yet, when viewed from above in backscatter, the smoke appears bluish-white. We present observations of smoke clouds and explain their varied colors using a simple one-dimensional two-stream multiple scattering/absorbing radiative transfer approach for a model cloud whose particles are much smaller than the wavelength of visible light, the Rayleigh limit. The colors are purely the result of Rayleigh scattering and are not significantly influenced by the intrinsic color (wavelength-dependent albedo) of the particles.

Simulating irradiance and color during lunar eclipses using satellite data
Stanley David Gedzelman and Michael Vollmer
Applied Optics, Vol. 47, Issue 34, pp. H149-H156 (December 2008) OSA Optics InfoBase
Irradiance and color during the total lunar eclipses of 2007 and 2008 are simulated using a ray tracing model that includes refraction, scattering by molecules, and observed or climatological distributions of aerosols, ozone, clouds, and topography around the terminator. Central portions of the umbra appear deep red for almost all eclipses due to preferential removal of short wavelengths in the spectrum of sunlight by scattering in the lower troposphere. The fringe of the umbra appears turquoise or blue due to selective removal of wavelengths around 600 nm by the Chappuis absorption bands of ozone in the stratosphere. Asymmetric distributions of clouds and aerosols, particularly for the 2008 eclipse, produce minimum calculated irradiance up to 17 arc min from the umbra center, while high ozone content over the arctic makes the northern edge of the umbra deepest blue.

Simulating halos and coronas in their atmospheric environment
Stanley David Gedzelman
Applied Optics, Vol. 47, Issue 34, pp. H157-H166 (December 2008) OSA Optics InfoBase
Models are developed that simulate the light and color of the sky and of circular halos and coronas as a function of atmospheric pressure, cloud height, width, and optical depth, solar zenith angle, aerosol concentration and size, and ozone content. Halos, coronas, and skylight are treated as singly scattered sunbeams that are depleted in their passage through the atmosphere and cloud. Multiple scattering is included only for background cloud light. Halos produced by hexagonal crystal prisms and coronas produced by monodisperse droplets are visible for cloud optical depths in the range 0.0003 ≤ τcld ≤ 7 and are brightest and most colorful when τcld is somewhat less than the cosine of the observer's zenith angle. When the Sun is low in the sky, halos and coronas can be bright only at smaller cloud optical depths and tend to be faint at their bottoms when produced in high cloud layers but can be bright at the horizon when produced by narrow cloud cells near ground level.

Antisolar halospot Free download
Günther P. Können, Mónika Bodó, and Ágnes Kiricsi
Applied Optics, Vol. 47, Issue 34, pp. H167-H170 (December 2008) OSA Optics InfoBase
An isolated colorless spot of 1° diameter located at the antisolar point was observed from a plane on the clouds beneath it. The spot can be explained by light scattering on randomly oriented ice crystals via light paths similar to those responsible for the subparhelic circle. Its peculiar polarization properties potentially permit its detection in cases where the spot is embedded in a glory.

The rainbow as interactive art: modeling the Elaisson Beauty installation at SFMOMA
Kenneth Sassen and Jiang Zhu
Applied Optics, Vol. 47, Issue 34, pp. H171-H175 (December 2008) OSA Optics InfoBase
The rainbow has had an important role in religion, art, and science. Recently, artists have attempted to create indoor rainbow displays as interactive exhibitions of art, but based, nonetheless, on the principles of the scattering behavior of raindrops and the experience of experiment. Motivated by recently viewing the Beauty, 1993, installation at the San Francisco Museum of Modern Art (SFMOMA), we describe here a modeling program to explain the diversity of rainbow phenomena one can see visually in the gallery. The most significant impression gleaned in the museum is the acute spatial dependence of rainbow form on the viewing position in the presence of a local divergent light source (i.e., a floodlamp), in stark contrast to the unchangeable natural rainbow produced by an unimaginably distant Sun. This represents a case of the local (divergent) versus solar (parallel) light ray source distinction in atmospheric optical displays, which is one of a handful of anthropogenic versus natural situations responsible for optics displays that have been so far described. Through geometrical optics and Airy's theory simulations we show a rich relationship between the locally produced rainbow phenomena and the chamber equipment geometry and viewing position.

Simulating rainbows in their atmospheric environment
Stanley David Gedzelman
Applied Optics, Vol. 47, Issue 34, pp. H176-H181 (December 2008) OSA Optics InfoBase
Light and color of geometric optics rainbows are simulated in their atmospheric environment. Sunlight passes through a molecular atmosphere with ozone and an aerosol layer near the ground to strike a cuboidal rain shaft below an overhanging cuboidal cloud. The rainbows are treated as singly scattered sunbeams that are depleted as they pass through the atmosphere and rain shaft. They appear in a setting illuminated by scattered light from behind the observer, from the background beyond the rain shaft, and from the rain shaft. In dark backgrounds the primary and secondary bows first become visible when the optical thickness of rain shafts τR ≅ 0.0003 and τR ≅ 0.003, respectively. The bows are brightest and most colorful for 0.1≤ τR ≤ 3, a range that is typical for most showers. The peaks of the scattering phase function for raindrops that correspond to the geometric optics rainbow are so pronounced that rainbows remain bright and colorful for optically thick rain shafts seen against dark backgrounds, but the bows appear washed out or vanish as the background brightens or where the rain shaft is shaded by an overhanging cloud. Rainbows also redden as the Sun approaches the horizon.

Retrieval of the optical depth using an all-sky CCD camera Free download
Francisco J. Olmo, Alberto Cazorla, Lucas Alados-Arboledas, Miguel A. López-Álvarez, Javier Hernández-Andrés, and Javier Romero
Applied Optics, Vol. 47, Issue 34, pp. H182-H189 (December 2008) OSA Optics InfoBase
A new method is presented for retrieval of the aerosol and cloud optical depth using a CCD camera equipped with a fish-eye lens (all-sky imager system). In a first step, the proposed method retrieves the spectral radiance from sky images acquired by the all-sky imager system using a linear pseudoinverse algorithm. Then, the aerosol or cloud optical depth at 500 nm is obtained as that which minimizes the residuals between the zenith spectral radiance retrieved from the sky images and that estimated by the radiative transfer code. The method is tested under extreme situations including the presence of nonspherical aerosol particles. The comparison of optical depths derived from the all-sky imager with those retrieved with a sunphotometer operated side by side shows differences similar to the nominal error claimed in the aerosol optical depth retrievals from sunphotometer networks.

Digital all-sky polarization imaging of partly cloudy skies Free download
Nathan J. Pust and Joseph A. Shaw
Applied Optics, Vol. 47, Issue 34, pp. H190-H198 (December 2008) OSA Optics InfoBase
Clouds reduce the degree of linear polarization (DOLP) of skylight relative to that of a clear sky. Even thin subvisual clouds in the “twilight zone” between clouds and aerosols produce a drop in skylight DOLP long before clouds become visible in the sky. In contrast, the angle of polarization (AOP) of light scattered by a cloud in a partly cloudy sky remains the same as in the clear sky for most cases. In unique instances, though, select clouds display AOP signatures that are oriented 90° from the clear-sky AOP. For these clouds, scattered light oriented parallel to the scattering plane dominates the perpendicularly polarized Rayleigh-scattered light between the instrument and the cloud. For liquid clouds, this effect may assist cloud particle size identification because it occurs only over a relatively limited range of particle radii that will scatter parallel polarized light. Images are shown from a digital all-sky-polarization imager to illustrate these effects. Images are also shown that provide validation of previously published theories for weak (∼2%) polarization parallel to the scattering plane for a 22° halo.

Rare display of eight concentric halos in Tampere, Finland, on 5 June 2008
Jari Luomanen
Applied Optics, Vol. 47, Issue 34, pp. H199-H202 (December 2008) OSA Optics InfoBase
On 5 June 2008 there was a rare display of eight concentric halos in Tampere, Finland. I present a preliminary analysis of this display. A brief comparison with earlier major odd-radius displays is made. Short faint arcs intersecting the Sun and their resemblance to the theoretical odd-radius helic arcs are discussed. A stacked image consisting of 72 individual frames of the display is presented. A single frame is provided for comparison, and the visual observation is described in some detail. Postprocessing techniques for halo photographs are discussed. A stacked simulation and the relevant crystal populations are presented.

Rainbows in the grass. I. External-reflection rainbows from pendant droplets Free download
James A. Lock, Charles L. Adler, and Richard W. Fleet
Applied Optics, Vol. 47, Issue 34, pp. H203-H213 (December 2008) OSA Optics InfoBase
In the mid-morning on a sunny day one can sometimes see glare spots associated with uncolored “rainbow” (i.e., fold) caustics due to the sunlight reflected from the surface of dew or guttation drops. We show that these dewdrop reflection rainbows are due to places on the droplet (i.e., from an “inflection circle”) where its Gaussian curvature becomes zero. We work out the theory of such caustics with horizontally incident light and present a comparison of the theory to measurements made in the laboratory.

Rainbows in the grass. II. Arbitrary diagonal incidence Free download
Charles L. Adler, James A. Lock, and Richard W. Fleet
Applied Optics, Vol. 47, Issue 34, pp. H214-H219 (December 2008) OSA Optics InfoBase
We consider external reflection rainbow caustics due to the reflection of light from a pendant droplet where the light rays are at an arbitrary angle with respect to the horizontal. We compare this theory to observation of glare spots from pendant drops on grass; we also consider the potential application of this theory to the determination of liquid surface tension.

Fountain rainbows Free download
Stanley David Gedzelman and Javier Hernández-Andrés
Applied Optics, Vol. 47, Issue 34, pp. H220-H224 (December 2008) OSA Optics InfoBase
We present the first measurements of radiance spectra of rainbows. The bows on two sunny days (3 and 6 June 2008) were produced by the fountain in the Parque de las Ciencias, Granada, Spain, that consists of a rectangular perimeter of 40 spray nozzles. Optical thickness of the spray from each nozzle was approximately 0.5. Spectral purity of the primary bow was highest for orange and blue, reaching values of 23% and 7%, respectively, while skylight 90° from the Sun had a color purity of 34% (on 6 June). The secondary bow had much lower color purity with red absent because the regions around the bows and in Alexander's dark band were pale blue. The narrow sickle shape of the chromaticity curves for the primary bows and the absence of supernumerary bows indicated that the drop radius was between 0.2 and 0.4 mm.

Solar glint from oriented crystals in cirrus clouds
Claire Lavigne, Antoine Roblin, and Patrick Chervet
Applied Optics, Vol. 47, Issue 33, pp. 6266-6276 (November 2008) OSA Optics InfoBase
Solar scattering on oriented cirrus crystals near the specular reflection direction is modeled using a mix method combining geometric optics and diffraction effects at three wavelengths in the visible and infrared domains. Different potential sources of phase function broadening around the specular direction, such as multiple scattering, solar disk, or tilt effects, are studied by means of a Monte Carlo method. The radiance detected by an airborne sensor located a few kilometers above the cirrus cloud and pointing in the specular scattering direction is calculated at four solar zenith angles showing a dramatic increase of the signal in relation to the usual assumption of random crystal orientation.

Comment on "Improved ray tracing air mass numbers model"
Siebren Y. van der Werf
Applied Optics, Vol. 47, Issue 2, pp. 153-156 (January 2008) OSA Optics InfoBase
Air mass numbers have traditionally been obtained by techniques that use height as the integration variable. This introduces an inherent singularity at the horizon, and ad hoc solutions have been invented to cope with it. A survey of the possible options including integration by height, zenith angle, and horizontal distance or path length is presented. Ray tracing by path length is shown to avoid singularities both at the horizon and in the zenith. A fourth-order Runge-Kutta numerical integration scheme is presented, which treats refraction and air mass as path integrals. The latter may optionally be split out into separate contributions of the atmosphere's constituents.


Recovering fluorescent spectra with an RGB digital camera and color filters using different matrix factorizations Free download
Juan L. Nieves, Eva M. Valero, Javier Hernández-Andrés and Javier Romero
Applied Optics, vol. 46, No. 19, p 4144-4154 (June 2007) OSA Optics InfoBase
The aim of a multispectral system is to recover a spectral function at each image pixel, but when a scene is digitally imaged under a light of unknown spectral power distribution (SPD), the image pixels give incomplete information about the spectral reflectances of objects in the scene. We have analyzed here how accurately the spectra of artificial fluorescent light sources can be recovered with a digital CCD camera. The RGB sensor outputs are modified by the use of successive cut-off color filters. Three algorithms for simplifying the spectra datasets are used: non-negative matrix factorization (NMF), independent component analysis (ICA), a direct pseudo-inverse method, and principal component analysis (PCA). The algorithms are tested using both simulated data and data from a real RGB digital camera. The methods are compared in terms of the minimum rank of factorization and the number of sensors required to derive acceptable spectral and colorimetric SPD estimations; PCA results are also given for the sake of comparison. The results show that all the algorithms surpass PCA when a reduced number of sensors is used. Experimental results suggest a significant loss of quality when more than one color filter is used, which agrees with previous results for reflectances. Nevertheless, an RGB digital camera with or without prefilter is found to provide good spectral and colorimetric recovery of indoor fluorescent lighting and can be used for color correction without need of a telespectroradiometer.

Anomalous celestial polarization caused by forest fire smoke: why do some insects become visually disoriented under smoky skies? Free download
Ramón Hegedüs, Susanne Åkesson, and Gábor Horváth
Applied Optics, Vol. 46, No. 14, p. 2717, May 2007 OSA Optics InfoBase
The effects of forest fire smoke on sky polarization and animal orientation are practically unknown. Using full-sky imaging polarimetry, we therefore measured the celestial polarization pattern under a smoky sky in Fairbanks, Alaska, during the forest fire season in August 2005. It is quantitatively documented here that the celestial polarization, a sky attribute that is necessary for orientation of many polarization sensitive animal species, above Fairbanks on 17 August 2005 was in several aspects anomalous due to the forest fire smoke: (i) The pattern of the degree of linear polarization p of the reddish smoky sky differed considerably from that of the corresponding clear blue sky. (ii) Due to the smoke, p of skylight was drastically reduced (pmax ≤14%, paverage ≤8%). (iii) Depending on wavelength and time, the Arago, Babinet, and Brewster neutral points of sky polarization had anomalous positions. We suggest that the disorientation of certain insects observed by Canadian researchers under smoky skies during the forest fire season in August 2003 in British Columbia was the consequence of the anomalous sky polarization caused by the forest fire smoke.

Selecting algorithms, sensors and linear bases for optimum spectral recovery of skylight Free download
Miguel A. López-Álvarez, Javier Hernández-Andrés, Eva M. Valero, and J. Romero
Journal of the Optical Society of America A, Vol. 24, No. 4, pp. 942-956, April 2007 OSA Optics InfoBase
In a previous work [ Applied Optics 44, 5688 (2005)] we found the optimum sensors for a planned multispectral system for measuring skylight in the presence of noise by adapting a linear spectral recovery algorithm proposed by Maloney and Wandell [J. Opt. Soc. Am. A 3, 29 (1986)]. Here we continue along these lines by simulating the responses of three to five Gaussian sensors and recovering spectral information from noise-affected sensor data by trying out four different estimation algorithms, three different sizes for the training set of spectra, and various linear bases. We attempt to find the optimum combination of sensors, recovery method, linear basis, and matrix size to recover the best skylight spectral power distributions from colorimetric and spectral (in the visible range) points of view. We show how all these parameters play an important role in the practical design of a real multispectral system and how to obtain several relevant conclusions.


Effect of aerosol microphysical properties on polarization of skylight: sensitivity study and measurements
Eyk Boesche, Piet Stammes, Thomas Ruhtz, Réne Preusker, and Juergen Fischer
Applied Optics, Vol. 45, No. 34, p. 8790, December 2006 OSA Optics InfoBase
We analyze the sensitivity of the degree of linear polarization in the Sun’s principal plane as a function of aerosol microphysical parameters: the real and imaginary parts of the refractive index, the median radius and geometric standard deviation of the bimodal size distribution (both fine and coarse modes), and the relative number weight of the fine mode at a wavelength of 675 nm. We use Mie theory for single-scattering simulations and the doubling–adding method with the inclusion of polarization for multiple scattering. It is shown that the behavior of the degree of linear polarization is highly sensitive to both the small mode of the bimodal size distribution and the real part of the refractive index of aerosols, as well as to the aerosol optical thickness; whereas not all parameters influence the polarization equally. A classification of the importance of the input parameters is given. This sensitivity study is applied to an analysis of ground-based polarization measurements. For the passive remote sensing of microphysical and optical properties of aerosols, a ground-based spectral polarization measuring system was built, which aims to measure the Stokes parameters I, Q, and U in the visible (from 410 to 789 nm) and near-infrared (from 674 to 995 nm) spectral range with a spectral resolution of 7 nm in the visible and 2.4 nm in the near infrared. We compare polarization measurements taken with radiative transfer simulations under both clear- and hazy-sky conditions in an urban area (Cabauw, The Netherlands, 51.58° N, 4.56° E). Conclusions about the microphysical properties of aerosol are drawn from the comparison.

Polarization properties of Scarabaeidae
Dennis H. Goldstein
Applied Optics, Vol. 45, No. 30, p. 7944, October 2006 OSA Optics InfoBase
Beetles of the scarab family are known to reflect circularly polarized light from incident unpolarized light. They are unusual in that there are many animals that use polarized light in some form and several that actually create it, but there are few examples of the creation of circularly polarized light by animals. Scarabs have been measured with a spectropolarimetric reflectometer and are found to reflect light that is generally left-hand circularly polarized. Previous work is summarized, and what is believed to be new measurements of several scarab specimens are presented.

Celestial polarization patterns during twilight
Thomas W. Cronin, Eric J. Warrant, and Birgit Greiner
Applied Optics, Vol. 45, No. 22, p. 5582, August 2006 OSA Optics InfoBase
Scattering of sunlight produces patterns of partially linearly polarized light in the sky throughout the day, and similar patterns appear at night when the Moon is bright. We studied celestial polarization patterns during the period of twilight, when the Sun is below the horizon, determining the degree and orientation of the polarized-light field and its changes before sunrise and after sunset. During twilight, celestial polarized light occurs in a wide band stretching perpendicular to the location of the hidden Sun and reaching typical degrees of polarization near 80% at wavelengths > 600 nm. In the tropics, this pattern appears ∼ 1 h before local sunrise or disappears ∼ 1 h after local sunset (within 10 min after the onset of astronomical twilight at dawn, or before its end at dusk) and extends with little change through the entire twilight period.

Attenuation and impulse response for multiple scattering of light in atmospheric clouds and aerosols
Adrian C. Selden
Applied Optics, Vol. 45, No. 13, p. 3144, May 2006 OSA Optics InfoBase
Model phase functions for atmospheric clouds and aerosols typically comprise a narrow forward lobe (corona), a broad diffuse background, and a narrow backscattering peak (glory), which can reach relatively high values, especially for polyhedral scattering particles, such as hexagonal ice columns and plates. The influence of these three major components on the asymptotic and transient attenuation of the scattered light is compared for several analytic phase functions to assess the dependence of radiative transfer in clouds and aerosols on the choice of phase function. The impulse response (temporal evolution of the angular intensity distribution) is sensitive to the higher moments of the phase function and could prove to be a useful technique for inferring the optical scattering parameters of clouds and aerosols.

Influence of crystal tilt on solar irradiance of cirrus clouds
Susann Klotzsche and Andreas Macke
Applied Optics, Vol. 45, No. 5, p. 1034, February 2006 OSA Optics InfoBase
The single and multiple scattering and absorption properties of hexagonal ice columns with different degrees of particle orientation are modeled in the solar spectral range by means of a ray-tracing singlescattering code and a Monte Carlo radiative-transfer code. The scattering properties are most sensitive to particle orientation for the solar zenith angles of 50° (asymmetry parameter) and 90° (single-scattering albedo). Provided that the ice columns are horizontally oriented, the usual assumption of random orientation leads to an overestimation (underestimation) of the reflected (transmitted) solar broadband radiation at high Sun elevation and to an underestimation (overestimation) at medium solar zenith angles. The orientation effect is more (less) pronounced in scattering and transmission (absorption) for smaller ice crystals.


Feature issue: Applied Optics, September 2005

Light and color in the open air: introduction to the feature issue
Charles L. Adler and Raymond L. Lee, Jr.
Applied Optics, Volume 44, Issue 27, 5623 September 2005 OSA Optics InfoBase

Atmospheric refraction: a history
Waldemar H. Lehn and Siebren van der Werf
Applied Optics, Volume 44, Issue 27, 5624 September 2005 OSA Optics InfoBase
We trace the history of atmospheric refraction from the ancient Greeks up to the time of Kepler. The concept that the atmosphere could refract light entered Western science in the second century B.C. Ptolemy, 300 years later, produced the first clearly defined atmospheric model, containing air of uniform density up to a sharp upper transition to the ether, at which the refraction occurred. Alhazen and Witelo transmitted his knowledge to medieval Europe. The first accurate measurements were made by Tycho Brahe in the 16th century. Finally, Kepler, who was aware of unusually strong refractions, used the Ptolemaic model to explain the first documented and recognized mirage (the Novaya Zemlya effect).

Speculations on the possible causes of the Whymper apparition
Cedric John Hardwick and Jason C. Knievel
Applied Optics, Volume 44, Issue 27, 5637 September 2005 OSA Optics InfoBase
During the first ascent of the Matterhorn, a remarkable optical effect comprising three crosses surrounded by a great arch was observed by Edward Whymper, the British mountaineer. The authors review previous published explanations of the apparition. There are no photographs, only a woodcut and sketch, so the size of the apparition is not known, and it is not possible to make a definitive conclusion about what caused it. A fogbow and ice crystal arcs could have produced a circle and crosses in a direction consistent with the apparition. Some simulations are presented; one has a form approximating Whymper’s sketch. However, while this simulation used a crystal type that can occur, it required an unusual alignment that would be very rare.

The Toboggan Sun
Wayne P. S. Davidson and Siebren Y. van der Werf
Applied Optics, Volume 44, Issue 27, 5644 September 2005 OSA Optics InfoBase
Special variants of the Novaya Zemlya effect may arise from localized temperature inversions that follow the height profile of hills or mountains. Rather than following its natural path, the rising or setting Sun may, under such circumstances, appear to slide along a distant mountain slope. We found early observations of this effect in the literature by Willem Barents (1597) and by Captain Scott and H. G. Ponting (1911). We show recent photographic material of the effect and present ray-tracing calculations to explain its essentials.

Variability of observed low-altitude astronomical refraction (LAAR) from different geographic locations: progress toward a global map of LAAR variability
Russell D. Sampson, Edward P. Lozowski, and Hans G. Machel
Applied Optics, Volume 44, Issue 27, 5652 September 2005 OSA Optics InfoBase
The variability of the astronomical refraction of the setting Sun as measured from Holetown, Barbados, West Indies, is compared to sunset refraction measured from Edmonton, Alberta, during the same time of year. At about 13 °N latitude, Holetown experiences a marine tropical climate, while Edmonton (53 °N) has a subarctic continental climate. The 17 sunsets recorded from Holetown between 27 December 2003, and 21 February 2004, and between 25 and 30 December 2004, show a mean astronomical refraction of 0°.475 and standard deviation of 0°.012. The 26 sunsets recorded from Edmonton between 31 December 1992, and 17 February 1993, show a mean astronomical refraction of 0°.699 and standard deviation of 0°.118. The Barbados mean is significantly less than the Edmonton mean, while the variability of the Barbados data is an order of magnitude less than the Edmonton data. The variability of refraction appears to be strongly correlated with the variability in the surface vertical temperature gradient recorded on the same day as the sunset observations. This suggests that mapping of the geographic distribution of low-altitude astronomical refraction variability could be based on climatology of the surface vertical temperature gradient.

Effects of absorbing particles on coronas and glories
Michael Vollmer
Applied Optics, Volume 44, Issue 27, 5658 September 2005 OSA Optics InfoBase
Light scattering from small particles changes if the particles are absorbing. Whereas the effect is small for coronas and Bishop’s ring, glories show pronounced attenuation with increasing absorption. Results indicate suitable wavelength regions for studies of glory scattering from cloud tops. The behavior of core–shell particles could have applications for studying the atmosphere of Venus; in addition it provides more insight into the simple ray-path model of the glory.

Atmospheric glories: simulations and observations Free download
Philip Laven
Applied Optics, Volume 44, Issue 27, 5667 September 2005 OSA Optics InfoBase
Mie theory can be used to provide full-color simulations of atmospheric glories. Comparison of such simulations with images of real glories suggests that most glories are caused by spherical water droplets with radii between 4 and 25 µm. This paper also examines the appearance of glories taking into account the size of the droplets and the width of the droplet size distributions. Simulations of glories viewed through a linear polarizer compare well with the few available pictures, but they show some features that need corroboration by more observations.

How are glories formed? Free download
Philip Laven
Applied Optics, Volume 44, Issue 27, 5675 September 2005 OSA Optics InfoBase
Mie theory can be used to generate full-color simulations of atmospheric glories, but it offers no explanation for the formation of glories. Simulations using the Debye series indicate that glories are caused by rays that have suffered one internal reflection within spherical droplets of water. In 1947, van de Hulst suggested that backscattering (i.e., scattering angle theta = 180°) could be caused by surface waves, which would generate a toroidal wavefront due to spherical symmetry. Furthermore, he postulated that the glory is the interference pattern corresponding to this toroidal wavefront. Although van de Hulst’s explanation for the glory has been widely accepted, the author offers a slightly different explanation. Noting that surface waves shed radiation continuously around the droplet (not just at theta = 180°), scattering in a specific direction theta = 180° + d can be considered as the vector sum of two surface waves: one deflecting the incident light by 180° + d and the other by 180° - d. The author suggests that the glory is the result of two-ray interference between these two surface waves. Simple calculations indicate that this model produces more accurate results than van de Hulst’s model.

Halos in cirrus clouds: why are classic displays so rare?
Kenneth Sassen
Applied Optics, Volume 44, Issue 27, 5684 September 2005 OSA Optics InfoBase
Upper tropospheric cirrus clouds consist of hexagonal ice crystals, which geometrical ray-tracing-theory predicts should regularly produce a variety of optical phenomena such as vivid 22° and 46° halos. Yet, cirrus inconsistently generate such optical displays, while a class of more exotic displays are reported, albeit rarely. I review current knowledge of the cirrus cloud microphysical factors that control ice crystal shape, and hence haloarc formation, but also appeal to halo enthusiasts to help investigate the causes of unusually complex, brilliant, or rare optical displays. Currently, a wealth of meteorological information can be tapped from the Internet to help advance our knowledge of the basic meteorological factors leading to these rare events

Designing a practical system for spectral imaging of skylight Free download
Miguel A. López-Álvarez, Javier Hernández-Andrés, Javier Romero, and Raymond L. Lee, Jr.
Applied Optics, Volume 44, Issue 27, 5688 September 2005 OSA Optics InfoBase
In earlier work [J. Opt. Soc. Am. A 21, 13–23 (2004)], we showed that a combination of linear models and optimum Gaussian sensors obtained by an exhaustive search can recover daylight spectra reliably from broadband sensor data. Thus our algorithm and sensors could be used to design an accurate, relatively inexpensive system for spectral imaging of daylight. Here we improve our simulation of the multispectral system by (1) considering the different kinds of noise inherent in electronic devices such as changecoupled devices (CCDs) or complementary metal-oxide semiconductors (CMOS) and (2) extending our research to a different kind of natural illumination, skylight. Because exhaustive searches are expensive computationally, here we switch to a simulated annealing algorithm to define the optimum sensors for recovering skylight spectra. The annealing algorithm requires us to minimize a single cost function, and so we develop one that calculates both the spectral and colorimetric similarity of any pair of skylight spectra. We show that the simulated annealing algorithm yields results similar to the exhaustive search but with much less computational effort. Our technique lets us study the properties of optimum sensors in the presence of noise, one side effect of which is that adding more sensors may not improve the spectral recovery.

Multispectral synthesis of daylight using a commercial digital CCD camera Free download
Juan L. Nieves, Eva M. Valero, Sérgio M. C. Nascimento, Javier Hernández-Andrés, and Javier Romero
Applied Optics, Volume 44, Issue 27, 5696 September 2005 OSA Optics InfoBase
Performance of multispectral devices in recovering spectral data has been intensively investigated in some applications, as in spectral characterization of art paintings, but has received little attention in the context of spectral characterization of natural illumination. This study investigated the quality of the spectral estimation of daylight-type illuminants using a commercial digital CCD camera and a set of broadband colored filters. Several recovery algorithms that did not need information about spectral sensitivities of the camera sensors nor eigenvectors to describe the spectra were tested. Tests were carried out both with virtual data, using simulated camera responses, and real data obtained from real measurements. It was found that it is possible to recover daylight spectra with high spectral and colorimetricaccuracy with a reduced number of three to nine spectral bands.

Short-term variability of overcast brightness Free download
Raymond L. Lee, Jr. and Javier Hernández-Andrés
Applied Optics, Volume 44, Issue 27, 5704 September 2005 OSA Optics InfoBase
Overcasts seen from below seldom are uniform, unchanging cloud shields, yet little is known about their short-term photometric variability (periods < 2 h). Visible-wavelength spectra of daytime and twilight overcast skies measured at 30-s intervals reveal unexpected temporal variability in horizontal illuminance Ev and zenith luminance Lv. Fourier analysis of these time series shows peak fluctuations at periods of 2–40 min. Factors such as cloud type and optical depth, presence of fog or snow, and instrument field of view can affect overcast brightness variability. Surprisingly, under some circumstances overcasttwilight Ev exceeds clear-sky Ev at the same Sun elevation.

Colors of the daytime overcast sky Free download
Raymond L. Lee, Jr. and Javier Hernández-Andrés
Applied Optics, Volume 44, Issue 27, 5712 September 2005 OSA Optics InfoBase
Time-series measurements of daylight (skylight plus direct sunlight) spectra beneath overcast skies reveal an unexpectedly wide gamut of pastel colors. Analyses of these spectra indicate that at visible wavelengths, overcasts are far from spectrally neutral transmitters of the daylight incident on their tops. Colorimetric analyses show that overcasts make daylight bluer and that the amount of bluing increases with cloud optical depth. Simulations using the radiative-transfer model MODTRAN4 help explain the observed bluing: multiple scattering within optically thick clouds greatly enhances spectrally selective absorption by water droplets. However, other factors affecting overcast colors seen from below range from minimal (cloud-top heights) to moot (surface colors).

Simulating colors of clear and partly cloudy skies
Stanley David Gedzelman
Applied Optics, Volume 44, Issue 27, 5723 September 2005 OSA Optics InfoBase
A model (SKYCOLOR) is developed that simulates the light and color of the sky and open cloud decks in the vertical plane including the Sun and the observer and animates the changes as the Sun goes down. Model skylight consists of sunbeams that are scattered toward the observer, but depleted by scattering and absorption in the Chappuis bands of ozone. SKYCOLOR includes the Earth’s curvature, atmospheric refraction, cloud shadows, and solar eclipses. Scattering is given a wavelength (lambda) dependence of lambda-4 for air molecules (Rayleigh scattering), lambda-1 for tropospheric aerosols, and lambda+1 for volcanic aerosol particles. Multiple scattering is calculated directly in clouds but is parameterized in clear air by decreasing the scattering rates of sunlight and of skylight in the Earth’s shadow by 30%.

On the colors of distant objects Free download
David K. Lynch and S. Mazuk Applied Optics, Volume 44, Issue 27, 5737 September 2005 OSA Optics InfoBase
Distant objects like clouds, mountains, and the Sun can appear to have colors that are significantly different from their intrinsic colors: the low Sun is often red, white clouds and snow-capped peaks appear yellow or pink, and dark green or gray mountains can appear blue or purple. The color alteration increases with distance, or alternatively, optical depth. We investigate the perceived colors of distant objects by computing the CIE chromaticity coordinates from their spectra. For sources viewed through significant amounts of atmosphere (e.g., the low Sun), MODTRAN4 radiative-transfer calculations are used to retrieve the spectra. In addition to clouds and mountains, the colors of stars, the Sun, and the sky are presented as a function of solar elevation under a variety of atmospheric conditions.

Experimental simulations of pollen coronas
Werner B. Schneider and Michael Vollmer
Applied Optics, Volume 44, Issue 27, 5746 September 2005 OSA Optics InfoBase
A procedure to experimentally simulate pollen coronas is discussed. Observed coronas are due to pine and birch pollen having different geometries. Using computer simulations, two-dimensional projections of a large number of pollenlike objects with adjustable shapes, with or without preferential orientation and statistical or regular spatial distribution, are generated. The photograph of the printout allows samples with typical sizes between 20 and 200 µm. Their diffraction patterns can closely resemble the ones observed in nature and predicted by theory.

Ice analog halos
Zbigniew Ulanowski
Applied Optics, Volume 44, Issue 27, 5754 September 2005 OSA Optics InfoBase
Crystals of sodium fluorosilicate are used to produce easy to set up visual displays of atmospheric halos, including the 22° halo, the Parry arc, and upper tangent arcs. Scattering phase functions for single ice-analog rosettes, including a rough one, and a column aggregate, measured in randomized orientation, are also given. The phase functions show prominent halo features, with the exception of the rough crystal.

Turbulent ship wakes: further evidence that the Earth is round Free download
David K. Lynch
Applied Optics, Volume 44, Issue 27, 5759 September 2005 OSA Optics InfoBase
When viewed from the stern, a ship’s turbulent wake appears as a narrow strip of bubble-whitened water converging toward the horizon. The wake does not reach a sharp point on the horizon but has a finite angular width, indicating that the Earth is not flat, but rather round. A simple analysis of the geometry of the observations shows that the radius of the Earth can be estimated using only simple instruments and observations.

Improved algorithm for simulations of divergent-light halos
Lars Gislén, Jan O. Mattsson, and Bo Söderberg
Applied Optics, Vol. 44, No. 18, pp. 3638-3645 (June 2005) OSA Optics InfoBase
Divergent-light halos are produced when light from nearby light sources is scattered by ice crystals in the atmosphere. We present a theory of divergent-light halos leading to an improved algorithm for the simulation of such halos. Contrary to the algorithm that we presented earlier for simulating such halos, the new algorithm includes a mathematically rigorous weighting of the events. The computer implementation is very compact, and the whole procedure is elegant and conceptually easy to understand. We also present a new simulation atlas showing halos produced by crystals of different shapes and orientations for a set of elevations of the light source.


How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study Free download
Bence Suhai and Gábor Horváth
J. Opt. Soc. Am. A, Vol. 21, No. 9, p. 1669 September 2004 OSA Optics InfoBase
We present the first high-resolution maps of Rayleigh behavior in clear and cloudy sky conditions measured by full-sky imaging polarimetry at the wavelengths of 650 nm (red), 550 nm (green), and 450 nm (blue) versus the solar elevation angle θs . Our maps display those celestial areas at which the deviation Δα < │αmeas - αRayleigh│ is below the threshold αthres < 5°, where αmeas is the angle of polarization of skylight measured by full-sky imaging polarimetry, and αRayleigh is the celestial angle of polarization calculated on the basis of the single-scattering Rayleigh model. From these maps we derived the proportion r of the full sky for which the single-scattering Rayleigh model describes well (with an accuracy of Δα < 5°) the E-vector alignment of skylight. Depending on θs , r is high for clear skies, especially for low solar elevations (40% < r < 70% for θs ≤ 13°). Depending on the cloud cover and the solar illumination, r decreases more or less under cloudy conditions, but sometimes its value remains remarkably high, especially at low solar elevations (rmax = 69% for θs = 0°). The proportion r of the sky that follows the Rayleigh model is usually higher for shorter wavelengths under clear as well as cloudy sky conditions. This partly explains why the shorter wavelengths are generally preferred by animals navigating by means of the celestial polarization. We found that the celestial E-vector pattern generally follows the Rayleigh pattern well, which is a fundamental hypothesis in the studies of animal orientation and human navigation (e.g. in aircraft flying near the geomagnetic poles and using a polarization sky compass) with the use of the celestial α pattern.

Geometrical-optics approximation of forward scattering by coated particles
Feng Xu, Xiaoshu Cai, and Kuanfang Ren
Applied Optics, Vol. 43, No. 9, 1870-1879 (March 2004) OSA Optics InfoBase
By means of geometrical optics we present an approximation algorithm with which to accelerate the computation of scattering intensity distribution within a forward angular range (0°–60°) for coated particles illuminated by a collimated incident beam. Phases of emerging rays are exactly calculated to improve the approximation precision. This method proves effective for transparent and tiny absorbent particles with size parameters larger than 75 but fails to give good approximation results at scattering angles at which refractive rays are absent. When the absorption coefficient of a particle is greater than 0.01, the geometrical optics approximation is effective only for forward small angles, typically less than 10° or so.

Spectral-reflectance linear models for color pattern recognition Free download
Juan L. Nieves, Javier Hernández-Andrés, Eva M. Valero and Javier Romero
Applied Optics, vol. 43, N. 9, pp. 1880-1891, March 2004 OSA Optics InfoBase
We suggest a new method for color pattern recognition using a linear description of spectral reflectance functions and the spectral power distribution of illuminants containing very few parameters. We report on methods in which these spectral functions are derived from linear models based on principal component analysis (PCA). The correlation is made in the subspace spanned by the coefficients that describe each reflectance according to a suitable basis. The method is first illustrated in a control experiment where the scenes are captured under known illuminant conditions. The discrimination capacity of the algorithm improves upon conventional RGB multi-channel decomposition when scenes are captured under different illuminant conditions, and is comparable to color recognition based on CIELab system. Then we tested the coefficient method in situations where the target is captured under a reference illuminant and the scene containing the target under an unknown spectrally different one. We show that the method avoid false alarms under changes in the illuminant. The correlation results are satisfactory even for the reduced dimensional basis used here to represent the surface reflectance function of the image pixels.

Spectral-daylight recovery by use of only a few sensors Free download
Javier Hernández-Andrés, Juan L. Nieves, Eva M. Valero, and Javier Romero
J. Opt. Soc. Am. A, Vol. 21, No. 1, p. 13 January 2004 OSA Optics InfoBase
Linear models have already been proved accurate enough to recover spectral functions. We have resorted to such linear models to recover spectral daylight with the response of no more than a few real sensors. We performed an exhaustive search to obtain the best set of Gaussian sensors with a combination of optimum spectral position and bandwidth. We also examined to what extent the accuracy of daylight estimation depends on the number of sensors and their spectral properties. A set of 2600 daylight spectra [J. Opt. Soc. Am. A 18, 1325 (2001)] were used to determine the basis functions in the linear model and also to evaluate the accuracy of the search. The estimated spectra are compared with the original ones for different spectral daylight and skylight sets of data within the visible spectrum. Spectral similarity, colorimetric differences, and integrated spectral irradiance errors were all taken into account. We compare our best results with those obtained by using a commercial CCD, revealing the CCD’s potential as a daylight-estimation device.


Scattering matrices for large ice crystal particles
Anatoli G. Borovoi and Igor A. Grishin
J. Opt. Soc. Am. A, Vol. 20, No. 11, p. 2071 November 2003 OSA Optics InfoBase
The problem of light scattering by ice crystal particles whose sizes are essentially larger than the incident wavelength is divided into two parts. First, the scattered field is represented as a set of plane-parallel outgoing beams in the near zone of the particle. Then, in the far zone the scattered field is represented as a result of both diffraction and interference of these beams within the framework of physical optics. A proper ray-tracing algorithm for calculation of the amplitude (Jones) scattering matrix is developed and applied. For large particles, a number of reduced Mueller matrices are introduced and discussed, since the pure Mueller matrix obtained from the Jones matrix becomes a rather cumbersome and quickly oscillating value. Backscattering by hexagonal ice crystals, including polarization properties, is considered in detail.

Procedure for simulating divergent-light halos
Lars Gislén
Applied Optics, Vol. 42, No. 33, pp. 6559-6563 (2003) OSA Optics InfoBase
Divergent-light halos are halos produced by light from nearby light sources, like street lamps being scattered by small crystals of ice floating in the air. The use of “brute-force” Monte Carlo methods to simulate such halos is extremely inefficient, as most scattered rays will not hit the eye of the observer. I present a new procedure for Monte Carlo simulations of divergent-light halos. This procedure uses rotational symmetries to make a selected sampling of events that greatly improves the computational efficiency of the algorithm. We can typically generate a simulated halo display in minutes using a personal computer, several orders of magnitude more rapid than a simple brute-force method. The algorithm can also optionally generate three-dimensional pictures of divergent-light halo displays.

Analytical models of optical refraction in the troposphere
Brett D. Nener, Neville Fowkes, and Laurent Borredon
J. Opt. Soc. Am. A, Vol. 20, No. 5, p. 867 May 2003 OSA Optics InfoBase
An extremely accurate but simple asymptotic description (with known error) is obtained for the path of a ray propagating over a curved Earth with radial variations in refractive index. The result is sufficiently simple that analytic solutions for the path can be obtained for linear and quadratic index profiles. As well as rendering the inverse problem trivial for these profiles, this formulation shows that images are uniformly magnified in the vertical direction when viewed through a quadratic refractive-index profile. Non-uniform vertical distortions occur for higher-order refractive-index profiles.

Role of the tunneling ray in near-critical-angle scattering by a dielectric sphere Free download
James A. Lock
J. Opt. Soc. Am. A, Vol. 20, No. 3, p. 499 March 2003 OSA Optics InfoBase
The scattering far zone for light transmitted through a sphere following p - 1 internal reflections by a family of near-grazing incident rays is subdivided into a lit region and a shadow region. The sharpness of the ray theory transition between the lit and the shadow regions is smoothed in wave theory by radiation shed by electromagnetic surface waves. It is shown that when higher-order terms in the physical optics approximation to the phase of the partial-wave scattering amplitudes are included, the transition between the lit and the shadow regions becomes a two-ray-to-zero-ray transition, called a superweak caustic in analogy to the more familiar scattering caustics and weak scattering caustics. One of the merged rays is a tunneling ray.

Feature issue: Applied Optics, January 2003

Light and color in the open air: introduction to the feature issueFree download
Charles L. Adler and James A. Lock
Applied Optics, Volume 42, Issue 3, 307-308 January 2003 OSA Optics InfoBase
This special feature of Applied Optics reports the results of new experimental and theoretical research concerning a number of naked-eye optical phenomena, including ice-crystal halo displays, mirages, rainbows, glories, optical caustics, clear-sky phenomena, cloud coronas, cloud iridescence, and the extinction of skylight.

Halo Polarization Profiles and Sampled Ice Crystals: Observations and Interpretation Free download
Günther P. Können, Herman R. A. Wessels, Jaap Tinbergen
Applied Optics, Volume 42, Issue 3, 309-317 January 2003 OSA Optics InfoBase
Simultaneous two-wavelength polarization and radiance distributions have been obtained for 22 ° parhelia in four Antarctic ice-crystal swarms that extended to ground level. Samples of crystals that produced these parhelia were collected and replicated. The wavelength dependence of the width of the halo polarization peak agrees with Fraunhofer diffraction theory, indicating that the broadening of the halos is caused primarily by diffraction. However, the observed broadening is much more than predicted from the size distribution of the replicated crystals. From one halo display to the other, the ratio of observed /predicted broadening is erratic, suggesting size-dependent collection efficiency in the sampling. This would imply that, for South Pole conditions, halo polarimetry (or even photometry) is a more reliable method for crystal size determination than actual sampling. It also implies that shapes of the sampled crystals need not necessarily be representative for the shapes of the halo-making crystals in the swarm. Our previous hypothesis [ Applied Optics 33, 4569 (1994) , that a spread of interfacial angles is the dominating cause of halo broadening, has proved untenable.]

Symmetry in Halo Displays and Symmetry in Halo-Making Crystals Free download
Günther P. Können
Applied Optics, Volume 42, Issue 3, 318-331 January 2003 OSA Optics InfoBase
The relation between the symmetry in halo displays and crystal symmetry is investigated for halo displays that are generated by ensembles of crystals. It is found that, regardless of the symmetry of the constituent crystals, such displays are always left-right (L -R) symmetric if the crystals are formed from the surrounding vapor. L -R symmetry of a halo display implies here that the cross sections for formation of a halo arc on the left-hand side of the solar vertical and its right-hand side mirror image are equal. This property leaves room for two types of halo display only: a full symmetric one (mmm -symmetric), and a partial symmetric one (mm2 -symmetric) in which halo constituents lack their counterparts on the other side of the parhelic circle. A partial symmetric display can occur only for point halos. Its occurrence implies that a number of symmetry elements are not present in the shape of the halo-making crystals. These elements are a center of inversion, any rotatory-inversion axis that is parallel to the crystal spin axis P , a mirror plane perpendicular to the P axis, and a twofold rotation axis perpendicular to the P axis. A simple conceptual method is presented to reconstruct possible shapes of the halo-generating crystals from the halos in the display. The method is illustrated in two examples. Halos that may occur on the Saturnian satellite Titan are discussed. The possibilities for the Huygens probe to detect these halos during its descent through the Titan clouds in 2005 are detailed.

Midlatitude Cirrus Cloud Climatology from the Facility for Atmospheric Remote Sensing. IV. Optical Displays
Kenneth Sassen, Jiang Zhu, Sally Benson
Applied Optics, Volume 42, Issue 3, 332-341 January 2003 OSA Optics InfoBase
In this fourth of a series of papers that describe long-term cloud research at the Facility for Atmospheric Remote Sensing at Salt Lake City, Utah, a ~10-year record of polarization lidar and photographic observations is analyzed to characterize the occurrence of optical displays in our local varieties of midlatitude cirrus clouds. The frequencies of occurrence of various types of halo, arc, and corona displays are evaluated according to their appearance and longevity over nominal 1-h observation periods and to the meteorological source of the cirrus. We find that complex halo-arc displays are rare at our locale and that even the so-called common 22° halo occurs infrequently as a complete long-lived ring. For example, only ~6% of the 1561-h daytime cirrus periods have bright and prolonged 22° halos, although a total of 37.3% have some indications of this halo, even if they are brief and fragmentary. Other fairly frequent features are the 22° upper tangent arc (8.6%), 22° parhelia (8.5%), and solar corona (7.2%). Of the optical displays observed, 83.6% are refraction based, only 1.9% are due to reflection phenomena, and a surprising 15.4% are caused by diffraction. Complex halo-arc displays are disproportionally associated with cirrus formed in tropical or subtropical airflow and also contain more horizontally oriented planar ice crystals. Lidar linear depolarization ratios from a subset of vivid displays show significant differences between halo- and the corona-producing cirrus, reflecting the effects of particle shape. Halos are associated with relatively warm cirrus that contain randomly and horizontally oriented planar ice crystals, whereas the colder corona cirrus produce much stronger depolarization from crystals too small to be uniformly oriented. Comparisons are made with available information from other locales, and we attempt to explain the geographical differences in terms of basic cirrus cloud processes

Comparison of Modeled and Observed Astronomical Refraction of the Setting Sun
Russell D. Sampson, Edward P. Lozowski, Arthur E. Peterson
Applied Optics, Volume 42, Issue 3, 342-353 January 2003 OSA Optics InfoBase
In this study a ray-tracing model that uses atmospheric data from VIZ and Vaisala RS80 rawinsondes is compared with the observed astronomical refraction presented by the setting Sun as seen from Stony Plain, Alberta, Canada. Photogrammetric measurements taken from photographs of the setting Sun show good agreement with the model for the 14 and 22 December 1998 sunsets. The poorer model results for the 8 December sunset appear to be caused by an obsolete and possibly defective VIZ rawinsonde. The results suggest that the ray-tracing model can produce improved refraction values when compared with the Pulkovo tables [Pulkovo Observatory, Refraction Tables of the Pulkovo Observatory , 5th ed. (Nauka, Leningrad, 1985) . However, they also indicate that the inverse solution (i.e., extracting the temperature profile from refraction measurements) may produce no improvement on U.S. Standard Atmosphere adjusted to the surface conditions.]

Ray Tracing and Refraction in the Modified US1976 Atmosphere
Siebren Y. van der Werf
Applied Optics, Volume 42, Issue 3, 354-366 January 2003 OSA Optics InfoBase
A new and flexible ray-tracing procedure for calculating astronomical refraction is outlined and applied to the US1976 standard atmosphere. This atmosphere is generalized to allow for a free choice of the temperature and pressure at sea level, and in this form it has been named the modified US1976 (MUSA76) atmosphere. Analytical expressions and numerical procedures are presented for calculating dry-air refractions and for the water-vapor correction. Results for all apparent altitudes are presented and compared with The Star Almanac for Land Surveyors (1951), The Nautical Almanac (1958), and the Pulkovo tables (Refraction Tables of the Pulkovo Observatory , 1985). Dependences on sea-level pressure, temperature, and temperature gradient and on humidity are discussed.

Novaya Zemlya Effect and Sunsets Free download
Siebren Y. van der Werf, Günther P. Können, Waldemar H. Lehn
Applied Optics, Volume 42, Issue 3, 367-378 January 2003 OSA Optics InfoBase
Systematics of the Novaya Zemlya (NZ) effect are discussed in the context of sunsets. We distinguish full mirages, exhibiting oscillatory light paths and their onsets, the subcritical mirages. Ray-tracing examples and sequences of solar images are shown. We discuss two historical observations by Fridtjof Nansen and by Vivian Fuchs, and we report a recent South Pole observation of the NZ effect for the Moon.

Gerrit de Veer's True and Perfect Description of the Novaya Zemlya Effect, 24 -27 January 1597 Free download
Siebren Y. van der Werf, Günther P. Können, Waldemar H. Lehn, Frits Steenhuisen, Wayne P. S. Davidson
Applied Optics, Volume 42, Issue 3, 379-389 January 2003 OSA Optics InfoBase
The first recordings of the Novaya Zemlya (NZ) effect were made during Willem Barents ’ third Arctic expedition. Ray-tracing analyses of the three key observations, on 24 -27 January 1597, show that all the reported details can be explained by adopting one common and realistic type of temperature inversion. In particular, the Moon-Jupiter conjunction could have been visible over the central mountain ridge of the island. We show that the NZ effect distorts the relative positions of Jupiter and the Moon in such a way that the looked-for fingerprint of the conjunction occurred almost 2 h after the true conjunction. The quoted direction for the apparent Moon-Jupiter conjunction is then found to be accurate to within 1°. This delay of the apparent conjunction largely explains the error of 29° in their longitude determination. The truthfulness of these observations, debated for four centuries, now appears to be beyond doubt.

Bright Superior Mirages Free download
Waldemar H. Lehn
Applied Optics, Volume 42, Issue 3, 390-393 January 2003 OSA Optics InfoBase
Superior mirages of unusual brightness are occasionally observed. Two such cases, photographed over the frozen surface of Lake Winnipeg, Canada, are documented. Visually, these mirages appear as featureless bright barriers far out on the lake. They are just images of the lake ice, yet the luminance in one case was 2.5 times (in the other, 1.7 times) the luminance of the ice surface in front of the mirage. The mirage itself can be modeled by means of a conduction inversion, but a proper explanation of the brightness is not yet available.

Halo and Mirage Demonstrations in Atmospheric Optics
Michael Vollmer, Robert Greenler
Applied Optics, Volume 42, Issue 3, 394-398 January 2003 OSA Optics InfoBase
Some laboratory demonstrations on atmospheric optics are presented. The focus is on dispersion effects in mirages, lateral mirages, and inferior mirages produced with small hot plates. We also show a demonstration of the upper-tangent-arc halo, produced with a hexagonal prism, rotating about two axes.

Imaging Polarimetry of the Rainbow Free download
András Barta, Gábor Horváth, Balázs Bernáth, Viktor Benno Meyer-Rochow
Applied Optics, Volume 42, Issue 3, 399-405 January 2003 OSA Optics InfoBase
Using imaging polarimetry, we measured the polarization patterns of a rainbow on the shore of the Finnish town of Oulu in July 2001. We present here high-resolution color-coded maps of the spatial distributions of the degree and angle of linear polarization of the rainbow in the red (650 +/- 30 nm), green (550 +/- 30 nm), and blue (450 +/- 30 nm) ranges of the spectrum. The measured polarization characteristics of the investigated rainbow support earlier theoretical and computational results and are in accordance with previous qualitative observations. To our knowledge, this is the first imaging polarimetric study of rainbow polarization.

Experimental Observation of Total-Internal-Reflection Rainbows Free download
Charles L. Adler, James A. Lock, Jonathon Mulholland, Brian Keating, Diana Ekelman
Applied Optics, Volume 42, Issue 3, 406-411 January 2003 OSA Optics InfoBase
A new class of rainbows is created when a droplet is illuminated from the inside by a point light source. The position of the rainbow depends on both the index of refraction of the droplet and the position of the light source, and the rainbow vanishes when the point source is too close to the center of the droplet. Here we experimentally measure the position of the transmission and one-internal-reflection total-internal-reflection rainbows, and the standard (primary) rainbow, as a function of light-source position.

Observation of the enhanced backscattering of light by the end of a tilted dielectric cylinder owing to the caustic merging transition
Philip L. Marston, Yibing Zhang, David B. Thiessen
Applied Optics, Volume 42, Issue 3, 412-417 January 2003 OSA Optics InfoBase
The scattering of light by obliquely illuminated circular dielectric cylinders was previously demonstrated to be enhanced by a merger of Airy caustics at a critical tilt angle. [ Applied Optics 37 , 1534 (1998)]. A related enhancement is demonstrated here for backward and near-backward scattering for cylinders cut with a flat end perpendicular to the cylinder's axis. It is expected that merged caustics will enhance the backscattering by clouds of randomly oriented circular cylinders that have appropriately flat ends.

Analysis of the Shadow-Sausage Effect Caustic Free download
James A. Lock, Charles L. Adler, Diana Ekelman, Jonathan Mulholland, Brian Keating
Applied Optics, Volume 42, Issue 3, 418-428 January 2003 OSA Optics InfoBase
We analyze the optical caustic produced by light refracted at the curved meniscus surrounding a cylindrical rod standing partially out of a liquid-filled container. When the rod is tilted from the vertical or when light is diagonally incident, the caustic is a four-cusped astroid with two of its cusps obscured by the rod's shadow. If a portion of the flat end of the rod is raised above the water level, the caustic evolves into a pattern of five interlocking cusps. The five cusps result from symmetry breaking of a three-cusped surface perturbation caustic.

Simulating glories and cloudbows in color
Stanley D. Gedzelman
Applied Optics, Volume 42, Issue 3, 429-435 January 2003 OSA Optics InfoBase
Glories and cloudbows are simulated in color by use of the Mie scattering theory of light upwelling from small-droplet clouds of finite optical thickness embedded in a Rayleigh scattering atmosphere. Glories are generally more distinct for clouds of droplets of as much as ~10 µm in radius. As droplet radius increases, the glory shrinks and becomes less prominent, whereas the cloudbow becomes more distinct and eventually colorful. Cloudbows typically consist of a broad, almost white band with a slightly orange outer edge and a dark inner band. Multiple light and dark bands that are related to supernumerary rainbows first appear inside the cloudbow as droplet radius increases above ~10 µm and gradually become more prominent when all droplets are the same size. Bright glories with multiple rings and high color purity are simulated when all droplets are the same size and every light beam is scattered just once. Color purity decreases and outer rings fade as the range of droplet sizes widens and when skylight, reflected light from the ground or background, and multiply scattered light from the cloud are included. Consequently, the brightest and most colorful glories and bows are seen when the observer is near a cloud or a rain swath with optical thickness of ~0.25 that consists of uniform-sized drops and when a dark or shaded background lies a short distance behind the cloud.

Simulation of Rainbows, Coronas, and Glories by use of Mie Theory Free download
Philip Laven
Applied Optics, Volume 42, Issue 3, 436-444 January 2003 OSA Optics InfoBase
Mie theory offers an exact solution to the problem of scattering of sunlight by spherical drops of water. Until recently, most applications of Mie theory to scattering of light were restricted to a single wavelength. Mie theory can now be used on modern personal computers to produce full-color simulations of atmospheric optical effects, such as rainbows, coronas, and glories. Comparison of such simulations with observations of natural glories and cloudbows is encouraging.

Measuring and Modeling Twilight's Purple Light Free download
Raymond L. Lee, Javier Hernández-Andrés
Applied Optics, Volume 42, Issue 3, 445-457 January 2003 OSA Optics InfoBase
During many clear twilights, much of the solar sky is dominated by pastel purples. This purple light’s red component has long been ascribed to transmission through and scattering by stratospheric dust and other aerosols. Clearly the vivid purples of post-volcanic twilights are related to increased stratospheric aerosol loading. Yet our time-series measurements of purple-light spectra, combined with radiative transfer modeling and satellite soundings, indicate that background stratospheric aerosols by themselves do not redden sunlight enough to cause the purple light's reds. Furthermore, scattering and extinction in both the troposphere and the stratosphere are needed to explain most purple lights.

Color and Luminance Asymmetries in the Clear Sky Free download
Javier Hernández-Andrés, Raymond L. Lee, Javier Romero
Applied Optics, Volume 42, Issue 3, 458-464 January 2003 OSA Optics InfoBase
A long-standing assumption about the clear sky is that its colors and luminances are distributed symmetrically about the principal plane. As useful as this approximation is, our digital-image analyses show that clear-sky color and luminance routinely depart perceptibly from exact symmetry. These analyses reconfirm our earlier measurements with narrow field-of-view spectroradiometers [J. Opt. Soc. Am. A 18, 1325 (2001) , and they do so with much higher temporal and angular resolution across the entire sky dome.

Neutral Points of Skylight Polarization Observed During the Total Eclipse on 11 August 1999 Free download
Gábor Horváth, István Pomozi, József Gál
Applied Optics, Volume 42, Issue 3, 465-475 January 2003 OSA Optics InfoBase
We report here on the observation of unpolarized (neutral) points in the sky during the total solar eclipse on 11 August 1999. Near the zenith a neutral point was observed at 450 nm at two different points of time during totality. Around this celestial point the distribution of the angle of polarization was heterogeneous: The electric field vectors on the one side were approximately perpendicular to those on the other side. At another moment of totality, near the zenith a local minimum of the degree of linear polarization occurred at 550 nm. Near the antisolar meridian, at a low elevation another two neutral points occurred at 450 nm at a certain moment during totality. Approximately at the position of these neutral points, at another moment of totality a local minimum of the degree of polarization occurred at 550 nm, whereas at 450 nm a neutral point was observed, around which the angle-of-polarization pattern was homogeneous: The electric field vectors were approximately horizontal on both sides of the neutral point.

Coronas and iridescence in mountain wave clouds Free download
Joseph A. Shaw, Paul J. Neiman
Applied Optics, Volume 42, Issue 3, 476-485 January 2003 OSA Optics InfoBase
We use Fraunhofer diffraction theory and meterological data to determine the nature of cloud-particle distributions and the mean particle sizes required for interpreting photographs of coronas and iridescence in mountain wave clouds. Traditional descriptions of coronas and iridescence usually explain these optical phenomena as diffraction by droplets of liquid water. Our analysis shows that the photographed displays have mean particle sizes from 7.6 to 24.3 µm, with over half the cases requiring diffraction by small ( ~20 µm) quasispherical ice particles rather than liquid water droplets. Previous documentation of coronas produced by ice particles are limited to observations in cirrus clouds that appear to be composed of small ice crystals, whereas our observations suggest that coronas and iridescence quite often can be created by tiny quasispherical ice particles that might be unique to mountain wave clouds. Furthermore, we see that the dominant colors in mountain wave-cloud coronas are red and blue, rather than the traditionally described red and green.

Cirrus cloud iridescence: a rare case study
Kenneth Sassen
Applied Optics, Volume 42, Issue 3, 486-491 January 2003 OSA Optics InfoBase
On the evening of 25 November 1998, a cirrus cloud revealing the pastel colors of the iridescence phenomenon was photographed and studied by a polarization lidar system at the University of Utah Facility for Atmospheric Remote Sensing (FARS). The diffraction of sunlight falling on relatively minute cloud particles, which display spatial gradients in size, is the cause of iridescence. According to the 14-year study of midlatitude cirrus clouds at FARS, cirrus rarely produce even poor iridescent patches, making this particularly long-lived and vivid occurrence unique. In this unusually high (13.2 -14.4 km) and cold ( -69.7 ° to -75.5 °) tropopause-topped cirrus cloud, iridescence was noted from ~6.0 ° to ~13.5 ° from the Sun. On the basis of simple diffraction theory, this indicates the presence of particles of 2.5 - 5.5 µm effective diameter. The linear depolarization ratios of d = 0.5 measured by the lidar verify that the cloud particles were nonspherical ice crystals. The demonstration that ice clouds can generate iridescence has led to the conclusion that iridescence is rarely seen in midlatitude cirrus clouds because populations of such small particles do not exist for long in the presence of the relatively high water-vapor supersaturations needed for ice-particle nucleation.

Solar Aureoles Caused by Dust, Smoke, and Haze
Forrest M. Mims
Applied Optics, Volume 42, Issue 3, 492-496 January 2003 OSA Optics InfoBase
The forward scattering of sunlight by atmospheric aerosols causes a bright glow to appear around the Sun. This phenomenon, the simplest manifestation of the solar corona, is called the solar aureole. Simple methods can be used to photograph the solar aureole with conventional and digital cameras. Aureole images permit both a visually qualitative and an analytically quantitative comparison of aureoles caused by dust, smoke, haze, pollen, and other aerosols. Many hundreds of aureole photographs have been made at Geronimo Creek Observatory in Texas, including a regular time series since September 1998. These images, and measurements extracted from them, provide an important supplement to studies of atmospheric aerosols.

Simulating Coronas in Color Free download
Stanley D. Gedzelman, James A. Lock
Applied Optics, Volume 42, Issue 3, 497-504 January 2003 OSA Optics InfoBase
Coronas are simulated in color by use of the Mie scattering theory of light by small droplets through clouds of finite optical thickness embedded in a Rayleigh scattering atmosphere. The primary factors that affect color, visibility, and number of rings of coronas are droplet size, width of the size distribution, and cloud optical thickness. The color sequence of coronas and iridescence varies when the droplet radius is smaller than ~6- µm. As radius increases to approximately 3.5 µm, new color bands appear at the center of the corona and fade as they move outward. As the radius continues to increase to ~6 µm, successively more inner rings become fixed in the manner described by classical diffraction theory, while outer rings continue their outward migration. Wave clouds or rippled cloud segments produce the brightest and most vivid multiple ringed coronas and iridescence because their integrated drop size distributions along sunbeams are much narrower than in convective or stratiform clouds. The visibility of coronas and the appearance of the background sky vary with cloud optical depth t. First the corona becomes visible as a white aureole in a blue sky when t ~ 0.001. Color purity then rapidly increases to an almost flat maximum in the range 0.05 < t < 0.5 and then decreases, so coronas are almost completely washed out by a bright gray background when t >= 4.

Evaluation of a one-dimensional cloud model for yellow and green thunderstorms
Frank W. Gallagher, William H. Beasley
Applied Optics, Volume 42, Issue 3, 505-510 January 2003 OSA Optics InfoBase
Many observers have reported observations of green light emanating from severe thunderstorms in the midwestern United States. Spectral measurements have demonstrated that the dominant wavelength of the light is in the green portion of the visible spectrum and that this is not just a subjective impression. According to the theory proposed by Bohren and Fraser [Bull. Am. Meteorol. Soc. 74 , 2185 (1993)], two effects combine to produce green light from thunderstorms. First, incident solar radiation is reddened by selective scattering by air molecules and particles in the atmosphere before it enters the cloud. Second, the radiation that passes through an optically thick cloud is attenuated in the longer wavelengths because of selective absorption by liquid water. Model calculations indicate that realizable combinations of mean drop diameters, mean liquid-water contents, and cloud thicknesses can satisfy the conditions required for shifting the dominant wavelength of the incident solar radiation to green.

Polarization-Based Vision Through Haze
Yoav Y. Schechner, Srinivasa G. Narasimhan, Shree K. Nayar
Applied Optics, Volume 42, Issue 3, 511-525 January 2003 OSA Optics InfoBase
We present an approach for easily removing the effects of haze from passively acquired images. Our approach is based on the fact that usually the natural illuminating light scattered by atmospheric particles (airlight) is partially polarized. Optical filtering alone cannot remove the haze effects, except in restricted situations. Our method, however, stems from physics-based analysis that works under a wide range of atmospheric and viewing conditions, even if the polarization is low. The approach does not rely on specific scattering models such as Rayleigh scattering and does not rely on the knowledge of illumination directions. It can be used with as few as two images taken through a polarizer at different orientations. As a byproduct, the method yields a range map of the scene, which enables scene rendering as if imaged from different viewpoints. It also yields information about the atmospheric particles. We present experimental results of complete dehazing of outdoor scenes, in far-from-ideal conditions for polarization filtering. We obtain a great improvement of scene contrast and correction of color.


Blue Spot on the Parhelic Circle
Mika Sillanp, Jarmo Moilanen, Marko Riikonen, Marko Pekkola
Applied Optics, Volume 40, Issue 30, 5275-5279 October 2001 OSA Optics InfoBase
We develop a theory for a new effect on the parhelic circle. We show that there is a colored segment on the parhelic circle at a certain large azimuth that depends on solar elevation. The color segment appears at solar elevations below 32° and is explained as a transition between total and partial internal reflection in the main ray paths of the parhelic circle in oriented ice crystals. Based on our simple refraction theory and computer simulations, we find that the color of the segment is mainly green and blue. The theory is tested with available photographs of the effect.

Heiligenschein and Related Phenomena in Divergent Light
Jan O. Mattsson, Lars Bärring
Applied Optics, Volume 40, Issue 27, 4799-4806 September 2001 OSA Optics InfoBase
When seen in divergent light, atmospheric optical phenomena could appear to be modified. We describe some geometric and retroreflectional effects of light divergence on heiligenschein and related phenomena that, to our knowledge, have not been previously reported. These geometric effects are compared with and set in relation to the geometric effects on other atmospheric optical phenomena.

Color and spectral analysis of daylight in southern Europe Free download
Javier Hernandez-Andrés, Javier Romero, Juan L. Nieves and Raymond L. Lee, Jr.
J. Opt. Soc. Am. A, Vol. 18, No. 6, p. 1325 June 2001 OSA Optics InfoBase
We have analyzed the colorimetric and spectral characteristics of 2600 daylight spectra (global spectral irradiances on a horizontal surface) measured for all sky states during a 2-year period at Granada, Spain. We describe in detail the chromaticity coordinates, correlated color temperatures (CCT), luminous efficacies, and relative UV and IR contents of Granada daylight. The chromaticity coordinates of Granada daylight lie far above the CIE locus at high CCTs (.9000 K), and a CCT of 5700 K best typifies this daylight. Our principal components analysis shows that Granada daylight spectra can be adequately represented by using sixdimensional linear models in the visible, whereas seven-dimensional models are required if we include the UV or near-IR. Yet on average only three-dimensional models are needed to reconstruct spectra that are colorimetrically indistinguishable from the original spectra.

Colorimetric and spectroradiometric characteristics of narrow-field-of-view clear skylight in Granada, Spain Free download
Javier Hernandez-Andrés, Javier Romero and Raymond L. Lee, Jr.
J. Opt. Soc. Am. A, Vol. 18, No. 2, p. 412 February 2001 OSA Optics InfoBase
As part of our ongoing research into the clear daytime sky’s visible structure, we analyze over 1500 skylight spectra measured during a seven-month period in Granada, Spain. We use spectral radiances measured within 3° fields of view (FOV’s) to define colorimetric characteristics along four sky meridians: the solar meridian and three meridians at azimuths of 45°, 90°, and 315° relative to it. The resulting clear-sky chromaticities in 44 different view directions (1) are close to but do not coincide with the CIE daylight locus, (2) form V-shaped meridional chromaticity curves along it (as expected from theory), and (3) have correlated color temperatures (CCT’s) ranging from 3800 K to ` K. We also routinely observe that sky color and luminance are asymmetric about the solar meridian, usually perceptibly so. A principal-components analysis shows that three vectors are required for accurate clear-sky colorimetry, whereas six are needed for spectral analyses.


Parry Arc: A Polarization Lidar, Ray-Tracing, and Aircraft Case Study
Kenneth Sassen, Yoshihide Takano
Applied Optics, Volume 39, Issue 36, 6738-6745 December 2000 OSA Optics InfoBase
Using simple ray-tracing simulations, the cause of the rare Parry arc has been linked historically to horizontally oriented columns that display the peculiar ability to fall with a pair of prism faces closely parallel to the ground. Although we understand the aerodynamic forces that orient the long-column axis in the horizontal plane, which gives rise to the relatively common tangent arcs of the 22° halo, the mechanism leading to the Parry crystal orientation has never been resolved adequately. On 16 November 1998, at the University of Utah Facility for Atmospheric Remote Sensing, we studied a cirrus cloud producing a classic upper Parry arc using polarization lidar and an aircraft with a new high-resolution ice crystal imaging probe. Scanning lidar data, which reveal extremely high linear depolarization ratios d a few degrees off the zenith direction, are simulated with ray-tracing theory to determine the ice crystal properties that reproduce this previously unknown behavior. It is found that a limited range of thick-plate crystal axis (length-to-diameter) ratios from 0.75 to 0.93 generates a maximum d =2.0 - 5.0 for vertically polarized 0.532 µm light when the lidar is tilted 1°-2° off the zenith. Halo simulations based on these crystal properties also generate a Parry arc. However, although such particles are abundant in the in situ data in the height interval indicated by the lidar, one still has to invoke an aerodynamic stabilization force to produce properly oriented particles. Although we speculate on a possible mechanism, further research is needed into this new explanation for the Parry arc.

Sunset science. III. Visual adaptation and green flashes Free download
Andrew T. Young
J. Opt. Soc. Am. A, Vol. 17, No. 12, p. 2129 December 2000 OSA Optics InfoBase
Photographs of green flashes do not preclude a role for physiological effects in these phenomena. While green flashes are certainly not after-images, there is compelling evidence that adaptation in the visual system strongly affects the perceived color of most sunset green flashes. Furthermore, the retinal image of the setting Sun is usually bright enough to bleach most of the red-sensitive photopigment in a few seconds, making the yellow stage of a sunset flash appear green. Even in air so hazy that no green light reaches the eye, a yellow flash may occur and appear green. Many, but not all, visual observations of sunset green flashes are of this yellow flash. The yellow portion of sunset green flashes helps explain their reported durations, which exceed those expected for the appearance of green light alone.
N.B. see related articles:
Sunset science. I. The mock mirage (Applied Optics, Vol. 36, No. 12, p. 2689, April 1997) OSA Optics InfoBase
Sunset science. II. A useful diagram (Applied Optics, Vol. 37, No. 18, p. 3785, June 1998) Free download
Sunset science. IV. Low-altitude Refraction (The Astronomical Journal, Vol. 127, pp. 3622–3637, June 2004) Free download
Halo Observations Provide Evidence of Airborne Cubic Ice in the Earth's Atmosphere
Marko Riikonen, Mika Sillanp, Leena Virta, Daniel Sullivan, Jarmo Moilanen, Ismo Luukkonen
Applied Optics, Volume 39, Issue 33, 6080-6085 November 2000 OSA Optics InfoBase
An ice crystal halo display that contains several previously unknown halo phenomena was observed in Northern Chile. Analysis of computer simulations of the halos demonstrates that most of the new halo arcs in the display can be explained by the presence of airborne and preferentially oriented crystals of cubic ice. These observations therefore provide evidence of the existence of the cubic phase of ice in the Earth's atmosphere.

Exterior caustics produced in scattering of a diagonally incident plane wave by a circular cylinder: semiclassical scattering theory analysis
James A. Lock, Charles L. Adler, and Edward A. Hovenac
J. Opt. Soc. Am. A, Vol. 17, No. 10, pp. 1846-1856 (October 2000) OSA Optics InfoBase
We use the semiclassical limit of electromagnetic wave scattering theory to determine the properties of the exterior caustics of a diagonally incident plane wave scattered by an infinitely long homogeneous dielectric circular cylinder in both the near zone and the far zone. The transmission caustic has an exterior/interior cusp transition as the tilt angle of the incident beam is increased, and each of the rainbow caustics has a far-zone rainbow/exterior cusp transition and an exterior/interior cusp transition as the incident beam tilt angle is increased. We experimentally observe and analyze both transitions of the first-order rainbow. We also compare the predictions of the semiclassical approximation with those of ray theory and exact electromagnetic wave scattering theory.

Experimenting with Minnaert's Cigar
Jan O. Mattsson, Lars Bärring, Esben Almqvist
Applied Optics, Volume 39, Issue 21, 3604-3611 July 2000 OSA Optics InfoBase
We have studied the seldom-seen halo phenomenon that can arise in divergent light, Minnaert's Cigar, which we produced in laboratory experiments and computer simulation. In the laboratory experiments halos or transections were produced in clouds of alum crystals precipitated in a solution of ethyl alcohol or in alum crystals deposited upon glass plates. The three-dimensional cigar form was less pronounced in our small-scale experiments than when the form was observed over several meters. In our experiments and simulations transections through Minnaert's Cigar include different halo forms that may arise on window panes or windshields covered with halo-active ice crystals or as horizontal halos on glittering frost-covered ground.


Calculating Correlated Color Temperatures Across the Entire Gamut of Daylight and Skylight Chromaticities Free download
Javier Hernandez-Andres, Raymond L. Lee, Javier Romero
Applied Optics, Volume 38, Issue 27, 5703-5709 September 1999 OSA Optics InfoBase
Natural outdoor illumination daily undergoes large changes in its correlated color temperature (CCT), yet existing equations for calculating CCT from chromaticity coordinates span only part of this range. To improve both the gamut and accuracy of these CCT calculations, we use chromaticities calculated from our measurements of nearly 7000 daylight and skylight spectra to test an equation that accurately maps CIE 1931 chromaticities x and y into CCT. We extend the work of McCamy Color Res. Appl. 12, 285 287 (1992) by using a chromaticity epicenter for CCT and the inverse slope of the line that connects it to x and y . With two epicenters for different CCT ranges, our simple equation is accurate across wide chromaticity and CCT ranges (3000 - 106 K) spanned by daylight and skylight.

Unusual Pyramidal Ice in the Atmosphere as the Origin of Elliptical Halos
Mika Sillanp, Jarmo Moilanen, Marko Pekkola, Martti Penttinen, Jari Piikki
Applied Optics, Volume 38, Issue 24, 5089-5095 August 1999 OSA Optics InfoBase
The formation mechanism of elliptical halos and Bottlinger s rings has long remained uncertain. The current model for elliptical halos requires multiple scattering from two different populations of ice crystals in a complex mode of motion. New evidence indicates that elliptical halos, and possibly Bottlinger s rings, are due to refraction through ice crystals shaped like obtuse pyramids. This unusual ice crystal may not have been documented previously.

A General Setting for Halo Theory Free download
Walter Tape, Günther P. Können
Applied Optics, Volume 38, Issue 9, 1552-1625 March 1999 OSA Optics InfoBase
We describe a general framework for systematically treating halos that are due to refraction in preferentially oriented ice wedges, and we construct an atlas of such halos. Initially we are constrained neither by the interfacial angles nor the orientations of real ice crystals. Instead we consider all possible refraction halos. We therefore make no assumption regarding the wedge angle, and only a weak assumption regarding the allowable wedge orientations. The atlas is thus a very general collection of refraction halos that includes known halos as a small fraction. Each halo in the atlas is characterized by three parameters: the wedge angle, the zenith angle of the spin vector, and the spin vector expressed in the wedge frame. Together with the sun elevation, the three parameter values for a halo not only permit calculation of the halo shape, they also give much information about the halo without extensive calculation, so that often a crude estimate of the halo s appearance is possible merely from inspection of its parameters. As a result, the theory reveals order in what seems initially to be a staggering variety of halo shapes, and in particular it explains why halos look the way they do. Having constructed and studied the atlas, we then see where real or conceivable refraction halos, arising in specific crystal shapes and crystal orientations, fit into the atlas. Although our main goal is to understand halos arising in pyramidal crystals, the results also clarify and unify the classical halos arising in hexagonal prismatic crystals.

Ray theory analysis of the shadow blister effect Free download
James A. Lock
Applied Optics, Vol. 37, No. 9, pp. 1573-1578, 20 March 1998 OSA Optics InfoBase
When an extended light source such as the Sun illuminates two objects so that their shadows lie close to each other, the shadow of one of the objects occasionally appears to bulge out toward the shadow of the other. This effect is caused by the overlap of the penumbras of the shadows and is analyzed here with ray theory. A laboratory demonstration of this phenomenon is performed and compared with theoretical predictions.

How big should hexagonal ice crystals be to produce halos?
M. I. Mishchenko, A.Macke
Applied Optics Vol. 38, No. 9, pp. 1626 -1629 (20 March 1999) OSA Optics InfoBase
It has been hypothesized that the frequent lack of halos in observations of cirrus and contrails and laboratory measurements is caused by small ice crystal sizes that put the particles outside the geometrical optics domain of size parameters. We test this hypothesis by exploiting a strong similarity of ray tracing phase functions for finite hexagonal and circular ice cylinders and using T -matrix computations of electromagnetic scattering by circular cylinders with size parameters up to 180 in the visible. We conclude that well-defined halos should be observable for ice crystal size parameters of the order of 100 and larger and discuss remote-sensing implications of this result.


Sunset science. II. A useful diagram Free download
Andrew T. Young and George W. Kattawar
Applied Optics, Vol. 37, No. 18, pp. 3785-3792, (June 1998) OSA Optics InfoBase
We present diagrams that show how layers in atmospheric thermal structure are related to the altitudes at which they are seen tangentially. These dip diagrams show that the inferior mirage greatly magnifies the apparent angular size of the lowest few centimeters of atmosphere. Conversely, inversion layers below eye level are compressed—even to zero apparent thickness, in ducts. The diagrams show that, even when distant objects are miraged, the ray crossings occur beyond the lowest point on each ray where the line of sight is tangent to a horizontal surface in the atmosphere. Therefore the apparent altitudes of these tangent points are a monotonic function of their actual heights in the atmosphere. This monotonicity explains an apparent paradox in low-Sun images.

Feature issue: Applied Optics, March 1998

Light and color in the open air: introduction to the feature issue
Kenneth Sassen and W. Patrick Arnott
Applied Optics, Vol. 37, No. 9, pp. 1425 - 1426, 20 March 1998 OSA Optics InfoBase
The topical meeting on light and color in the open air was held 9–12 February 1997 in Santa Fe, New Mexico. The series of papers that follows represents the fruition of this meeting, revealing the range of current scientific explorations into the play of light and color in nature.

Can cirrus clouds produce glories?
Kenneth Sassen, W. Patrick Arnott, Jennifer M. Barnett, and Steve Aulenbach
Applied Optics, Vol. 37, No. 9, pp. 1427 - 1433, 20 March 1998 OSA Optics InfoBase
A vague glory display was photographed over central Utah from an airplane beginning its descent through a cirrus cloud layer with an estimated cloud top temperature of -45 and -55 °C. Photographic analysis reveals a single reddish-brown ring of 2.5–3.0° radius around the antisolar point, although a second ring appeared visually to have been present over the brief observation period. Mie and approximate nonspherical theory scattering simulations predict a population of particles with modal diameters between 9 and 15 µm. Although it is concluded that multiple-ringed glories can be accounted for only through the backscattering of light from particles that are strictly spherical in shape, the poor glory colorization in this case could imply the presence of slightly aspherical ice particles. The location of this display over mountainous terrain suggests that it was generated by an orographic wave cloud, which we speculate produced numerous frozen cloud droplets that only gradually took on crystalline characteristics during growth.

Halo arcs from airborne, pyramidal ice crystals falling with their c axes in vertical orientation
Marko Pekkola, Marko Riikonen, Jarmo Moilanen, and Jukka Ruoskanen
Applied Optics, Vol. 37, No. 9, pp. 1435 - 1440, 20 March 1998 OSA Optics InfoBase
Many halo arcs are caused by pyramidal crystals that have [1 0 - 1 1] crystal faces. We treat halo arcs arising from pyramidal crystals that fall in the air with their c axes vertically oriented. To our knowledge only 6 of the 12 possible halo phenomena that belong to this category have been dealt with in the literature. Surprisingly the yet undiscussed halos are predicted to be of comparable intensity with those already treated. They are produced by reflections from pyramidal crystal basal faces. A theoretical summary and computer simulations are presented of the mentioned 12 halo phenomena and of the individual arcs into which they break in the sky. We give an overview to the current level of documentation of these phenomena by listing the first published photographs of each phenomenon known to the authors.

Comparison of Sun pillars with light pillars from nearby light sources
A. James Mallmann, Jeffrey L. Hock, and Robert G. Greenler
Applied Optics, Vol. 37, No. 9, pp. 1441 - 1449, 20 March 1998 OSA Optics InfoBase
Using a Monte Carlo method, we simulate the appearance of light pillars produced by nearby light sources and compare their appearance with simulations of Sun pillars. Photographs of light pillars are also compared with the simulations. We expand the idea of light and Sun pillars by examining the reflected-light patterns from several different known distributions of airborne ice crystals. Polarization properties of light pillars from nearly horizontally oriented plate crystals are also simulated.

Identification of odd-radius halo arcs and of 44°/46° parhelia by their inner-edge polarization Free download
Günther P. Können
Applied Optics, Vol. 37, No. 9, pp. 1450 - 1456, 20 March 1998 OSA Optics InfoBase
Birefringence of ice causes the inner edges of refraction halos to be polarized. The direction of this polarization relates directly to the projection of the crystal main axis onto the sky. This implies that the inner-edge polarization can serve as an observational diagnostic for determining the actual nature of a halo arc if two competing explanations exist. The direction and the visibility of the inner-edge polarization of arcs and circular halos arising from usual ice crystals and from ice crystals with pyramidal ends are calculated. It is found that the observation of inner-edge polarization can be decisive for the identification of a spot that might be either a 44° parhelion or a 46° parhelion, of an arc that might be either a 22° sunvex Parry arc or a 20° Parroid arc arising from plate-oriented pyramidal crystals, and of an arc that might be either a 22° suncave Parry arc or a 23° Parroid arc from plate-oriented pyramidal crystals. (With a Parroid arc, a halo is that which arises from an ice wedge made up of two faces of a crystal that rotates about a vertically oriented spin axis, and the edge of the wedge is perpendicular to this spin axis.) Polarization properties of other rare arcs are discussed. Practical hints are given for observing visually the inner-edge polarization of halos.

Polarization structures in parhelic circles and in 120° parhelia Free download
Günther P. Können and Jaap Tinbergen
Applied Optics, Vol. 37, No. 9, pp. 1457 - 1464, 20 March 1998 OSA Optics InfoBase
Parhelic circles due to plate-oriented crystals ~hence, with main axes vertical! and 120° parhelia change in position when viewed through a rotating polarizer. The parhelic circle moves vertically; its largest shift is found at an azimuthal distance between 90° and 120° from the Sun. The 120° parhelia move both vertically and horizontally. The magnitudes of the shifts are between 0.1° and 0.3°, depending on solar elevation. The mechanism is polarization-sensitive internal reflection by prism faces of the ice crystals. We outline the theory and present three visual and one instrumental observation of the displacements of these halos in polarized light.

Digital imaging of clear-sky polarization Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 37, No. 9, pp. 1465 - 1476, 20 March 1998 OSA Optics InfoBase
If digital images of clear daytime or twilight skies are acquired through a linear polarizing filter, they can be combined to produce high-resolution maps of skylight polarization. Here polarization P and normalized Stokes parameter Q are measured near sunset at one inland and two coastal sites. Maps that include the principal plane consistently show that the familiar Arago and Babinet neutral points are part of broader areas in which skylight polarization is often indistinguishably different from zero. A simple multiple-scattering model helps explain some of these polarization patterns.

Corona-producing ice clouds: a case study of a cold mid-latitude cirrus layer
Kenneth Sassen, Gerald G. Mace, John Hallett, and Michael R. Poellot
Applied Optics, Vol. 37, No. 9, pp. 1477 - 1485, 20 March 1998 OSA Optics InfoBase
A high (14.0-km), cold (-71.0 °C) cirrus cloud was studied by ground-based polarization lidar and millimeter radar and aircraft probes on the night of 19 April 1994 from the Cloud and Radiation Testbed site in northern Oklahoma. A rare cirrus cloud lunar corona was generated by this 1–2-km-deep cloud, thus providing an opportunity to measure the composition in situ, which had previously been assumed only on the basis of lidar depolarization data and simple diffraction theory for spheres. In this case, corona ring analysis indicated an effective particle diameter of ~22 µm. A variety of in situ data corroborates the approximate ice-particle size derived from the passive retrieval method, especially near the cloud top, where impacted cloud samples show simple solid crystals. The homogeneous freezing of sulfuric acid droplets of stratospheric origin is assumed to be the dominant ice-particle nucleation mode acting in corona-producing cirrus clouds. It is speculated that this process results in a previously unrecognized mode of acid-contaminated ice-particle growth and that such small-particle cold cirrus clouds are potentially a radiatively distinct type of cloud.

Solar corona caused by juniper pollen in Texas
Forrest M. Mims III
Applied Optics, Vol. 37, No. 9, pp. 1486 - 1488, 20 March 1998 OSA Optics InfoBase
Coronas are colorful, concentric rings centered on a bright light such as the Sun, the Moon, or even a streetlamp. Coronas are most commonly caused by water droplets or ice particles of relatively uniform size. Observers in Finland have reported spectacular clear-sky coronas caused by pollen grains. A clear-sky corona in central Texas occurred during the peak of the juniper pollinating season. The aerosol optical thickness at each of three wavelengths was highest when the corona was most prominent. Photographic measurements of the corona infer a particle diameter of ~32.4 µm. Because juniper pollen grains have a diameter of from 22 to 30 µm, they are the aerosol most likely to have caused the corona.

Long-range superior mirages Free download
Waldemar H. Lehn and Thomas L. Legal
Applied Optics, Vol. 37, No. 9, pp. 1489 - 1494, 20 March 1998 OSA Optics InfoBase
Superior mirages of simple appearance are occasionally observed over distances exceeding 70 km. These mirages cannot be explained in terms of standard textbook models; rather, they are shown to arise from fairly complex atmospheres. Two observations of different types, observed at Resolute Bay, Canada, are presented. The first is the basic three-image mirage in which one inverted and one erect image float above the object. The second is a single-image mirage in which the object is elevated but undistorted. For each, the most suitable atmospheric model contains several distinct atmospheres, and the first one requires sloped atmospheric layers as well.

Simulation of inferior mirages observed at the Halligen Sea
Eberhard Tränkle
Applied Optics, Vol. 37, No. 9, pp. 1495 - 1505, 20 March 1998 OSA Optics InfoBase
Two unusual forms of inferior mirage are observed and photographed at the Halligen Sea. With heuristic analytic functions for the temperature profiles, numerical integration of the refraction differential equation on a flat earth is performed. The simulation shows that a double inferior mirage can appear if a light wind carries hot air from above dry sandbanks in the mud flats. Horizontal stripes can appear in the mirage image if a water channel crosses the line of sight between the observer and the object.

Mie theory, Airy theory, and the natural rainbow Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 37, No. 9, pp. 1506-1519, 20 March 1998 OSA Optics InfoBase
Compared with Mie scattering theory, Airy rainbow theory clearly miscalculates some monochromatic details of scattering by small water drops. Yet when monodisperse Airy theory is measured by perceptual (rather than purely physical) standards such as chromaticity and luminance contrast, it differs very little from Mie theory. Considering only the angular positions of luminance extrema, Airy theory’s errors are largest for small droplets such as those that dominate cloudbows and fogbows. However, integrating over a realistic drop-size distribution for these bows eliminates most perceptible color and luminance differences between the two theories.

Generalized tertiary rainbow of slightly oblate drops: observations with laser illumination
Dean S. Langley and Philip L. Marston
Applied Optics, Vol. 37, No. 9, pp. 1520-1526, 20 March 1998 OSA Optics InfoBase
The tertiary rainbow of acoustically levitated water drops was observed in the laboratory. Nontrivial caustics were observed for relatively small values of eccentricity. The angular locations of caustics were modeled with matrix methods of generalized ray tracing. Photographs of the scattering were in general agreement with models. Possible effects on the appearance of natural tertiary bow features are discussed.

Amplification of High-Order Rainbows of a Cylinder with an Elliptical Cross Section Free download
James A. Lock, Charles L. Adler, Bradley R. Stone, Patrick D. Zajak
Applied Optics, Volume 37, Issue 9, 1527-1533 March 1998 OSA Optics InfoBase
The intensity of high-order rainbows for normally incident light and certain rotation angles of a cylinder with an elliptical cross section is greatly amplified with respect to the intensity for a circular cross-sectional cylinder. The amplification is due to a number of the internal reflections occurring past the critical angle for total internal reflection, and the effect is especially strong for odd-order rainbows, beginning with the third order. Experimentally, the fourth- and the fifth-order rainbows of a nearly elliptical cross-sectional glass rod were observed and analyzed.

Scattering observations for tilted transparent fibers: evolution of Airy caustics with cylinder tilt and the caustic merging transition
Catherine M. Mount, David B. Thiessen, and Philip L. Marston
Applied Optics, Vol. 37, No. 9, pp. 1534-1539, 20 March 1998 OSA Optics InfoBase
When a dielectric circular cylinder is obliquely illuminated, the scattering angle associated with the Airy caustics of the cylinder’s primary rainbow depends on the tilt of the cylinder. We display records of the scattering pattern for a transparent poly (methyl methacrylate) fiber ranging from small values of tilt through values of tilt that are sufficiently large for the Airy caustics from both sides of the fiber to merge in a meridional plane containing the incident wave vector and the fiber’s axis. The records are compared directly with the evolution of the caustic projected onto the observation plane, and certain qualitative features of the global evolution of the caustics are confirmed. Although the observations used laser illumination, they are relevant to anticipating the scattering by sunlit transparent tilted cylinders.

Rainbow scattering by a cylinder with a nearly elliptical cross section Free download
Charles L. Adler, James A. Lock, and Bradley R. Stone
Applied Optics, Vol. 37, No. 9, pp. 1540-1550, 20 March 1998 OSA Optics InfoBase
We both theoretically and experimentally examine the behavior of the first- and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotated about its major axis. We decompose the measured rainbow angle, taken as a function of the rod’s rotation angle, into a Fourier series and find that the rod’s refractive index, average ellipticity, and deviation from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glass rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with direct measurements, but that the rod’s diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly larger than that obtained by direct measurement. We also determine the conditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the second-order rainbow to be observed in a rain shower.

Descartes glare points in scattering by icicles: color photographs and a tilted dielectric cylinder model of caustic and glare-point evolution
Philip L. Marston
Applied Optics, Vol. 37, No. 9, pp. 1551-1556, 20 March 1998 OSA Optics InfoBase
Glare points associated with the Airy caustics of once and twice internally reflected rays are visible in the scattering by sunlit icicles. Supporting color photographs include an image of the far-field scattering. Relevant rays are analogous to the Descartes rays of primary and secondary rainbows of drops; however, the caustic conditions for the icicle are predicted to be affected by tilt of the illumination relative to the axis of the icicle. A model for the caustic evolution, given for a circular dielectric cylinder, manifests a transition in which the Airy caustic (and associated glare points) merge in the meridional plane at a critical tilt. At this critical tilt the merged glare point is predicted to be very bright. The calculations use the Bravais effective refractive index and generalized ray tracing.

Laboratory experiments in atmospheric optics
Michael Vollmer and Robert Tammer
Applied Optics, Vol. 37, No. 9, pp. 1557-1568,20 March 1998 OSA Optics InfoBase
Old and new laboratory experiments on atmospheric optics with a focus on mirages, rainbows, and halos are presented. Some qualitative demonstrations serve primarily didactical purposes, e.g., by proving the existence of curved light rays in media with a gradient of the index of refraction, by directly visualizing the minimum-deviation curve for rainbow paths in water droplets, or by helping to elucidate the ray classes in hexagons that contribute to a specific halo. In addition, quantitative experiments allow a direct comparison of angular positions and intensities with analytical computations or simulations of light scattering from small water droplets or ice hexagons. In particular, the latter can help us to understand complex halo phenomena.

Observations of glistening in the environment and its relationship to stereovision
Harry E. Bates and Grant Warner
Applied Optics, Vol. 37, No. 9, pp. 1569-1572, 20 March 1998 OSA Optics InfoBase
The relationship between glistening and stereovision is explored. Glistening is defined as the existence of points of light in the field of view of the observer that are observed substantially in only one eye. We define each glistening point to be essentially a point of stereonoise. A theory of the probability of glistening is developed and shows that a threshold point for 100% glistening should exist. The results of field experiments are presented.

Effects of a butterfly scale microstructure on the iridescent color observed at different angles
Haruna Tada, Seth E. Mann, Ioannis N. Miaoulis, and Peter Y. Wong
Applied Optics, Vol. 37, No. 9, pp. 1579-1584, 20 March 1998 OSA Optics InfoBase
Multilayer thin-film structures in butterfly wing scales produce a colorful iridescence from reflected sunlight. Because of optical phenomena, changes in the angle of incidence of light and the viewing angle of an observer result in shifts in the color of butterfly wings. Colors ranging from green to purple, which are due to nonplanar specular reflection, can be observed on Papilio blumei iridescent scales. This refers to a phenomenon in which the curved surface patterns in the thin-film structure cause the specular component of the reflected light to be directed at various angles while affecting the spectral reflectivity at the same time by changing the optical path length through the structure. We determined the spectral reflectivities of P. blumei iridescent scales numerically by using models of a butterfly scale microstructure and experimentally by using a microscale-reflectance spectrometer. The numerical models accurately predict the shifts in spectral reflectivity observed experimentally.

Thirty years of observing and documenting sky optical phenomena
Peter-Paul Hattinga Verschure
Applied Optics, Vol. 37, No. 9, pp. 1585-1588, 20 March 1998 OSA Optics InfoBase
A homogeneous series of systematic observations of sky optical phenomena in the Netherlands has been gathered by the Dutch Observing Network since 1965. This continues the Dutch observation series that started at the end of the nineteenth century. A time series of ice-crystal halo frequencies from 1920 to 1996 and frequency diagrams of some specific halos the period from 1970 to 1996 are shown and discussed. Systematic observation recording by means of diaries and exchanging routines among observers are described. Methods are given for establishing and maintaining a network of volunteers that can provide, in a homogeneous time series, sky optical phenomena recordings.


Analysis of an infrared mirage sequence Free download
Waldemar H. Lehn
Applied Optics, Volume 36, Issue 21, p. 5217 (July 1997) OSA Optics InfoBase
Infrared observations of seaborne thermal sources are subject to the effects of atmospheric refraction. For low elevation angles at long ranges, out to the limit of visibility, the inevitable atmospheric temperature gradients frequently produce mirages. I present an analysis of a 22-min sequence of images recorded on 18 February 1994 at the U.S. Naval Surface Warfare Center at Wallops Island, Virginia. The infrared target is a heat source carried on a ship moving in a straight line toward the camera. The images show a quasi-periodic variation of the horizon elevation, as well as an extended range of visibility. A model that reasonably reproduces the observed features consists of a small temperature inversion in a slightly sloped atmosphere, with an atmospheric gravity wave moving across the line of sight.

Optical properties of contrail-induced cirrus: discussion of unusual halo phenomena
Ralf Sussmann
Applied Optics Volume 36, No. 18, pp. 4195-4201 (June 1997) OSA Optics InfoBase
Photographs of a 120° parhelion and a 22° parhelion within persistent contrails are presented. These phenomena result from hexagonal plate-shaped ice crystals oriented horizontally with diameters between 300 μm and 2 mm. From our observations and reinvestigation of previous reports, we conclude that a subset of the population in persistent contrails can consist of highly regular, oriented, hexagonal plates or columns comparable to the most regular crystals in natural cirrus clouds. This is explained by measured ambient humidities below the formation conditions of natural cirrus. The resulting strong azimuthal variability of the scattering phase function impacts the radiative transfer through persistent contrails.

Origin of Kern’s arc
Yoshihide Takano and Kuo-Nan Liou
Applied Optics, Volume 36, Issue 15, p. 3560 (May 1997) OSA Optics InfoBase
With the aid of computer-simulated halo patterns, we show that Kern’s arc, as seen on the latitude of the circumzenithal arc and on the other side of the zenith, is produced by double-plate ice crystals with a vertical principal axis. Light rays that contribute to Kern’s arc are demonstrated by geometric ray tracing. We also discuss the condition under which an arc that is opposite a circumhorizontal arc can appear.

Sunset science: 1. The mock mirage
Andrew T. Young, George W. Kattawar, and Pekka Parviainen
Applied Optics, Volume 36, Issue 12, p. 2689 (April 1997) OSA Optics InfoBase
A previously unrecognized phenomenon, which we call the mock mirage, produces inverted images of the Sun and Moon near the horizon when the observer looks downward through a thermal inversion. No ducting is involved; the rays can be concave toward the Earth throughout their length, with a radius of curvature larger than the radius of the Earth. Quite mild inversions produce surprisingly large effects, which increase with the height of the observer. Although the phenomenon has frequently been photographed, published pictures have been misinterpreted. Finally, we distinguish between features that are due to waves on inversion layers and the larger features that are due to the inversions themselves.


Elliptical halos, Bottlinger's rings, and the ice-plate snow-star transition
Eberhard Tränkle, Marko Riikonen
Applied Optics, Volume 35, Issue 24, p. 4871-4878, August 1996 OSA Optics InfoBase
Elliptical halos and Bottlinger's rings are simulated by the use of a Monte Carlo algorithm that includes multiple scattering. High multiple reflections are required to obtain a sufficient brightness of the elliptical halos. By introducing three populations of nearly horizontal, gyrating, and swinging crystals, we obtain good agreement for four photographs of displays with ringlike and disklike structures. Through model experiments on the aerodynamical behavior of crystals, we find a new interpretation of the three populations. In this view elliptical halos and Bottlinger's rings occur in the transition region of ice plates with broad branches and stellar crystals at temperatures near 15 C and large supersaturations. This interpretation is supported by a review of 23 reports of elliptical halo phenomena by members of the Finnish Halo Observers Network.

Ray scattering by an arbitrarily oriented spheroid: 1. Diffraction and specular reflection Free download
James A. Lock
Applied Optics, Vol. 35 Issue 3 Page 500 (January 1996) OSA Optics InfoBase
Diffraction and reflection of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit are considered in the context of ray theory. A closed-form solution for both diffraction and reflection is obtained, and the polarization character of the diffracted plus reflected electric field is obtained. It is found that the magnitude of the reflected electric field is multivalued for forward scattering. This is interpreted in terms of the variation of the spheroid’s Gaussian curvature at the points where grazing ray incidence occurs.

Ray scattering by an arbitrarily oriented spheroid. 2. Transmission and cross-polarization effects Free download
James A. Lock
Applied Optics, Vol. 35 Issue 3 Page 515 (January 1996) OSA Optics InfoBase
Transmission of an arbitrarily polarized plane wave by an arbitrarily oriented spheroid in the short-wavelength limit is considered in the context of ray theory. The transmitted electric field is added to the diffracted plus reflected ray-theory electric field that was previously derived to obtain an approximation to the far-zone scattered intensity in the forward hemisphere. Two different types of cross-polarization effects are found. These are (a) a rotation of the polarization state of the transmitted rays from when they are referenced with respect to their entrance into the spheroid to when they are referenced with respect to their exit from it and (b) a rotation of the polarization state of the transmitted rays when they are referenced with respect to the polarization state of the diffracted plus reflected rays.


Feature issue: Applied Optics, July 1994

Light and color in the open air -- introduction by the feature editors Free download
James A. Lock and Craig F. Bohren
Applied Optics, Vol. 33 Issue 21 Page 4535 (July 1994) OSA Optics InfoBase
The natural environment is still rich in new observable phenomena despite centuries of scientific observation. Reflecting this fact, the papers in this feature issue of Applied Optics report the observation and analysis of both new and well-known naked-eye optical phenomena.

Observations of vertically elliptical halos
Marko Riikonen, Jukka Ruoskanen
Applied Optics, Vol. 33 Issue 21 Page 4537 (July 1994) OSA Optics InfoBase
The Finnish Amateur Astronomers' Network, working under the Ursa Astronomical Association, has photographed several vertically elliptical halo displays. Four of these observations with photographs are presented.

The sylvanshine: retroreflection from dew-covered trees
Alistair B. Fraser
Applied Optics, Vol. 33 Issue 21 Page 4539 (July 1994) OSA Optics InfoBase
Some dew-covered plants are strongly retroreflective. The bright glow seen when the antisolar point falls on grass is known as the heiligenschein. Its widely accepted explanation requires that the grass be covered with hair. The discovery of the sylvanshine, a closely related phenomenon best seen at night, revealed that strong retroreflection can occur on hairless dew-covered plants. A simple model shows that below a contact angle of 90°, the enhancement in the backscatter direction is virtually identical to that given by a diffusely reflecting surface, but as the contact angle climbs to 140°, enhancement increases by 2 orders of magnitude. Plants that exhibit such large contact angles are not the norm, but can be found chiefly among coniferous trees, a few of which display the sylvanshine with great brilliance.

Vertical elliptical coronas caused by pollen
Pekka Parviainen, Craig F. Bohren, Veikko Makela
Applied Optics, Vol. 33 Issue 21 Page 4548 (July 1994) OSA Optics InfoBase
Near-forward scattering by cloud droplets is known to give rise to colored rings, centered on the Sun or the Moon, which are called the corona. Because of the spherical shape of the droplets, the corona can be circular. A Finnish amateur astronomers' network has found a corona, in a seemingly cloudless sky, with a regular vertically elliptical shape. The aspect ratio of these ellipses changes with the altitude of the Sun or the Moon. Some brightening in the coronas has also been reported. Because of observations of high pollen concentrations at the time of occurrence of these coronas, we propose that some coronas can be explained as a result of scattering by birch pollen grains, which are more or less spheroidal. To explain other observed coronas, pollen grains with more complicated shapes, such as pine and spruce pollen grains, must be invoked. Our analysis is limited to spheroidal grains, for which the Fraunhofer theory gives analytical expressions of simple form. The more complicated shapes require numerical simulations or laboratory experiments, which we have not done.

Simulation and analysis of pollen coronas
Eberhard Trankle, Bernd Mielke
Applied Optics, Vol. 33 Issue 21 Page 4552 (July 1994) OSA Optics InfoBase
By numerical simulation of light scattering by birch and pine pollen grains, we create color plates of coronas with vertical elliptical shapes and strong brightenings, respectively. The shape of the pollen is modeled by the union of n ellipsoids. The Fraunhofer integral is solved by the use of the fast Hartley transform. The sensitivity of the patterns to pollen orientation, Sun elevation, and pollen shape and size is discussed. Good agreement is obtained with amazing photographs made by a Finnish network of amateur astonomers, in the case of strong vertical orientation of the pollen axis.

Supernumerary ice-crystal halos? Free download
Michael V. Berry
Applied Optics, Vol. 33 Issue 21 Page 4563 (July 1994) OSA Optics InfoBase
Geometric-optics singularities in the intensity profiles of refraction halos formed by randomly oriented ice crystals are softened by diffraction and decorated with fine supernumerary fringes. If the crystals have a fixed symmetry axis (as in parhelia), the geometric singularity is a square-root divergence, as in the rainbow. However, the universal curve that describes diffraction is different from the rainbow's Airy function, with weak maxima (supernumerary fringes) on the geometrically dark region inside the halo (and even fainter fringes outside); these are much smaller than their counterparts on the light side of rainbows. If the crystals have no preferred orientation (as in the 22° halo), the geometric singularity is a step. In this case the universal diffraction function has no maxima, and its supernumeraries are shoulders rather than maxima. The low contrast of the fringes is probably the main reason why supernumerary halos are rarely if ever seen.

Halo polarization profiles and the interfacial angles of ice crystals Free download
G. P. Können , Sara H. Muller, J. Tinbergen
Applied Optics, Vol. 33 Issue 21 Page 4569 (July 1994) OSA Optics InfoBase
Polarization and radiance of various types of refraction halo in ice-crystal swarms that extend to ground level were measured as a function of scattering angle. Simultaneously, samples of the crystals that produce these halos were collected and replicated. The halo polarization peaks are wider than the Fraunhofer theory of diffraction predicts for the observed size distribution of the replicated crystals. The explanation we put forward is that the angles between crystal prism faces are not always exact integer multiples of 60°, and the basal faces are not always exactly parallel, as is usually assumed. The collected crystals confirm this. The widths of the halo polarization peaks can be explained if the distributions of the interfacial angles around their means reach their half-maximum values at a deviation of 0.49° ± 0.05°. This corresponds to a deviation of 0.35° ± 0.03° of the face normals from their crystallographic positions. The presence of variation in interfacial angles in low-level halos seems to arise from the fact that the crystals are growing. Some hitherto unexplained features in halo displays can be understood by considering variations in the interfacial angles.

Subsuns, Bottlinger's rings, and elliptical halos Free download
David K. Lynch, Stanley D. Gedzelman, Alistair B. Fraser
Applied Optics, Vol. 33 Issue 21 Page 4580 (July 1994) OSA Optics InfoBase
Subsuns, Bottlinger's rings, and elliptical halos are simulated by the use of a Monte Carlo model; reflection of sunlight from almost horizontal ice crystals is assumed. Subsuns are circular or elliptical spots seen at the specular reflection point when one flies over cirrus or cirrostratus clouds. Bottlinger's rings are rare, almost elliptical rings centered about the subsun. Elliptical halos are small rings of light centered around the Sun or the Moon that rarely occur with other halo phenomena. Subsuns and Bottlinger's rings can be explained by reflection from a single crystal, whereas elliptical halos require reflection from two separate crystals. All three phenomena are colorless and vertically elongated with an eccentricity that increases with increasing solar zenith angle. For several cases of Bottlinger's rings the simulations are compared with density scans of photographs. Clouds that consist of large swinging or gyrating plates and dendritic crystals, which form near -15 °C, seem the most likely candidates to produce the rings and elliptical halos. Meteorological evidence is presented that supports these conditions for elliptical halos. Simulations suggest that the most distinct elliptical halos may be produced by hybrid clouds that contain both horizontal and gyrating crystals.

Effects of ice-crystal structure on halo formation: cirrus cloud experimental and ray-tracing modeling studies
Kenneth Sassen, Nancy C. Knight, Yoshihide Takano, Andrew J. Heymsfield
Applied Optics, Vol. 33 Issue 21 Page 4590 (July 1994) OSA Optics InfoBase
During the 1986 Project FIRE (First International Satellite Cloud Climatology Project Regional Experiment) field campaign, four 220 halo-producing cirrus clouds were studied jointly from a groundbased polarization lidar and an instrumented aircraft. The lidar data show the vertical cloud structure and the relative position of the aircraft, which collected a total of 84 slides by impaction, preserving the ice crystals for later microscopic examination. Although many particles were too fragile to survive impaction intact, a large fraction of the identifiable crystals were columns and radial bullet rosettes, with both displaying internal cavitations, and radial plate-column combinations. Particles that were solid or displayed only a slight amount of internal structure were relatively rare, which shows that the usual model postulated by halo theorists, i.e., the randomly oriented, solid hexagonal crystal, is inappropriate for typical cirrus clouds. With the aid of new ray-tracing simulations for hexagonal hollow-ended column and bullet-rosette models, we evaluate the effects of more realistic ice-crystal structures on halo formation and lidar depolarization and consider why the common halo is not more common in cirrus clouds.

Volcanic Bishop's ring: evidence for a sulfuric acid tetrahydrate particle aureole
Kenneth Sassen, Thomas Peter, Beiping P. Luo, Paul J. Crutzen
Applied Optics, Vol. 33 Issue 21 Page 4602 (July 1994) OSA Optics InfoBase
Following the massive 1883 Krakatoa volcanic eruption, a new atmospheric optical phenomeon was identified by Rev. S. E. Bishop. This inconspicuous one-ringed corona, or aureole, was immediately linked to the global spread of volcanic debris injected into the stratosphere, but little refinement in the mechanisms responsible for Bishop's ring has since been made. On the basis of our combined studies of sulfuric acid droplet-freezing theory and polarization (0.694 μm) lidar measurements of Bishop's ring aerosols from the June 1991 Mt. Pinatubo eruption that show average linear depolarization ratios of 0.05, it appears that this solar diffraction phenomenon is caused by accumulations of nonspherical sulfuric acid tetrahydrate (SAT) particles. The diffraction-theory aureole-derived SAT particle radius of about 0.8 μm is consistent with the freezing of the large mode of volcanic acid droplets created by coagulation, which, according to theory, is necessary for concentrating a sufficient insoluble mass to promote heterogeneous drop freezing at temperatures below approximately -65 °C.

Simulating rainbows and halos in color
Stanley David Gedzelman
Applied Optics, Vol. 33 Issue 21 Page 4607 (July 1994) OSA Optics InfoBase
Geometric optics rainbows and ice-crystal halos that include some effects of a Rayleigh-scattering atmosphere and a cloud of finite optical thickness are simulated in color by the use of a Monte Carlo approach.

Influence of a solar eclipse on twilight
Edward H. Geyer, M. Hoffmann, H. Volland
Applied Optics, Vol. 33 Issue 21 Page 4614 (July 1994) OSA Optics InfoBase
The morning twilight of the pre-sunrise sky was measured at the Hoher-List Observatory during the total eclipse of 22 July 1990. The location of observation was far away from the central eclipse zone. The luminance showed a deep minimum in twilight during the main phase of the solar eclipse compared with normal conditions. A first order scattering model explains the observations reasonably well and shows that the sky radiation during the first phase of twilight at a location far away from the central umbra depends primarily on the height profile of the air pressure between 100 and 200 km.

Horizon brightness revisited: measurements and a model of clear-sky radiances Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 33 Issue 21 Page 4620 (July 1994) OSA Optics InfoBase
Clear daytime skies persistently display a subtle local maximum of radiance near the astronomical horizon. Spectroradiometry and digital image analysis confirm this maximum's reality, and they show that its angular width and elevation vary with solar elevation, azimuth relative to the Sun, and aerosol optical depth. Many existing models of atmospheric scattering do not generate this near-horizon radiance maximum, but a simple second-order scattering model does, and it reproduces many of the maximum's details.

Twilight and daytime colors of the clear sky Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 33 Issue 21 Page 4629 (July 1994) OSA Optics InfoBase
Digital image analysis of the cloudless sky's daytime and twilight chromaticities challenges some existing ideas about sky colors. First, although the observed colors of the clear daytime sky do lie near the blackbody locus, their meridional chromaticity curves may resemble it very little. Second, analyses of twilight colors show that their meridional chromaticity curves vary greatly, with some surprising consequences for their calorimetric gamuts.

Mirages with atmospheric gravity waves Free download
Waldemar H. Lehn, Wayne K. Silvester, David M. Fraser
Applied Optics, Vol. 33 Issue 21 Page 4639 (July 1994) OSA Optics InfoBase
The temperature inversions that produce superior mirages are capable of supporting gravity (buoyancy) waves of very low frequency and long wavelength. This paper describes the optics of single mode gravity waves that propagate in a four-layer atmosphere. Images calculated by ray tracing show that (1) relatively short waves add a fine structure to the basic static mirage, and (2) long waves produce cyclic images, similar to those observed in the field, that display significant variation from a base image.

Moving through a mirage
Peter D. Sozou, George Loizou
Applied Optics, Vol. 33 Issue 21 Page 4644 (July 1994) OSA Optics InfoBase
We consider image motion in the visual field of an observer moving through a rigid environment under mirage conditions, in which light rays follow curved trajectories as a result of a non-uniform atmospheric refractive index. We show that, under these conditions, the translation motion field does not conform to the simple pattern observed in the absence of refraction; instead it depends on the transfer characteristic of the mirage. An interesting finding is that if the mirage has a transfer characteristic that folds, as occurs for example in the desert mirage, the motion field will, in general, be infinite at the fold point.

Glory of clouds in the near infrared
James D. Spinhirne, Teruyuki Nakajima
Applied Optics, Vol. 33 Issue 21 Page 4652 (July 1994) OSA Optics InfoBase
Spectrally resolved visible and infrared images of marine stratus clouds were acquired from the NASA ER-2 high-altitude aircraft during the 1987 First International Cloud Climatology Program Regional Experiment. The images were obtained by cross-track scanning radiometers. Data images at near-infrared wavelengths show frequent and readily apparent brightness features that are due to glory single scattering. The observations and subsequent analysis by radiative transfer calculations show that the glory is a significant feature of near-infrared solar reflectance from water clouds. Glory observations and calculations based on in-cloud microphysics measurements agree well. The most dramatic difference from the visible glory is that the scattering angles are significantly larger in the near infrared. The glory is also apparently more distinct in the near infrared than in the visible, as scattering size parameters are in a range that effectively produces a glory feature, and also there is less obscuration by multiple scattering reflectance because of absorption of radiation by droplets in the near infrared. For both the visible and the near infrared, the principal factors that wash out the glory are dispersion and, to a lesser degree, the effective radius of the cloud droplet-size distribution. The obscuration by multiple scattering in optically thick clouds is secondary. Rather than being a novelty, glory observations would be an accurate and unambiguous technique to sense the droplet size of water clouds remotely.

Correlated light scattering by a dense distribution of condensation droplets on a window pane Free download
James A. Lock, Chin-Lien Chiu
Applied Optics, Vol. 33 Issue 21 Page 4663 (July 1994) OSA Optics InfoBase
An analytical model of the scattering structure factor for an assembly of non-interacting hard disks has recently appeared in the literature [Phys. Rev. A 42, 5978-5989 (1990)]. We employ this model to calculate correlated light scattering by monodispersions and binary mixtures of condensation droplets on a window pane. We find that an area fraction of f ≥ 0.6 is required for producing the near-forward direction scattering suppression and that a moderately wide polydispersion of droplet sizes is capable of producing the experimentally observed bright ring of colored light.

Rainbow-enhanced forward glory from fused-silica spheres
John J. D'Amico, Marcus D. Knudson, Dean S. Langley
Applied Optics, Vol. 33 Issue 21 Page 4672 (July 1994) OSA Optics InfoBase
A tertiary rainbow enhances the forward glory scattering from a fused-silica sphere because of its refractive index m 1.465. The scattered light contains a strong cross-polarized component and varies rapidly in brightness with changes in m. In experiments m is varied by the use of a range of argon and dye laser wavelengths. The forward cross-polarized scattering is found to be in agreement with Mie theory calculations. A reflective coating on small areas around the equator and polar caps of the sphere increases the forward scattering by a factor of 180.

Rainbow scattering by a coated sphere Free download
James A. Lock, J. Michael Jamison, Chih-Yang Lin
Applied Optics, Vol. 33 Issue 21 Page 4677 (July 1994) OSA Optics InfoBase
We examine the behavior of the first-order rainbow for a coated sphere by using both ray theory and Aden-Kerker wave theory as the radius of the core α12 and the thickness of the coating δ are varied. As the ratio δ/α12 increases from 10-4 to 0.33, we find three classes of rainbow phenomena that cannot occur for a homogeneous-sphere rainbow. For δ/α12 < 10-3, the rainbow intensity is an oscillatory function of the coating thickness; for δ/α12 ≈ 10-2, the first-order rainbow breaks into a pair of twin rainbows; and for δ/α12 ≈ 0.33, various rainbow-extinction transitions occur. Each of these effects is analyzed, and their physical interpretations are given. A Debye series decomposition of coated-sphere partial-wave scattering amplitudes is also performed and aids in the analysis.

E6 diffraction catastrophe of the primary rainbow of oblate water drops: observations with white-light and laser illumination
Gregory Kaduchak, Philip L. Marston, Harry J. Simpson
Applied Optics, Vol. 33 Issue 21 Page 4691 (July 1994) OSA Optics InfoBase
Oblate drops of water illuminated perpendicular to their symmetry axis exhibit catastrophe patterns near the primary-rainbow scattering angle. Previous patterns include the hyperbolic umbilic focal section and separate lips events [see, e.g., H. J. Simpson and P. L. Marston, Applied Optics 30, 3468 (1991)]. The present observations concern a much higher-order singularity analyzed by J. F. Nye [Proc. R. Soc. London Ser. A 438, 397 (1992)], the E6 or symbolic umbilic, in the scattering by levitated drops with monochromatic and collimated white-light illumination. Photographs show the colors produced when the drop is illuminated by white light. The E6 occurs when the Gaussian curvature of the scattered wave front vanishes in both principal directions, resulting in a high degree of directional focusing. This type of focusing, although only slightly explored, is applicable to the more general problem of scattering from penetrable spheroids.

Hyperbolic umbilic and E6 diffraction catastrophes associated with the secondary rainbow of oblate water drops: observations with laser illumination
Gregory Kaduchak, Philip L. Marston
Applied Optics, Vol. 33 Issue 21 Page 4697 (July 1994) OSA Optics InfoBase
Previous observations of oblate drops of water illuminated perpendicular to their axis of symmetry exhibit catastrophe patterns near the primary-rainbow scattering angle [see, e.g., Applied Optics 30, 3468 (1991). The present research concerns observation of diffraction catastrophes near the secondary-rainbow scattering angle under similar experimental conditions. Illumination with laser light exhibits similar caustic structures in the secondary rainbow including the hyperbolic umbilic focal section and the E6 or symbolic umbilic focal section. The range of drop aspect ratios explored includes aspect ratios as small as those found for freely falling drops in air as well as highly flattened drops. The new features of the secondary rainbow occur for highly flattened drops.

Generalized rainbows and unfolded glories of oblate drops: organization for multiple internal reflections and extension of cusps into Alexander's dark band
Philip L. Marston, Gregory Kaduchak
Applied Optics, Vol. 33 Issue 21 Page 4702 (July 1994) OSA Optics InfoBase
Oblate drops of water can produce caustics where, unlike a simple Airy caustic, more than two rays merge. We extend previous treatments of generalized primary rainbows based on catastrophe optics [Opt. Lett. 10, 588 (1985); Proc. R. Soc. (London) A 438, 397 (1992)] to rays having (p - 1) = 2 to 5 internal reflections. The analysis is for a horizontally illuminated ellipsoid with a vertical symmetry axis. Aspect ratios causing a vanishing of the vertical curvature at the equator for the outgoing wave front are found from generalized ray tracing. In response to infinitesimal deformation, the axial caustic of real glory rays unfolds producing cusps. Laboratory observations with laser illumination demonstrate that cusps resulting from rays with five internal reflections extend into Alexander's dark band when the drop's aspect ratio is near 1.08. The evolution of this p = 6 scattering pattern as cusps meet the quinary rainbow is suggestive of an E6 catastrophe. For ellipsoids of varying aspect ratio and refractive index N, there is an organizing singularity associated with an exceptionally flat outgoing wave front from spheres with N = p.

Black-and-white fringes and the colors of caustics Free download
Michael V. Berry, A. N. Wilson
Applied Optics, Vol. 33 Issue 21 Page 4714 (July 1994) OSA Optics InfoBase
Fine-scale interference fringes that decorate caustics produced with white light appear black and white with high contrast. This is surprising, as the elementary expectation, supported by theory and computer simulation, is that the fringes should be highly colored. The fringe separation is several arc minutes and therefore close to the resolution limit of the eye. Under magnification (even of a photograph), the colors are revealed. Therefore black-and-white fringes are an illusion, giving a dramatic naked-eye illustration of the fact that the angular resolution of the visual system is better for luminance than for color.

Blue shadows: physical, physiological, and psychological causes
Michael E. Churma
Applied Optics, Vol. 33 Issue 21 Page 4719 (July 1994) OSA Optics InfoBase
The apparent blueness of outdoor shadows has two main causes: the illumination of the shadows by blue skylight and the enhancement of the perception of blue by simultaneous color contrast. Other physiological mechanisms, such as brightness contrast and afterimages, can also affect the perception of a shadow's blueness. Preferential scattering by the cornea does not seem to make a major contribution. Despite these effects, color constancy causes most people to observe an empirically blue shadow as colorless.

Mach bands and airplane shadows cast on dry terrain
J. T. Enright
Applied Optics, Vol. 33 Issue 21 Page 4723 (July 1994) OSA Optics InfoBase
Luminous rings are often seen surrounding the shadow of a high-flying airplane. Some of these phenomena are due to water droplets (glories, the Heiligenschein), but a different sort of explanation is required when a luminous ring (sometimes simply a bright spot) is seen while the plane is flying over dry terrain. Demonstrations involving distances and shadows manyfold smaller than those of an airliner's shadow show that Mach bands can produce illusory luminance phenomena that greatly resemble those associated with a plane's shadow over dry terrain. Luminance rings have recently also been observed over dry, sparsely vegetated terrain, around the shadow of an adjacent airplane (i.e., far from the observer's antisolar point), thereby excluding all previous alternative interpretations; Mach bands are thus a likely explanation for at least some instances of dry-terrain luminous rings around airplane shadows.

Colors of the spectrum: Do you wonder where the yellow went?
John N. Kidder
Applied Optics, Vol. 33 Issue 21 Page 4727 (July 1994) OSA Optics InfoBase
The spectrum of white light dispersed by a prism or grating often appears as just three main colored bands, red, green, and blue, with yellow barely discernible. When this spectrum is compared with the appearance of narrow wavelength bands seen in isolation, the lack of color is surprising. An explanation is offered based on two factors: (1) The yellow-appearing wavelengths of the spectrum comprise only 5% of the whole and have a luminance comparable with that of the adjacent red and green portions and (2) the response of double-opponent cells, observed in the primate visual cortex, could enhance the red and green and obscure the yellow in the spectral image.

Appearance of the Sun and the Moon seen through clouds
Jeffery R. Linskens, Craig F. Bohren
Applied Optics, Vol. 33 Issue 21 Page 4733 (July 1994) OSA Optics InfoBase
If the Sun can be seen at all through thin clouds it usually has a sharp edge, although occasionally it appears fuzzy, especially through altostratus, but rarely, if ever, through fog. Experiments with suspensions of polystyrene spheres of different sizes and optical thicknesses suggest that the range of cloud optical thicknesses over which a fuzzy Sun is seen increases with particle size. Nonsphericity, turbulence, and cloud horizontal inhomogeneity are not necessary for fuzziness. A possible explanation for what is observed is that, for a given optical thickness, the modulation contrast function of a cloud decreases more rapidly with increasing frequency the greater the particle size. Consequently the transition from optical thicknesses for which contrast is above the contrast threshold at all spatial frequencies to optical thicknesses for which contrast is below the threshold at high frequencies is sufficiently gradual to permit fuzziness of the Sun to be observed through clouds of constantly changing optical thickness.

Color recognition and discrimination under full-moon light
George Smith, Algis J. Vingrys, Jennifer D. Maddocks, Christopher P. Hely
Applied Optics, Vol. 33 Issue 21 Page 4741 (July 1994) OSA Optics InfoBase
The ability to recognize and discriminate colors under full-moon light was measured. Color naming was performed at three sizes (0.5°, 20° and 40°) by the use of one white and six colored chips that spanned the spectrum at two levels of saturation. The results show that correct color recognition is possible under full-moon light. However, the recognition rate depends on a complex interaction between hue, level of saturation, and size of test field. For small fields and desaturated colors, the recognition rate is low. However, for saturated colors, most hues can be recognized at better than chance levels, with red being recognized very accurately.

Intraocular light scattering in vision, artistic painting and photography
Claes Beckman, Olle Nilsson, Lars-Erik Paulsson
Applied Optics, Vol. 33 Issue 21 Page 4749 (July 1994) OSA Optics InfoBase
Light scattering in the eye is reviewed, and its influence on vision is discussed in some detail. Isotropic scattering and formation of halos around point sources are described with reference to theory and experiments. Artists usually take intraocularly scattered light into account when painting natural scenes. A method to achieve similar effects in photography by the use of diffraction filters in front of the camera lens is demonstrated. A number of photos that illustrate the effects of such filters are shown.

Disputing Viking navigation by polarized skylight
Curt Roslund
Applied Optics, Vol. 33 Issue 21 Page 4754 (July 1994) OSA Optics InfoBase
The widely held notion that the Vikings utilized polarization of skylight on overcast days for navigational purposes is demonstrated to have no scientific basis. The use of polarized skylight for navigation under partly cloud-free skies should be treated with caution and skepticism.

Possible halo depictions in the prehistoric rock art of Utah
Kenneth Sassen
Applied Optics, Vol. 33 Issue 21 Page 4756 (July 1994) OSA Optics InfoBase
In western American rock art the concentric circle symbol, which is widely regarded as a sun symbol, is ubiquitous. We provide evidence from Archaic and Fremont Indian rock art sites in northwestern Utah that at least one depiction was motivated by an observation of a complex halo display. Cirrus cloud optical displays are linked in both folklore and meteorology to precipitation-producing weather situations, which, in combination with an abundance of weather-related rock art symbolism, indicate that such images reflected the ceremonial concerns of the indigenous cultures for ensuring adequate precipitation. As has been shown to be the case with rock art rainbows, conventionalization of the halo image may have resulted in simple patterns that lacked recognizable details of atmospheric optical phenomena. However, in one case in which an Archaic-style petroglyph (probably 1500 yr or more old) satisfactorily reproduced a complicated halo display that contained parhelia and tangent arcs, sufficient geometric information is rendered to indicate a solar elevation angle of 40° at the time of observation.

Variability in atmospheric light-scattering properties with altitude
Frank W. Gibson
Applied Optics, Vol. 33 Issue 21 Page 4919 (July 1994) OSA Optics InfoBase
The altitudinal variability in angular scattering properties of the troposphere and stratosphere was measured with a balloonborne polar nephelometer. An analysis of interdependent experimental parameters provides information on the scattering phase function and inferred size distribution of aerosol particles as a function of altitude. These aerosol characteristics are extractable from the scattering dissymmetry index and its relationship to spectral dispersion in turbidity and the aerosol phase function. The problem of the correlation between backscatter and extinction is addressed from the perspectives of in situ observations.

Color Plates (strangely in black & white!)
Applied Optics, Vol. 33 Issue 21 Page 4953 (July 1994) OSA Optics InfoBase

Scattering of light by polyhedral ice crystals
Andreas Macke
Applied Optics, Vol. 32 Issue 15 Page 2780 (May 1993) OSA Optics InfoBase
The single-scattering phase functions of polyhedral-shaped ice particles are calculated by means of geometric optics and the diffraction theory. Particle orientation is assumed to be random in space. Particle shapes are taken both from ice-crystal classifications and from in situ measurements. The effects of particle concavity on the scattering signature are discussed in detail. A common feature is the pronounced forward-scattering peak, as well as different halo peaks that are due to a minimum deviation at corresponding ice prisms. An unusual halo phenomena, which results from a minimum deviation in a double-prism configuration, is found and verified. The comparison of different particle types shows that backscattering is a sensitive indicator for the identification of types of ice-crystal. Aggregate particles, like bullet rosettes, basically show the scattering characteristics of their individual components.
Simulation of mirages Free download
W. H. Lehn and W. Friesen
Applied Optics, Vol. 31 Issue 9 Page 1267 (March 1992) OSA Optics InfoBase
A mirage is seen when atmospheric refraction distorts or displaces an image. We describe a mirage simulator that uses digital imaging equipment to generate mirage images from normal photographs. The I simulation program relocates horizontal image lines into positions that they appear to occupy, according to rays traced from observer to object. Image-brightness adjustments are not required; we show that, while the atmosphere can change the size or shape of an object, it does not change its apparent brightness. The realistic quality of the computed images makes this simulator a useful tool in mirage analysis.

Assessing the contributions of surface waves and complex rays to far-field Mie scattering by use of the Debye series Free download
Edward A. Hovenac and James A. Lock
J. Opt. Soc. Am. A, Vol. 9, No. 5, p. 781 May 1992 OSA Optics InfoBase
The contributions of complex rays and the secondary radiation shed by surface waves to scattering by a dielectric sphere are calculated in the context of the Debye-series expansion of the Mie scattering amplitudes. Also, the contributions of geometrical rays are reviewed and compared with those of the Debye series. Interference effects among surface waves, complex rays, and geometrical rays are calculated, and the possibility of observing these interference effects is discussed. Experimental data supporting the observation of a surface-wave geometrical-ray-interference pattern are presented.

Differential geometric approach to atmospheric refraction Free download
William C. Kropla and Waldemar H. Lehn
J. Opt. Soc. Am. A, Vol. 9, No. 4, p. 601 April 1992 OSA Optics InfoBase
Differential geometric techniques are presented and used to model the optical properties of the atmosphere under conditions that produce superior mirages. Optical path length replaces the usual Euclidean metric as a distance-measuring function and is used to construct a surface on which the paths of light rays are geodesics. The geodesic equations are shown to be equivalent to the ray equation in the plane. A differential equation that relates the Gaussian curvature of the surface and the refractive index of the atmosphere is derived. This equation is solved for the cases in which the curvature vanishes or is constant. Illustrative examples based on observation demonstrate the use of geometric techniques in the analysis of mirage images.

Glare points
H. C. van de Hulst, Ru T. Wang
Applied Optics, Vol. 30 Issue 33 Page 4755 (November 1991) OSA Optics InfoBase
Glare points are the intensity maxima seen when a water drop illuminated by a wide beam is viewed from a certain direction and imaged. We show that good resolution in both the scattering angle and the glare point position can be achieved only if the size parameter x = 2πa/λ is >> 1 and that the positions of the glare points can be computed by a Fourier transform from the familiar Lorenz-Mie scattering function. Sample computations made with x = 10,000 and x = 20,000 are presented. Glare points corresponding to rays that have suffered as many as 15 internal reflections can be identified, in agreement with experimental findings.

Calculation of far-field scattering from nonspherical particles using a geometrical optics approach
Edward A. Hovenac
Applied Optics, Vol. 30, Issue 33, pp. 4739-4746 (November 1991) OSA Optics InfoBase
A numerical method was developed using geometrical optics to predict far-field optical scattering from particles that are symmetric about the optic axis. The diffractive component of scattering is calculated and combined with the reflective and refractive components to give the total scattering pattern. The phase terms of the scattered light are calculated as well. Verification of the method was achieved by assuming a spherical particle and comparing the results to Mie scattering theory. Agreement with the Mie theory was excellent in the forward-scattering direction. However, small-amplitude oscillations near the rainbow regions were not observed using the numerical method. Numerical data from spheroidal particles and hemispherical particles are also presented. The use of hemispherical particles as a calibration standard for intensity-type optical particle-sizing instruments is discussed.

Feature issue: Applied Optics, August 1991

Light and color in the open air: introduction by the feature editor Free download
Applied Optics, Vol. 30 Issue 24 Page 3381 (August 1991) OSA Optics InfoBase
James A. Lock and Craig F. Bohren

Polarimetry of a 22° halo Free download
G. P. Können, J. Tinbergen
Applied Optics, Vol. 30 Issue 24 Page 3382 (August 1991) OSA Optics InfoBase
The linear polarization and intensity of a 22° halo has been measured simultaneously at seven wavelengths as a function of scattering angle. The polarization pattern is found to be dominated by a narrow peak centered at the halo angle. The amount of polarization in this peak is much higher than expected from Fresnel refraction alone. The observations are explained with a birefringence-diffraction halo polarization model. The effective diameter of the hexagonal face of the halo-generating crystals is found to be 41 and 54 μm for two separate scans. An independent single-wavelength parhelion observation indicates a stronger birefringence peak concentrated in an even smaller angular scattering range and a crystal diameter of 220 μm. Crystal sizes derived from the halo intensity distributions are found to be consistent with those obtained from polarization. The data demonstrate the power of halo polarimetry as a tool for detection and identification of birefringent crystals in terrestrial or extraterrestrial atmospheres.

What are “all the colors of the rainbow”? Free download
Raymond L. Lee, Jr.
Applied Optics, Vol. 30 Issue 24 Page 3401 (August 1991) OSA Optics InfoBase
Both folklore and theory imply that naturally occurring rainbows display a wide range of nearly pure colors. However, digital image analysis of color slides shows that the natural rainbow's colors are not especially pure and that the bow's background causes much of this desaturation.

Mie theory model of the corona Free download
James A. Lock, Leiming Yang
Applied Optics, Vol. 30 Issue 24 Page 3408 (August 1991) OSA Optics InfoBase
We performed a calculation of the corona colors that employed Mie theory to obtain the scattered light intensity. The scattered intensity was integrated over the visible spectrum for a number of different cloud droplet size distributions. The results were converted to chromaticity coordinates, convolved with the angular size of the sun, and plotted on the 1931 CIE chromaticity diagram. The results were compared to observations of multiple-ring coronas. It was found that, when using Mie theory to estimate cloud droplet sizes, water droplets with diameters in the 7 μm < D < 15 μm range produced the 13 multiple-ring coronas that were observed.

Rainbows and fogbows Free download
David K. Lynch, Ptolemy Schwartz
Applied Optics, Vol. 30 Issue 24 Page 3415 (August 1991) OSA Optics InfoBase
The optics of rainbows and fogbows is investigated theoretically for monodisperse drops using Mie theory. Included in the calculations are a realistic solar illumination spectrum and the finite size of the sun. Drop sizes range from 3 to 300 μm (3800 > X > 38). Results are presented on the location, width, contrast, polarization, and color of both primary and secondary rainbows. Particular attention is given to rainbows formed in small drops (fogbows).

Corona-producing cirrus cloud properties derived from polarization lidar and photographic analyses
Kenneth Sassen
Applied Optics, Vol. 30 Issue 24 Page 3421 (August 1991) OSA Optics InfoBase
Polarization lidar data are used to demonstrate that clouds composed of hexagonal ice crystals can generate multiple-ringed colored coronas. Although relatively uncommon in our mid-latitude cirrus sample (derived from Project FIRE extended time observations), the coronas are associated with unusual cloud conditions that appear to be effective in generating the displays. Invariably, the cirrus cloud tops are located at or slightly above elevated tropopauses (12.7-km MSL average height) at temperatures between -60° and -701C. The cloud top region also generates relatively strong laser backscattering and unusually high 0.5-0.7 linear depolarization ratios. Color photograph analysis of corona ring angles indicates crystals with mean diameters of from 12 to 30 μm. The cirrus cloud types were mainly subvisual to thin (i.e., bluish-colored) cirrostratus, but also included fibrous cirrus. Estimated cloud optical thicknesses at the 0.694 μm laser wavelength ranged from 0.001 to 0.2, where the upper limit reflects the effects of multiple scattering and/or unfavorable changes in particle characteristics in deep cirrus clouds.

Unfolded optical glory of spheriods: backscattering of laser light from freely rising spheriodal air bubbles in water Free download
W. Patrick Arnott, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3429 (August 1991) OSA Optics InfoBase
Enhancement in backscattering known as glory scattering results from geometric and material properties of spherically symmetric scatterers. The wave-front shape near the spherical scatterer is locally a circular torus. Radiation from a toroidal wave front is axially focused on the backward-directed axis. It is shown that the axial point caustic unfolds to an astroid caustic as the scatterer's shape changes from spherical to slightly spheroidal. The wave front pertinent for slightly spheroidal scatterers was modeled as a toroidal wave front with a superimposed harmonic angular perturbation. Experimental observations are displayed for crosspolarized backscattering by freely vertical rising, slightly oblate spheroidal air bubbles in water illuminated by a horizontally propagating laser beam. These patterns were recorded with a camera for two different incident-beam polarization directions relative to the axis of rotational symmetry of the bubble. Angular scattering patterns were also computed using a perturbation analysis based on use of the harmonically perturbed toroidal wave front and physical optics. Bubble oblateness was estimated from features of the angular scattering pattern and from hydrodynamic relations.

Opening rate of the transverse cusp diffraction catastrophe in light scattered by oblate spheroidal drops
Cleon E. Dean, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3443 (August 1991) OSA Optics InfoBase
Light scattered by an oblate drop of water has been observed to produce cusp caustics in the general vicinity of the rainbow region [P. L. Marston and E. H. Trinh, Nature London 312, 529-531 (1984)]. The principal curvatures of the generic local wave front that produces the far-field transverse cusp are examined. This wave front is shown to generate a transverse cusp curve (U - Uc)3 = - d∞ V2, where U and V are horizontal and vertical scattering angles and Uc is the cusp point direction. The far-field opening rate d∞ is calculated for the transverse cusp. It is shown that d∞ has a simple dependence on the parameters of the generic wave front. We define the aspect ratio of the drop q = D/H, where H is the height and D is the equatorial width for the scattering drop. The method of generalized ray tracing is used to relate q to principal curvatures and shape parameters of the outgoing wave front and hence to d∞. Measurements of d∞ for scattering laser light from acoustically levitated drops appear to support the calculation. As q goes to q4 ≈ 1.31, the critical value for generation of a hyperbolic-umbilic focal section, the predicted d∞ goes to infinity. The nature of the divergence was numerically investigated as was the rate at which d∞ vanishes as q approaches critical values for lips and transition events.

Forward glory scattering from bubbles
Dean S. Langley, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3452 (August 1991) OSA Optics InfoBase
The scattering enhancement known as the glory was observed in forward scattering from bubbles in liquids. A physical-optics model of the forward glory is detailed, based on transmitted waves reflected within the bubble. Some aspects of the model are compared with the Mie theory and with features in the cross-polarized light from single bubbles. Clouds of small bubbles rising in water show an angular structure in the forward glory light that is useful for estimating the bubble size.

Rainbow-enhanced forward and backward glory scattering
Dean S. Langley, Michael J. Morrell
Applied Optics, Vol. 30 Issue 24 Page 3459 (August 1991) OSA Optics InfoBase
When the refractive index m of a sphere is such that rainbows occur in the forward or backward direction, the glory scattering becomes exceptionally strong. A number of these refractive-index values have been determined from the geometry of ray paths. A physical-optics model of the scattering leads to an a2x4/3 dependence in the scattered irradiance, where a is the radius of the sphere, and x = ka is the size parameter. Normal glory scattering gives an irradiance proportional to x. Mie theory computations illustrate the presence of rainbow glories at predicted m values and the x4/3 irradiance factor. As in normal glory scattering, the rainbow-enhanced glory light contains a strong cross-polarized component. Experiments using single glass spheres immersed in liquids show the predicted cross-polarized scattering with a sensitive dependence on m.

Scattering of white light from levitated oblate water drops near rainbows and other diffraction catastrophes
Harry J. Simpson, Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3468 (August 1991) OSA Optics InfoBase
Oblate drops of water illuminated perpendicular to their symmetry axis generate a hyperbolic-umbilic diffraction catastrophe near the primary rainbow [P. L. Marston and E. H. Trinh, Nature London 312, 529- 531 (1984)]. Observations were made of this diffraction catastrophe generated by white-light illumination of acoustically levitated drops of water in air. The observations suggest what generalized rainbows would look like if they were produced in nature when sunlight illuminates large raindrops. Unlike the usual rainbow arc, the transverse cusp of the unfolded catastrophe is not distinctly colored. The hyperbolic-umbilic focal section is distinctly colored as is another diffraction catastrophe generated in the rainbow region when the drop is highly oblate.

On the gamut of colors seen through birefringent airplane windows
Craig F. Bohren
Applied Optics, Vol. 30 Issue 24 Page 3474 (August 1991) OSA Optics InfoBase
Colors in birefringent airplane windows seen through polarizing filters are not especially pure nor are all colors equally probable. This is a consequence of the shape of transmission vs wavelength for a retarder-polarizer combination illuminated by partially polarized skylight. Although transmission can have a single peak in the blue or green, a peak in the red is accompanied by one in the blue. This and the general blueness of skylight are why the purest colors seen in airplane windows are greens, yellowish-greens, and purples (mixtures of red and blue). Purer colors and a wider gamut are obtained for birefringent sheets interposed between dichroic polarizing filters and illuminated by tungsten light.

Colors observed when sunlight is scattered by bubble clouds in seawater
Philip L. Marston
Applied Optics, Vol. 30 Issue 24 Page 3479 (August 1991) OSA Optics InfoBase
Colored bands photographed in sunlit subsurface bubble clouds are described. The colors are found to be associated with the transition from partial-to-total reflection by the bubbles. The most pronounced band is a red-yellow band located near the transition region. Theoretical evidence is also summarized that the colored bands observed are only weakly affected by thin coatings and the oblate shape of freely rising bubbles.

Investigation into the scattering of light by human hair
Helen K. Bustard, Robin W. Smith
Applied Optics, Vol. 30 Issue 24 Page 3485 (August 1991) OSA Optics InfoBase
We describe a general investigation into the scattering of light by human hair. The main features of the intensity distribution produced by light scattered by an individual hair are identified. Qualitative explanations for the features are advanced in terms of the arrangement of the outer structure of the hair and its level of pigmentation. Contrast gloss values are calculated in an attempt to quantify the appearance of hair. These values are found to depend not only on the properties of hair, such as color and condition, but also on the direction and polarization state of the incident light. In assessing the effects of cosmetic treatments on hair, gloss values are shown to be useful where readings from treated hairs are compared with those from a control sample investigated in the same conditions.

Light and color on the wing: structural colors in butterflies and moths
Helen Ghiradella
Applied Optics, Vol. 30 Issue 24 Page 3492 (August 1991) OSA Optics InfoBase
All butterfly and moth scales share the same basic architecture, but various elements of this architecture are particularly complex in those scales that exhibit structural colors. These elements include the scales' ridges and their associated lamellae and microribs, and the trabeculae, the pillars normally that act as spacers within scales. The additional ornamentation produces thin film, Tyndall blue or diffraction colors and represents a particularly striking example of precision in biological pattern formation.

Can normal outdoor activities be carried out during civil twilight?
Herschel W. Leibowitz, D. A. Owens
Applied Optics, Vol. 30 Issue 24 Page 3501 (August 1991) OSA Optics InfoBase
Ambient illumination during civil twilight, which occurs approximately a half hour before sunrise and after sunset, has traditionally been characterized as posing no restriction on normal visual activities. However, consideration of the selective degradation of visual-recognition functions and the concurrent sparing of visual-guidance functions at the prevailing (relevant) luminance levels suggests that this characterization of civil twilight is no longer appropriate, particularly in light of the visual demands of industrialized society. Rather, special notice should be taken of the implications of selective degradation of visual recognition during civil twilight for traffic safety and other visually demanding hazardous tasks.

Toying with the moon illusion
G. R. Lockhead, Myron L. Wolbarsht
Applied Optics, Vol. 30 Issue 24 Page 3504 (August 1991) OSA Optics InfoBase
We propose that the correct interpretation of the moon illusion is that the zenith moon appears small, not that the horizon moon appears large. This illusion is caused by the visual gap between the observer and the overhead moon. Because of the gap, the observer has no or little optical information about the distance of the moon. This results in empty field myopia where the moon is neurally, although not necessarily cognitively, processed as being at about arm's length. When the moon is seen on the horizon, there usually is optical information about distance. That results in reduced accommodation, and so the moon is processed as at a greater distance. Consistent with the size-distance-invariance hypothesis, the moon is then judged as large. This is a specific example of the more general fact that all distant objects appear small in the absence of a stimulus for accommodation to be distant. This outcome produces the toy illusion.

Step brightness changes of distant mountain ridges and their perception Free download
David K. Lynch
Applied Optics, Vol. 30 Issue 24 Page 3508 (August 1991) OSA Optics InfoBase
When successive ridges of distant mountains are seen, observers often report that, near the ridge where the brightness changes abruptly, the upper part of the nearer ridge appears darker than at its lower portions. Similarly, they report that the base of the more distant mountain seems brighter adjacent to the nearer ridge than on its upper portions. The explanation of this phenomenon, known as the step contrast effect, is a special case of Mach bands. It is usually attributed to a visual illusion involving lateral inhibition in the eye, which is most apparent in the vicinity of step brightness changes. Using analytic techniques and numerical integrations to simulate the airlight-induced brightness distributions of such scenes, we show that in many cases the perceived brightness distribution is qualitatively similar to the true brightness distribution and thus is not a visual illusion.

Atmospheric optics in art
Stanley David Gedzelman
Applied Optics, Vol. 30 Issue 24 Page 3514 (August 1991) OSA Optics InfoBase
A brief historical overview of the atmospheric optical phenomena that appear in works of fine art is presented. It is shown that artists have recorded many features of the color and brightness of the sky and clouds, aerial perspective and visibility effects, and phenomena, including crepuscular rays, rainbows, halos, and coronas. Artistic biases resulting from prevailing styles and societal influences are noted. Attention is drawn to a number of phenomena recorded by artists that have not yet been explained or modeled.

Rainbows in the Indian rock art of desert western America
Kenneth Sassen
Applied Optics, Vol. 30 Issue 24 Page 3523 (August 1991) OSA Optics InfoBase
For thousands of years the image of the rainbow was pecked and painted by native Americans onto the rocks of the Great Basin and the Southwest. This long-lived tradition, which transcended major developments in lifestyles and cultures, underscores the important symbolic significance of the rainbow to the inhabitants of this arid region. The rainbow rock art depictions were usually associated with humanlike ceremonial figures, snakes, clouds, rain, and lightning bolts, suggesting that the rainbow symbol was employed as part of an elaborate sacred tradition. Although such ceremonial usage of the rainbow image tends to lead to abstraction and symbolic representation, there are examples, including a properly colorized rainbow painting from central Utah (approximately a thousand years old), that indicate observationally based rainbow reproductions of relatively great antiquity.

Ulloa's observations of the glory, fogbow, and an unidentified phenomenon Free download
David K. Lynch, Susan N. Futterman
Applied Optics, Vol. 30 Issue 24 Page 3538 (August 1991) OSA Optics InfoBase
Ulloa's complete print of the glories and fogbows on Mt. Pambamarca in Peru (now Ecuador) is presented. It shows two other phenomena, an erupting volcano and an as yet unidentified optical effect. The glories and fogbow are analyzed to obtain the drop size of the fog, and the unidentified features are discussed.

Finnish Halo Observing Network: search for rare halo phenomena
Marko Pekkola
Applied Optics, Vol. 30 Issue 24 Page 3542 (August 1991) OSA Optics InfoBase
The Finnish Halo Observing Network obtains information about rare halos through literature study and amateur network observations. Recent photographs and historical drawings of some yet unexplained halo effects are presented.

Rainbows: Mie computations and the Airy approximation
Ru T. Wang and H. C. van de Hulst
Applied Optics Vol. 30, 1, p. 106 (January 1991) OSA Optics InfoBase
Efficient and accurate computation of the scattered intensity pattern by the Mie formulas is now feasible for size parameters up to x = 50,000 at least, which in visual light means spherical drops with diameters up to 6 mm. We present a method for evaluating the Mie coefficients from the ratios between Riccati-Bessel and Neumann functions of successive order. We probe the applicability of the Airy approximation, which we generalize to rainbows of arbitrary p (number of internal reflections = p - 1), by comparing the Mie and Airy intensity patterns. Millimeter size water drops show a match in all details, including the position and intensity of the supernumerary maxima and the polarization. A fairly good match is still seen for drops of 0.1 mm. A small spread in sizes helps to smooth out irrelevant detail. The dark band between the rainbows is used to test more subtle features. We conclude that this band contains not only externally reflected light (p = 0) but also a sizable contribution from the p = 6 and p = 7 rainbows, which shift rapidly with wavelength. The higher the refractive index, the closer both theories agree on the first primary rainbow (p = 2) peak for drop diameters as small as 0.02 mm. This may be useful in supporting experimental work.


Green icebergs and remote sensing Free download
Raymond L. Lee, Jr.
J. Opt. Soc. Am. A, Vol. 7, No. 10, p. 1862 (October 1990) OSA Optics InfoBase
The curious phenomenon of green icebergs has fascinated polar travelers for centuries. Although translucent green icebergs might be caused by colorants, a recently obtained sample of a green iceberg contained little inherently green material. This fact, combined with the blue-green absorption minimum of pure, homogeneous ice, suggests that a sufficient (rather than necessary) condition for green icebergs may be reddened sunlight illuminating intrinsically blue-green ice. Lacking in situ spectral reflectances of green icebergs, we develop two remote-sensing techniques to analyze their optical properties. Estimates of a green iceberg's reflectance spectra are derived from spectrodensitometry and from video digitizing of original color slides. Proxies for polar daylight spectra yield the iceberg's chromaticities, which agree closely with those predicted by two multiple-scattering theories.

Halo phenomena modified by multiple scattering
Yoshihide Takano and Kuo-Nan Liou
J. Opt. Soc. Am. A, Vol. 7, No. 5, p. 885 (May 1990) OSA Optics InfoBase
Halo phenomena produced by horizontally oriented plate and column ice crystals are computed. Owing to the effect of multiple scattering, a number of optical features, in addition to the well-known halos and arcs caused by single scattering, can be produced in the sky. These include the 44° parhelion, the 66° parhelion, the anthelion, the uniform and white parhelic circle, and the uniform and white circumzenithal circle in the case of horizontally oriented plates. The anthelion is a result of double scattering that involves horizontally oriented columns that produce the Parry arc. The optical phenomena identified in the present study are compared with those of previous research and discussed. .


Observability of atmospheric glories and supernumerary rainbows Free download
James A. Lock
J. Opt. Soc. Am. A, Vol. 6, No. 12, p. 1924 (December 1989) OSA Optics InfoBase
The finite spatial coherence width of sunlight at the Earth imposes restrictions on the production of scattering phenomena based on the interference of light waves. With the spatial coherence properties of sunlight taken into account, the visibility of the supernumerary rainbow sequence adjacent to the primary rainbow and the radii of the water droplets that produce the optimum glory intensity were calculated. A substantial reduction was found in the contrast of all the supernumeraries beyond the first few, and the peak observability of the glory occurred for water droplets with radii between 10 and 20 µm.

Scattering of light by crystals: a modified Kirchhoff approximation
Karri Muinonen
Applied Optics Vol. 28, 15, p. 3044 (August 1989) OSA Optics InfoBase
A modified Kirchhoff approximation (MKA) is developed for the scattering of light by randomly oriented crystals. The reflected and transmitted near fields are calculated from ray tracing; the corresponding far fields are then obtained via the vector Kirchhoff integral. On the shadow side of the particle, an additional near field exactly cancels the incident field and causes the forward diffraction. MKA contains a particle size dependence, which is not included in ray optics treatments, and satisfactory results can be obtained for size parameters larger than ten. The scattering phase functions and degrees of linear polarization are calculated for some hexagonal and cubic water ice crystals using MKA. The Kirchhoff approximation for particles other than crystals is discussed, and attention is paid to the backscattering enhancement due to the cyclic passage of internally or multiply externally reflected electromagnetic waves.

Non-Debye enhancements in the Mie scattering of light from a single water droplet Free download
James A. Lock and Judith R. Woodruf
Applied Optics Vol. 28, 3, p. 523 (February 1989) OSA Optics InfoBase
The glare spots usually seen on a single water droplet which has been illuminated by a plane wave are produced by geometrical rays which correspond to the different terms of the Debye series expansion of the Mie scattered field. Recently other glare spot enhancements have been predicted which correspond to scattering resonances coupling to the orbiting rays associated with high-order geometrical rainbows. We observed the non-Debye enhancement of the eleventh-order rainbow glare spot at an observation angle of 90° on a 3.5-mm water droplet illuminated by polarized He-Ne laser light.


Rainbows in strong vertical atmospheric electric fields
Stanley David Gedzelman
J. Opt. Soc. Am. A, Vol. 5, No. 10, p. 1717 (October 1988) OSA Optics InfoBase
The effects of strong vertical atmospheric electric fields and electrically charged raindrops on the primary rainbow are considered. A vertical electric field alters the bow by stretching the raindrops vertically. The effects may be visible only for the extremely large electric fields (E > 105 V/m) sometimes encountered in thunderstorms. The electric field raises and brightens the top of the primary bow but reduces the relative intensity and spacing between the supernumeraries. Electrical charges do not have any visible effect on the rainbow because they significantly increase the ellipticity of only the largest and most highly charged drops, which do not contribute to the bow's top.

Optical simulation of Huygens's principle
G. Bickel and G. Hausler
J. Opt. Soc. Am. A, Vol. 5, No. 6, p. 843 (June 1988) OSA Optics InfoBase
The two-dimensional stationary-wave equation (Helmholtz equation) can be solved by a simple linear-optical filtering experiment for arbitrary source distributions. The experiment can be considered as direct visualization of Huygens's principle, i.e., each point of an initial wave front can be regarded as the source of an elementary wave. Many phenomena can be visualized: diffraction, interference (including Talbot effect, Bragg effect) with monochromatic and polychromatic light, birefringence, etc. Optical filtering can be applied to other linear differential equations with constant coefficients too, such as the Poisson equation and the diffusion equation.

Optical glory of small freely rising gas bubbles in water: observed and computed cross-polarized backscattering patterns Free download
W. Patrick Arnott and Philip L. Marston
J. Opt. Soc. Am. A, Vol. 5, No. 4, p. 496 (April 1988) OSA Optics InfoBase
Light scattered from spherical bubbles in water manifests an enhancement in the backward direction analogous to the well-known optical glory of a drop. Unlike the glory for water drops, in which the rays travel partially on the drop's surface, the glory for bubbles is due to rays that are refracted and multiply reflected within the scatterer and is an example of a transmitted wave glory. Photographs of glory scattering for freely rising air bubbles in water are displayed for bubbles having diameters of less than 300 µm. A physical-optics model for backscattering is developed for spherical bubbles. Computed glory patterns from both Mie-series calculations and the physical optics model agree with the observed patterns. The patterns of freely rising air bubbles having a diameter of <300 µm are essentially those predicted for a spherical scatterer. The interference of different classes of glory rays is more clearly seen for bubbles in water than for the previously studied case of bubbles in oil.


Theory of the observations made of high-order rainbows from a single water droplet Free download
James A. Lock
Applied Optics Vol. 26, 24, p. 5291 (December 1987) OSA Optics InfoBase
Over a dozen rainbows have been observed in a single water droplet. They appear as glare spots on the water droplet which take on coloration at the appropriate rainbow angles. The appearance of rainbows as colored glare spots in this situation is understood in terms of the caustics created in the vicinity of the droplet by the refracting light rays. The angular positions of the glare spots are understood in terms of the Fourier transform of the geometric scattering amplitude. The rainbow glare spots are also found to appear numerically in the Fourier transform of the Mie scattered fields. An additional glare spot produced by rays at grazing incidence and not attributable to geometric optics also appears numerically in the Fourier transformed Mie fields.

Appearance of supernumeraries of the secondary rainbow in rain showers Free download
G. P. Können
J. Opt. Soc. Am. A/Vol. 4, No. 5, p. 810 (May 1987) OSA Optics InfoBase
The secondary rainbow scattering angle for spheroidal drops of water is virtually independent of aspect ratio for most visible wavelengths. For most solar heights the residual aspect-ratio dependence shifts the bow toward a smaller deviation angle if the drop size increases. These two facts explain why the supernumeraries of the secondary rainbow are never seen in rain showers. At high solar elevations the flattening of drops results in a shift of the secondary rainbow toward a larger deviation angle. -It is shown that this shift is still large enough to cause the formation of the first supernumerary in red light. This red supernumerary of the secondary rainbow may be observable by eye in natural showers if a red filter is used to remove the obscuring contribution of shorter wavelengths to the light of the rainbow. For indices of refraction far from that of water, a strong aspect-ratio dependence of the secondary rainbow angle is shown to be present. Some possible implications of this for the formation of a hyperbolic umbilic diffraction catastrophe in the secondary rainbow pattern are indicated.

Feature issue: Journal of Optical Society of America A, March 1987

Disruption of images: the caustic-touching theorem Free download
M. V. Berry
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 561 (March 1987) OSA Optics InfoBase
Because of the distortions of geometrical optics, image curves and the outlines of the objects that generate them need not have the same topology. New image loops appear when the object curve touches the caustic of the family of (imaginary) rays emitted by the observing eye. Such disruption may be elliptic (loop born from an isolated point) or hyperbolic (loop pinched off from an already existing one). The number of images need not be odd (unlike the number of rays reaching the eye from each object point). Two examples are employed to illustrate caustic touching. The first is the Sun's disk seen in rippled water (as the height of the eye increases, the boundary of all the images becomes a fractal curve with dimension 2). The second is sunset seen through the Earth's atmosphere from near space (when there is an inversion layer) or from the Moon during a lunar eclipse (when there need not be one).

Polarization and Brewster angle properties of light pillars
Kenneth Sassen
J. Opt. Soc. Am. A, Vol. 4, No. 3. p. 570 (March 1987) OSA Optics InfoBase
Numerical simulation of the nocturnal light pillar, an atmospheric optical phenomenon inadvertently caused by humans, reveals that the pillars are virtually completely polarized at the Brewster angle for ice as a result of the geometry of rays reflected off near-horizontally aligned ice crystals from a nearby light source. It s also shown for plate crystals that the first-order internal reflection contributes importantly to the display and that the depth of the crystal-containing layer and the effects of atmospheric attenuation serve to limit the height above the horizon to which the pillars are visible. The model findings have been verified with experiments involving the generation of artificial pillars from linearly polarized light sources. Both observations and model predictions support the view that the plate ice crystals causing the display have tilt angles that are distributed normally from the horizontal plane.

Faceted snow crystals
John Hallett
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 581 (March 1987) OSA Optics InfoBase
Colored halos are produced by refraction of light by solid hexagonal snow crystals with well-defined facets whose size is sufficiently large (>20 ,um) to avoid significant diffraction effects. Large crystals fall with their major axes horizontal and oscillate by eddy shedding to give dogs and arcs. The formation of such crystals is strongly dependent on changing growth conditions, particularly ice supersaturation, air pressure, temperature, and the thermal radiation environment. Optimum meteorological conditions for formation of such crystals are suggested.

Laboratory simulation of inferior and superior mirages
Robert G. Greenler
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 589 (March 1987) OSA Optics InfoBase
A small scene, viewed over a heated plate, exhibits many of the typical inferior-mirage effects. As the viewing point is lowered, a mirage lake appears, and a vanishing line rises on the scene, showing objects apparently reflected in a rising surface of water. Several kinds of superior mirages are simulated by viewing objects through a water tank containing fresh water layered over salt water. The system simulates towering, stooping, various forms of the Fata Morgana, and the three-part mirage.

Multiple-scattering effects in halo phenomena
E. Trankle & Robert G. Greenler
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 591 (March 1987) OSA Optics InfoBase
Using a hit-and-miss Monte Carlo method, we followed many paths of Sun rays through a layer of hexagonal ice crystals. The angle of scattering by a single crystal is determined by tracing the path of the Sun rays through the crystal with its particular orientation. In this way we produced point plots of the intensity of the scattered sunlight for a specified population of crystals. By comparing the intensity patterns from single and multiple scattering, we looked for additional effects caused by multiple scattering. Several new secondary structures appear; however, their intensities are significant only when they result from spotlike primary structures. It appears that secondary structures from two combinations should be observable: from thick-plate crystals, the sun dogs of the sun dogs; and for long-column crystals in the Parry-arc orientation, the subsun of the lower tangent arc for Sun elevations around 15°. We show that multiple scattering is essential to explain the Saskatoon display.

Skylight polarization during a total solar eclipse: a quantitative model Free download
G. P. Können
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 601 (March 1987) OSA Optics InfoBase
The polarization distribution in the sky during a total solar eclipse is calculated with a simple secondary light scattering model. This model uses the light-intensity measurements near the horizon during the eclipse and the pretotality and posttotality skylight polarization observations as input. It is found thaf the model can explain various observations during totality, including the quantitative measurements of Shaw [ Applied Optics 14, 388 (1975)] of the polarization distribution of the sky in the solar vertical during the 1973 total eclipse.

Optics of sunbeams Free download
David K. Lynch
J. Opt. Soc. Am. A, Vol. 4, No. 3, p. 609 (March 1987) OSA Optics InfoBase
Crepuscular and solar rays are visible by means of the contrast between sunlit and (usually) cloud-shaded portions of the atmosphere. Their visibility depends on (1) the volume angular-scattering coefficient β(φ), (2) the brightness of the sunlit sky, and (3) the integrated optical path through the shadowed regions of the atmosphere. We show that the geometry of path length through the umbra (3) is sufficiently important that it can account for most of the observed properties of rays, except when the volume angular-scattering coefficient β(φ) is sharply peaked in the forward direction.


What size of ice crystals causes the halos?: comment
Andrew J. Weinheimer
J. Opt. Soc. Am. A, Vol.3, No. 3, p. 376 (March 1986) OSA Optics InfoBase
The paper by Fraser [A. B. Fraser, J. Opt. Soc. Am. 69, 1112 (1979)] provides a critical assessment of the commonly made assumption that halos around the Sun are produced by randomly oriented ice crystals. He concludes that crystals that are small enough to be randomly oriented are, in addition, too small to contribute significantly to the production of a halo; thus the commonly made assumption is false. However, some doubt is cast on this conclusion by the fact that it is based on what may be regarded either as a misapplication of Maxwell-Boltzmann statistics or as, perhaps, a mathematical error. The purpose of this Communication is simply to point this out. Left unanswered are the important questions of how big an error this is and even of whether its correction would weaken or strengthen Fraser's main conclusion.


Intensity profile of the 22° halo Free download
David K. Lynch and Ptolemy Schwartz
J. Opt. Soc. Am. A, Vol. 2, No. 4, p. 584 (April 1985) OSA Optics InfoBase
We report the first relative intensity measurements made to our knowledge of the 22° halo, obtained from photographic photometry of a halo of exceptional brightness and uniformity. The maximum brightness occurs at 22.8°, and a relative minimum occurs at 19.7°. The full width at one half the maximum intensity is 3.4°. A low-intensity tail reaches from 29° to 39°.


Refraction halos in the solar system. I. Halos from cubic crystals that may occur in atmospheres in the solar system
Edward Whalley and Graham E. McLaurin
J. Opt. Soc. Am. A, Vol. 1, No. 12, p. 1166 (December 1984) OSA Optics InfoBase
It is suggested that halos and other refraction effects caused by crystals of various solids that may occur in their atmospheres might occur on the planets of the solar system and their satellites. The detection of the halos would provide valuable information about the nature and the crystalline form of the solids. The halos caused by the octahedral and cubic crystals of carbon monoxide, carbon dioxide, ice Ic, ammonia, methane, and the structure-I clathrate hydrates of nitrogen, carbon monoxide, carbon dioxide, sulfur dioxide, and methane have been predicted over the range of temperatures that may occur in the atmospheres of the planets.

Monte Carlo simulation and analysis of halo phenomena
F. Pattloch and E. Trankle
J. Opt. Soc. Am. A, Vol. 1, No. 5, p. 520 (May 1984) OSA Optics InfoBase
We trace the paths of sun rays through hexagonal ice crystals by a hit-and-miss Monte Carlo algorithm, interpreting the Fresnel equations as reflection and transmission probabilities. In this way, we calculate the intensity of the scattered sunlight for a specified distribution of crystals. In particular, we obtain the relative intensities of all arcs and spots produced by the crystals. The distribution function for the tilting and rotation angles of oriented crystals corresponds to a superposition of damped oscillations. We use the method to analyze the relative intensities of the 22° and 46° halos and to simulate a complex ice-crystal display produced by oriented column-like, oriented plate-like, and unoriented cube-like crystals.


Feature issue: Journal of Optical Society of America, December 1983

Inversion of superior mirage data to compute temperature profiles Free download
Waldemar H. Lehn
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1622 (December 1983) OSA Optics InfoBase
Information derived from the superior mirage is used to compute the average vertical temperature profile in the atmosphere between the observer and a known object. The image is described by a plot of ray-elevation angle at the eye against elevation at which that ray intersects the object. The computational algorithm, based on the tracing of rays that have at most one vertex, iteratively adjusts the temperature profile until the observed image characteristics are reproduced. An example based on an observation made on the Beaufort Sea illustrates the process.

Why can the supernumerary bows be seen in a rain shower?
Alistair B. Fraser
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1626 (December 1983) OSA Optics InfoBase
Although the spectra of drop radii in rain showers are broad, the supernumerary bows are caused by only those drops with radii of about 0.25 mm. The angle of minimum deviation, the rainbow angle, is a function of drop size, being large for big drops, owing to drop distortion, and large for small drops, owing to interference. Between these extremes, there is a minimum rainbow angle. The drops that cause it give rise to the supernumerary bows

Polarization and intensity distributions of refraction halos Free download
G. P. Können
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1629 (December 1983) OSA Optics InfoBase
By using Taylor expansions, simple expressions are obtained for the deflection of light by ice crystals. With these simplified formulas, the intensity distributions of halos as a function of scattering angle are calculated analytically near the halo angle. It is found that the intensity distributions of halos depend on the number of degrees of freedom of the generating set of crystals. The differences in the purity of the colors of various types of halo are explained subsequently on the basis of their intensity distributions. An analytical description of the shape of the halo or of the halocaustic near the halo angle is obtained also. On the basis of the obtained intensity distributions, the polarization of refraction halos as a function of scattering angle is calculated, in which both contributions (birefringence of ice and polarization by refraction) are taken into account. It is found that the polarization of parhelia and tangent arcs shows a strong maximum near the inner edge of the halo over an angular range of 0.1°, followed by a similar maximum of reversed polarization at 0.5° from the first one. The 22° halo shows a less strong maximum near its edge over an angular range of 0.5°. Halos at 46° from the sun also show a strong polarization near their inner edges, but the direction of the polarization is perpendicular to the polarization of the 22° halo edges. The possibility for detecting ice crystals on Venus by polarimetry near the halo angle is discussed briefly.

Some ice crystals that made halos
Walter Tape
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1641 (December 1983) OSA Optics InfoBase
During low-level halo displays, ice crystals in the atmosphere at ground level were collected and studied. I discuss the crystals in connection with the halos present at the time of collection.

Colors of snow, frozen waterfalls, and icebergs
Craig F. Bohren
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1646 (December 1983) OSA Optics InfoBase
Snow presents more than just a uniformly white face. Beneath its surface a vivid blueness, the purity of which exceeds that of the bluest sky, may be seen. This subnivean blue light results from preferential absorption of red light by ice; multiple scattering by ice grains, which is not spectrally selective, merely serves to increase the path length that photons travel before reaching a given depth. Although snow is usually white on reflection, bubbly ice, which can be found in frozen waterfalls and icebergs, may not be. To a first approximation, bubbly ice is equivalent to snow with an effective grain size that increases with decreasing bubble volume fraction. Ice grains in snow are too small to give it a spectrally selective albedo, but the much larger effective grain sizes of bubbly ice can give it bluish-green hues of low purity on reflection.

Landscape as viewed in the 320-nm ultraviolet
W. Livingston
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1653 (December 1983) OSA Optics InfoBase
Wood's 1910 study of the UV landscape by photography [R. W. Wood, Photog. J. 50, 329 (1910)] is resumed. Through a narrow-band filter at 320 nm we find uniform skies even under broken clouds, a Rayleigh veiling that attenuates distant detail, an absence of shadows, and a low reflectivity for most natural substances (except snow). Rainbows broaden by a factor of more than 2 when the UV is included. The fact that glass is opaque at 320 nm causes cities to be dark at night in this wavelength, with astronomical consequences. The aphakic human eye (i.e., the eye after removal of its crystalline lens for a cataract condition) proves to have a practical sensitivity at 320 nm so that the aphakic observer can verify the unique character of the UV scene.

Critical-angle scattering of white light from a cylindrical bubble in glass: photographs of colors and computations
P. L. Marston, J. L. Johnson, S. P. Love and B. L. Brim
J. Opt. Soc. Am., Vol. 73, No. 12, p. 1658 (December 1983) OSA Optics InfoBase
A novel effect in the scattering of white light from bubbles consists of colored bands that appear near the critical scattering angle. The bands were photographed in the far-zone scattering from a cylindrical bubble in glass. Their existence is associated with the coarse structure present in the exact scattered intensity. A digital Butterworth filter was developed to remove (from computed intensities) fine structures that are lost when the optical bandwidth is large. The colors are found to be due to the combined effects of interference and diffraction (near the critical scattering angle) and dispersion of the refractive index. Coarse structures were previously modeled in the monochromatic scattering from spherical air bubbles in water. Colors are also to be expected in the appearance of clouds of bubbles in water. Such colors were reported [C. Pulfrich, Ann. Phys. Chem. (Leipzig) 33, 209 (1888)]. Some implications for the optical measurement of bubble size and surface quality are noted.

Effects of the El Chichon volcanic cloud in the stratosphere on the intensity of light from the sky
Kinsell L. Coulson
Applied Optics Vol. 22, 15, p. 2265 (August 1983) OSA Optics InfoBase
This is the second of two papers dealing with the effects of volcanic debris from the eruption of El Chichon on light from the sunlit sky. The polarization of skylight was considered in the first of the two, whereas this one is devoted to skylight intensity. It is shown here that the magnitude of the skylight intensity is modified very significantly from its clear sky value by the volcanic cloud, as is its change with solar depression angle during twilight and its distribution over the sky during the day. Emphasis is on measurements at a wavelength of 0.07 Atm. Generally the volcanic cloud produces a diminution of zenith intensity during twilight with a considerable enhancement of intensity over the sky throughout the main part of the day. The solar aureole is not as sharp as it is in normally clear conditions, but the volcanic cloud causes a very diffuse type of aureole which covers a large portion of the sky. The preferential scattering of the longer wavelengths of sunlight, which is made evident by brilliant red and yellow colors in the sunrise period, causes a pronounced change of longwave/shortwave color ratios during twilight from their values in clear atmospheric conditions. The combination of intensity data shown here with polarization data in the previous paper should give a relatively complete picture of the effects of volcanic debris on solar radiation in the atmosphere and be useful in the verification of radiative transfer models of atmospheric turbidity.

Video polarimetry: a new imaging technique in atmospheric science
T. Prosch, D. Hennings, and E. Raschke
Applied Optics Vol. 22, 9, p. 1360 (May 1983) OSA Optics InfoBase
An imaging polarimeter has been built to study the polarization of solar radiation (X = 550 nm) scattered and reflected from the natural environment. The instrument generates false color images as multiparameter display of the degree of polarization, azimuth of polarization, and the radiance. These video signals can be digitized into a computer-compatible format. As an example of application, the polarization properties of light reflected from a lake and its environment are discussed here.

Light scattering by horizontally oriented spheroidal particles
Shoji Asano
Applied Optics Vol. 22, 9, p. 1390 (May 1983) OSA Optics InfoBase
Light scattering properties of spheroidal particles oriented randomly with their long axes in the horizontal are studied. A computational scheme has been developed to calculate the scattering matrices as well as the extinction and scattering cross sections and asymmetry factors in a manner consistent with our previous treatment of 3-D orientations. The single scattering properties strongly depend on the elevation angle of incident light. The dependence of the extinction and scattering cross sections is particularly prominent, while the dependence of the single scattering albedo and asymmetry factor is rather small but still significant. For a given elevation angle, the scattered intensity is a function of not only the scattering angle but also the azimuth angle of emergence. Implications of the anisotropic scattering by horizontally oriented nonspherical particles with respect to the elevation angle are also discussed.

Effects of the El Chichon volcanic cloud in the stratosphere on the polarization of light from the sky
Kinsell L. Coulson
Applied Optics Vol. 22, 7, p. 1036 (April 1983) OSA Optics InfoBase
A dense volcanic cloud from the El Chichon volcanic eruption has been observed in the stratosphere over Hawaii since it was first discovered at the Mauna Loa Observatory 9 Apr. 1982. Lidar observations have shown the cloud to have been dense and highly layered in its early stages, but as the cloud matured it became more homogeneous and the top portion underwent considerable enhancement. Measurements of the degree of polarization of skylight at the zenith and across the sky in the sun's vertical show that the polarization field is strongly modified by the effects of the cloud and that the modifications are of a different nature from those produced by high turbidity in the lower layers of the atmosphere. The degree of polarization at the zenith during twilight shows a secondary maximum at a solar depression D = 4.8-5°, a secondary minimum at D = 4, a primary maximum at D = 1-2°, and a rapid decrease to values generally <10% in the immediate sunrise period. The positions of the neutral points are strongly affected by the cloud, the Arago point being shifted from its normal position by as much as 15-20° and the Babinet point being shifted even farther. Multiple Babinet points were observed on some occasions. The measurements indicate the polarization field to be modified more by the El Chichon cloud than it was by the clouds from previous eruptions which have occurred during this century.

Effects on skylight at South Pole Station, Antarctica, by ice crystal precipitation in the atmosphere
Bruce W. Fitch and Kinsell L. Coulson
Applied Optics Vol. 22, 1, p. 71 (January 1983) OSA Optics InfoBase
Measurements of the radiance and polarization of the skylight at South Pole Station, Antarctica, were made for clear cloud-free skies and cloudless skies with ice crystal precipitation. The measurements were made at six narrowband wavelengths from 321 to 872 nm in the principal plane. The data show that scattering by ice crystals increases the radiance in the backscatter plane, decreases it in the solar plane, and shifts the radiance minfimum to a point closer to the sun. The crystals decrease the maximum value of linear polarization and shift the position of the maximum away from the sun. The influence of ice crystal scattering is greatest at the longer wavelengths.


Polarized light scattering by hexagonal ice crystals: theory
Qiming Cai and Kuo-Nan Liou
Applied Optics Vol. 21, 19, p. 3569 (October 1982) OSA Optics InfoBase
A scattering model involving complete polarization information for arbitrarily oriented hexagonal columns and plates is developed on the basis of the ray tracing principle which includes contributions from geometric reflection and refraction and Fraunhofer diffraction. We present a traceable and analytic procedure for computation of the scattered electric field and the associated path length for rays undergoing external reflection, two refractions, and internal reflections. We also derive an analytic expression for the scattering electric field in the limit of Fraunhofer diffraction due to an oblique hexagonal aperture. Moreover the theoretical foundation and procedures are further developed for computation of the scattering phase matrix containing 16 elements for randomly oriented hexagonal crystals. Results of the six independent scattering phase matrix elements for randomly oriented large columns and small plates, having length-to-radius ratios of 300/60 and 8/10 gm, respectively, reveal a number of interesting and pronounced features in various regions of the scattering angle when a visible wavelength is utilized in the ray tracing program. Comparisons of the computed scattering phase function, degree of linear polarization, and depolarization ratio for randomly oriented columns and plates with the experimental scattering data obtained by Sassen and Liou for small plates are carried out. We show that the present theoretical results within the context of the geometric optics are in general agreement with the laboratory data, especially for the depolarization ratio.

Rainbow brightness
Stanley David Gedzelman
Applied Optics Vol. 21, 16, p. 3032 (August 1982) OSA Optics InfoBase
A theory for the brightness of rainbows is presented. The light reaching the observer consists of a beam of singly scattered sunlight, originating from the directly illuminated portion of a rainswath, which, in turn, has suffered depletion by scattering or absorption in its path through the atmosphere. The model incorporates the relevant features of cloud geometry and solar position in relation to the observer appropriate to rainbows. The model helps explain why the bottom (or near-horizon portion) of the rainbow tends to be both brighter and redder than the top (or horizontal portion furthest above the ground) when the sun is near the horizon. The greater brightness of the bottom of the bow derives principally from the greater length of the directly illuminated part of the rainswath near the horizon, while the increased redness of the bow’s bottom is due to the severe depletion of the short-wavelength contribution to the rainbow beam in its passage through the atmosphere.

Glory in backscattering: Mie and model predictions for bubbles and conditions on refractive index in drops
Philip L. Marston and Dean S. Langley
J. Opt. Soc. Am., Vol. 72, No. 4, p. 456 (April 1982) OSA Optics InfoBase
Mie calculations illustrate the dependences of scattered intensity on polarization, angle, and size for bubbles with radii ~0.3 mm in a siloxane liquid. Computations give evidence of the axial focusing observed in recent experiments and predicted by a model. Conditions for glory rays in drops and bubbles are derived, and errors in the literature are noted.


Zenith polarization and color ratio during twilight
Frederic E. Volz
Applied Optics Vol. 20, 24, p. 4172 (December 1981) OSA Optics InfoBase
The excellent data of zenith polarization and color ratio (CR) during twilight obtained by Coulson at the Mauna Loa Observatory, Hawaii are subjected to a reinterpretation, especially with regard to the frequent deviations from the clear average. It is shown that a moderate lift of the earth's shadow by distant clouds (or by low level haze) will reduce the red/green CR, while greater lift shifts the CR peak to a smaller solar depression. The effect on zenith polarization at wavelengths >0.6 /Am is seen to correspond to a slight reduction of overall'polarization for a moderate lift, and for a large lift to a shift of the polarization minimum (depolarization by stratospheric aerosol) from 40 solar depression angle to 2°. A generally high level of polarization, but with a barely noticeable 4° minimum, had also been observed earlier in Germany by Steinhorst when the stratospheric aerosol load was very small. The difference is explained by a higher and stronger aerosol layer in the tropics combined with a higher and cleaner troposphere.

Novaya Zemlya effect: analysis of an observation Free download
W. H. Lehn and B. A. German
Applied Optics Vol. 20, 12, p. 2043 (June 1981) OSA Optics InfoBase
The Novaya Zemlya effect, historically identified with the premature rebirth of the sun during the polar night, is a long range optical ducting phenomenon in the lower atmosphere. An occurrence of the effect was observed at Tuktoyaktuk, Canada (69 026'N, 133 002'W) on 16 May 1979, when the minimum solar altitude was -1°34'. The sun's image remained above the horizon, within a gray horizontal band, and assumed the various expected shapes, ranging from a bright rectangle filling the band, to three flat suns stacked one over the other, to several thin vertically separated strips. A model for the corresponding atmospheric conditions was identified by matching the observations with images calculated from a computer simulation study.

Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity. 2: Intensity and color ratio
Kinsell L. Coulson
Applied Optics Vol. 20, 9, p. 1516 (May 1981) OSA Optics InfoBase
This is the second of two papers based on an extensive series of measurements of the intensity and polarization of light from the zenith sky during periods of twilight made at an altitude of 3400 m on the island of Hawaii. Part 1 dealt with the skylight polarization; part 2 is on the measured intensity and quantities derived from the intensity. The principal results are that (1) the polarization and intensity of light from the zenith during twilight are sensitive indicators of the existence of turbid layers in the stratosphere and upper troposphere, and (2) at least at Mauna Loa primary scattering of the sunlight incident on the upper atmosphere during twilight is strongly dominant over secondary or multiple scattering at wavelengths beyond -0.60 in whereas this is much less true at shorter wavelengths. It is suggested that the development and general use of a simple twilight polarimeter would greatly facilitate determinations of turbidity in the upper layers of the atmosphere.

Zenith sky brightness and airglow emissions during the equatorial solar eclipse of 30 June 1973
E. H. Carman, N. J. Skinner, and M. P. Heeran
Applied Optics Vol. 20, 5, p. 778 (March 1981) OSA Optics InfoBase
Experimental and calibration procedures used for photometric zenith measurements at Loiyengalani (2.75 0N, 36.61E) during the total solar eclipse of 30 June 1973 are described briefly. Comparison was made between sky brightness at wavelengths in the 3914-6300-A range during totality and morning twilight at Dar es Salaam. The twilight 3914- and 6300-A sky background ratio is sometimes close to the expected value for a pure Rayleigh molecular scattering process, but the corresponding ratio at eclipse mid-totality is about one-third this, indicating a shift toward the red consistent with an atmosphere containing aerosols. The zenith sky brightness at 5600 A was <1 kR/A, somewhat lower than has been observed at low latitudes during the past 50 years. Comparison of the 6300-A line emission rate of 1.4 + 0.6 kR with the Jan. 1974 Atmosphere Explorer satellite dayglow analysis suggests the main source of O(1)D atoms during totality is by excitation of 0(3p) atoms in the lower thermosphere. About 1 kR of 5577 A was also observed, but the 5200-A emission was too low for reliable detection. An unexpectedly high 3914-A emission rate of at least 1 kR was apparent, the high rate being supported by observation at 4278 A.


Atmospheric phenomena before and during sunset
M. Menat
Applied Optics Vol. 19, 20, p. 3458 (October 1980) OSA Optics InfoBase
The atmospheric transmittance and the astronomical refraction for low-elevation trajectories are discussed and quantitatively developed. The results are used to describe and calculate some of the fascinating atmospheric phenomena occurring shortly before and during sunset, such as the diminishing apparent luminance of the sun, its shape during sunset, and the green flash.

Characteristics of skylight at the zenith during twilight as indicators of atmospheric turbidity. 1: Degree of polarization
Kinsell L. Coulson
Applied Optics Vol. 19, 20, p. 3469 (October 1980) OSA Optics InfoBase
An extensive series of measurements of the intensity and polarization of the light from the zenith sky during periods of twilight was made at an altitude of 3400 m on the island of Hawaii during a 5-month period in 1977. This first of two papers is on the twilight polarization; the second will deal with intensity. The measurements were made in eight narrow spectral ranges between 0.32 and 0.90 Azm under clear sky conditions. The data show that the degree of polarization at the zenith is a sensitive indicator of the existence of turbid layers at high levels in the atmosphere, and by monitoring the zenith skylight as a function of time during the twilight, it is possible to obtain qualitative information on both the altitude and relative density of the layers.

Analytic foundations of halo theory Free download
Walter Tape
J. Opt. Soc. Am., Vol. 70, No. 10, p. 1175 (October 1980) OSA Optics InfoBase
This article develops a unified approach to the computation of refraction ice crystal halos and their caustics. An explicit formula is given for the halo function, that is, the function that expresses points of light on the celestial sphere as a function of crystal orientation. Restricting the halo function to various subsets of its domain produces different halos. The caustic of a halo is the image of the set of singular points of the (suitably restricted) halo function. Computation of the kernel of the Jacobian of the unrestricted halo function leads to a general approach to the construction of caustics of arbitrary halos. The halos used as examples are circular halos, upper and lower tangent arcs, infralateral and supralateral arcs, Lowitz arcs, and parhelia. The above methods are used to generate computer plots of several of these halos and their caustics, together with the sets of crystal orientations responsible for the halos.

Visibility of halos and rainbows
Stanley David Gedzelman
Applied Optics Vol. 19, 18, p. 3068 (September 1980) OSA Optics InfoBase
A theory for the visibility of halos and rainbows is presented. The light reaching the observer's eye from the direction of the halo or rainbow is assumed to consist of two parts: (1) a beam of singly scattered sunlight (or moonlight) from a cloud of ice crystals or a rainswath, which, in turn, has suffered depletion by scattering or absorption in its passage to the observer, and (2) the general background brightness. The model is able to account for several long-known qualitative observations concerning halos, namely, that the brightest halos are produced by optically thin cirrostratus clouds (i.e., for which the cloud optical depth Tc< 1) and that when the sun is low in the sky the top of the halo is visible much more frequently than the bottom. (This is shown to result in good part from extinction by the turbid atmosphere.) With the rainbow the brightness of the beam increases monotonically with the optical depth Tr of the sunlit part of the rainswath, but the increase is quite small for Tr >= 1. On the other hand, the brightness of the background increases more rapidly with Tr for Tr > 1 so that the rainbow appears most easily visible for Tr < 1. This implies that the most easily visible rainbows are produced by light or moderate showers rather than heavy downpours. Finally, suggestions are made for applying the theory to other atmospheric optical phenomena, such as coronas and glories.

Analytic sun pillar model
Alistair B. Fraser and Gary J. Thompson
J. Opt. Soc. Am., Vol. 70, No. 9, p. 1145 (September 1980) OSA Optics InfoBase
An analytic sun pillar model is developed which indicates that large hexagonal ice columns can cause sun pillars. The model shows that the Stuchtey method for explaining sun pillars is not incorrect, only incomplete. The model uses an expression for the intensity of the sun pillar that considers both the optical mapping of light for a single crystal orientation and for the probability of having that particular orientation. The model, which is extended to a sun of finite size, clearly shows that the portion of the pillar that is seen above the horizon is brightest when the sun is below the horizon.

Mountain shadow phenomena. 2: The spike seen by an off-summit observer Free download
David K. Lynch
Applied Optics Vol. 19, 10, p. 1585 (May 1980) OSA Optics InfoBase
The oblique spike or contrast edge seen by an off-summit observer on a mountain shadow when the sun is low is shown to be a perspective effect that depends on the observer's position within the shadow. The degree of visibility of the shadow is due to contrast effects between differently illuminated aerosols. Numerical simulations are used to demonstrate these points.

Rainbow phenomena and the detection of nonsphericity in drops
Philip L. Marston
Applied Optics Vol. 19, 5, p. 680 (March 1980)
Liquid drops were levitated and deformed with acoustic techniques and illuminated with monochromatic light. Changes in the rainbow-angle scattering induced by the deformations were detected. Reflected and rays form an interference pattern that changes with shape and the angle of Airy's diffraction pattern shifts. A calculation by W. Mobius [Ann. Phys. (Leipzig) 33, 1493 (1910)] was modified to facilitate the use of these changes for the measurement of micron amplitude shape oscillations of millimeter radius drops.

Marcel Minnaert and optics in nature
W. C. Livingston
Applied Optics Vol. 19, 5, p. 648 (March 1980) OSA Optics InfoBase
This historical note was presented at the OSA Topical Meeting on Meteorological Optics held at Keystone in August 1978. It seemed appropriate to publish it in the issue that gathered together some related papers given at the other Keystone meeting last August, on atmospheric spectroscopy, but that honorable intention was thwarted because the author wanted to do some more work on his manuscript. We now publish a revision of the introductory comments given at Keystone. Some of the meteorological optics papers have been published in the Journal of the Optical Society of America.


Observations of eclipse shadow bands and related phenomena
E. J. Seykora
Applied Optics Vol. 18, 21, p. 3538 (November 1979) OSA Optics InfoBase
No abstract

Airglow events visible to the naked eye
Alan W. Peterson
Applied Optics Vol. 18, 20, p. 3390 (October 1979) OSA Optics InfoBase
During IR photographic airglow observations covering several years, three naked-eye events have been recorded. Two of these are moving, luminous acoustic gravity wave groups of some 10-15-km wavelength, which occur near high lunar tide in the atmosphere. The events appear quickly, endure 0.5-1 h, then fade. Visible photos of two events appear enhanced while little enhancement is present in the IR photos, although the structures are well correlated. If these events are due to OH, we suggest that some unrecognized mechanism, perhaps a gravity wave interaction, enhances the visible transitions of the OH over the IR transitions. If the events are due to an unrecognized continuum emitter, perhaps NO, its emission must occur at the same height as the OH. Spectra seem to be the only reasonable approach to solving this problem.

Feature issue: Journal of Optical Society of America, August 1979

Polarization and scattering characteristics in the atmospheres of Earth, Venus, and Jupiter
David L. Coffeen
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1051 August 1979 OSA Optics InfoBase
Our understanding of atmospheric scattering phenomena has increased through the combined developments of new electro-optical instrumentation, theoretical solutions for complex model atmospheres, and large computers enabling computation of such solutions. Earth satellites permit external, planetwide observations of our atmosphere, while spacecraft permit detailed measurements of the scattering by other planetary atmospheres. Some recent results are: elucidation of the effects of ozone absorption and high-altitude aerosol scattering on twilight colors and polarization; identification of a cloudbow on Venus and consequent deduction of the cloud particle shape, size distribution, and refractive index; and, the interpretation of Rayleigh scattering on Jupiter in terms of cloud-top topography.

Visual observations from space
Owen K. Garriott
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1064 August 1979 OSA Optics InfoBase
Visual observations from space reveal a number of fascinating natural phenomena of interest to meteorologists and aeronomists, such as aurorae, airglow, aerosol layers, lightning, and atmospheric refraction effects. Other man-made radiation, including city lights and laser beacons, are also of considerable interest. Of course, the most widely used space observations are of the large-scale weather systems viewed each day by millions of people on their local television. From lower altitudes than the geostationary meteorological satellite orbits, obliques and overlapping stereo views are possible, allow height information to be obtained directly, often a key element in the use of the photographs for research purposes. However, this note will discuss only the less common observations mentioned at the beginning of this paragraph.

Complex angular momentum theory of the rainbow and the glory
H. M. Nussenzveig
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1068 August 1979 OSA Optics InfoBase
A survey is given of the applications of complex angular momentum theory to Mie scattering, with special emphasis on the recent treatments of the rainbow and the glory. The theory yields uniform asymptotic expansions of the scattering amplitudes for rainbows of arbitrary order, for size parameters >~ 50, in close agreement with the exact results. The Airy theory fails for parallel polarization in the primary bow and for both polarizations in higher-order rainbows. The theory provides for the first time a complete physical explanation of the glory. It leads to the identification of the dominant contributions to the glory and to asymptotic expressions for them. They include a surface-wave contribution, whose relevance was first conjectured by van de Hulst, and the effect of complex rays in the shadow of the tenth-order rainbow. Good agreement with the exact results is obtained. Physical effects that play an important role include axial focusing, cross polarization, orbiting, the interplay of various damping effects, and geometrical resonances associated with closed or almost closed orbits. All significant features of the glory pattern found in recent numerical studies are reproduced.

Iridescence in an aircraft contrail
Kenneth Sassen
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1080 August 1979 OSA Optics InfoBase
The available diffraction-corona theory for the interpretation of the cloud iridescence phenomenon is reviewed and applied to photographic observations of an iridescent contrail. It is concluded that the simple-diffraction theory qualitatively explains the occurrence of corona and iridescence under the cloud microphysical conditions with which these phenomena are typically associated, and that the theoretical predictions of cloud droplet diameters of 1-3 um during initial contrail formation appear to be reasonable for a highly supersaturated environment. However, additional Mie theory simulations utilizing narrow droplet size distributions should be performed to assess the impact of anomalous diffraction in realistic cloud compositions in order that iridescence observations may be more precisely interpreted for cloud microphysical studies.

Angular scattering and rainbow formation in pendant drops
Kenneth Sassen
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1083 August 1979 OSA Optics InfoBase
Angular scattering measurements obtained with a polar nephelometer employing a linearly polarized laser source are used to examine the general scattering behavior and rainbow generation of pendant water drops, a type of near-spherical particle that has certain similarities to the shape of distorted raindrops. Comparison of the experimental data with theoretical predictions of spherical drop scattering reveals that in many respects the near-spherical particles behave like spheres when the measurements are performed in the horizontal scattering plane, the plane in which the drops display circular cross sections. Furthermore, the angular positions of the rainbow intensity maxima corresponding to the main rainbow peak and supernumerary bows are shown to be predicted accurately by the approximate Airy theory for both the primary and secondary rainbows. Pendant drops whose shapes are significantly elongated in the vertical direction are indicated to generate anomalously strong rainbows from three or more internal reflections. The implications of these findings to rainbow formation in the atmosphere are discussed.

Theory of the rainbow
S. D. Mobbs
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1089 August 1979 OSA Optics InfoBase
A new theory of the rainbow based on Huygens's principle is given and compared with the complex angular momentum theory. There is good agreement over a large range of angles and size parameters for both the magnetic and electric polarizations.

Arcs associated with halos of unusual radii
R. A. R. Tricker
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1093 August 1979 OSA Optics InfoBase
A display of halos of unusual radii occurred on 14 April 1974, and was visible in southern England and in Holland. Photographs of the display were taken by Professor Scorer and the present author was privileged to examine them. They showed not only circular halos but also arcs tangential to some of them. The investigation described in the following paper was undertaken to try to elucidate the mechanisms by which these arcs might be formed. It led to a new theory of the formation of circular halos and also of the tangential or quasitangential arcs associated with them. It also led to a picture of the shape of the ice crystals giving rise to this particular display.

Polarization models of halo phenomena. 1. The parhelic circle Free download
David K. Lynch
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1100 August 1979 OSA Optics InfoBase
An optical model of the parhelic circle is computed which includes the Stokes parameters of polarization. The model is based on one of two closely related mechanisms in crystals which are known to exist in cirrus clouds. An analysis of the circumstances of occurrence shows that one mechanism - external reflection from the side faces of ice crystal plates with c axes vertical-probably generates most parhelic circles.

Arcs of Lowitz
James R. Mueller, Robert G. Greenler and A. James Mallmann
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1103 August 1979 OSA Optics InfoBase
A computer simulation technique is used to investigate the origins of the arcs of Lowitz. The model explored consists of light passing through a hexagonal ice plate, spinning about a major diagonal axis that remains horizontal as the crystal falls.

Origins of anthelic arcs, the anthelic pillar, and the anthelion
A. James Mallmann, Robert G. Greenler
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1107 August 1979 OSA Optics InfoBase
The existence of hexagonal, pencil-shaped ice crystals that fall with their long axes horizontal is well established. We have used a computer simulation technique to examine the consequences of five mechanisms suggested in the literature to explain the origins of anthelic arcs. The results show that pencil crystals with horizontal axes may be responsible for the anthelic arcs, the anthelic pillar, and the anthelion.

What size of ice crystals causes the halos?
Alistair B. Fraser
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1112 August 1979 OSA Optics InfoBase
It is shown that, contrary to classical theory, the circular halos need not be caused by randomly oriented crystals. Furthermore, if Brownian motion is the disorienting mechanism then the circular halos cannot be caused by the randomly oriented crystals, which are too small to produce a reasonably sharp diffraction pattern. However, the circular halos can be caused by crystals that are in the region where there is a transition between randomness and high orientation. These crystals have diameters between about 12 and 40 µm. Larger crystals produce the parhelia and tangent arcs. It is shown that the 46° halo is rare because it can be produced only by solid columns, and then for only a restricted range of sun heights.

Frequency analysis of the circumzenithal arc: Evidence for the oscillation of ice-crystal plates in the upper atmosphere
Robin S. McDowell
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1119 August 1979 OSA Optics InfoBase
The results of a quantitative treatment of the visibility of the circumzenithal arc as a function of solar elevation are compared with records of the arc's occurrence in France and the Netherlands, 1894-1931. Both calculated and observed frequency distributions peak at a solar elevation of 22° (minimum deviation), and the width of the observed frequency distribution can be closely matched with the assumption that plate ice crystals in quiet air undergo oscillations of around 1° from equilibrium. This result agrees with other estimates based on studies of the subsun and parhelic circle. The circumzenithal arc is shown to be vertically polarized, with I vert/ I horz = 1.4 in the solar vertical near minimum deviation.

Geometry of halo formation Free download
Walter Tape
J. Opt. Soc. Am., Vol. 69, No. 8, p. 1122 August 1979 OSA Optics InfoBase
The formation of many ice crystal halos can be visualized in an appropriate coordinate system on the sphere. A given crystal orientation is first represented by a point on the sphere. When the same sphere is regarded as the celestial sphere, it is easy to find the point of light on the sphere that results from the given crystal orientation. The analysis gives crude information on intensities of halos, not just along the caustic curve but for the entire sky.

Polarized rainbow Free download
G. P. Können and J. H. de Boer
Applied Optics Vol. 18, 12, p. 1961 (June 1979) OSA Optics InfoBase
The Airy theory of the rainbow is extended to polarized light. For both polarization directions a simple analytic expression is obtained for the intensity distribution as a function of the scattering angle in terms of the Airy function and its derivative. This approach is valid at least down to droplet diameters of 0.3 mm in visible light. The degree of polarization of the rainbow is less than expected from geometrical optics; it increases with droplet size. For a droplet diameter >1 mm the locations of the supernumerary rainbows are equal for both polarization directions, but for a diameter <1 mm the supernumerary rainbows of the weaker polarization component are located between those in the strong component.

Origin of the anthelion Free download
David K. Lynch, Pt. Schwartz
J. Opt. Soc. Am., Vol. 69, No. 3, p. 383 March 1979 OSA Optics InfoBase
The formation of the anthelion is discussed. Previous theories by Bravais, Humphreys, and others are shown to be imcompatible with observation, or highly improbable. An explanation is set forth in which the anthelion is formed in common hexagonal columns with the c axis horizontal and with two side faces vertical. Light enters an upper oblique face, is reflected twice by the end and opposite vertical face, then emerges from the crystal through the lower oblique face on the same side of the crystal it entered. In agreement with the observations, this mechanism produces no anthelion when the solar elevation is greater than 46'.

Mountain shadow phenomena Free download
William Livingston and David Lynch
Applied Optics Vol. 18, 3, p. 265 (February 1979) OSA Optics InfoBase
Regardless of profile, whether flat topped or pointed, to the summit observer all mountain peaks cast triangular shadows when the sun is low. A theory for such anomalous shadows is developed. The shadow apex angle is shown to depend only on the ratio of the breadth of the mountain to its height.


Ray tracing theory and mirage occurrence conditions
E. Woyk (Chvojkova)
Applied Optics Vol. 17, 13, p. 2108 (July 1978) OSA Optics InfoBase
The new ray tracing theory, deduced from geometrical optics and widely developed for radio propagation in cosmic atmospheres, is now applied to optics. This paper is confined to the duct mode propagation which represents a singularity. A narrow horizontal beam emitted inside the waveguide can propagate a long path around the earth with very good periodic focusing: the central circular path coincides with the stratification of the atmosphere while rays above or below it are more or less curved. Perfect symmetry is not needed; but two specific conditions must be satisfied, and their occurrence just coincides with conditions under which mirages occur: a quiet mirage with sharp contours, evidently not much affected by scatter, occurs only during a temperature inversion, above a large hot desert, above a hot rather convex asphalt road, or (under convenient conditions) above a quiet level sea, which means only when favorable conditions establish the very sporadically occurring waveguide. A density maximum need not occur at all.

Sky radiance during a total solar eclipse: a theoretical model
Glenn E. Shaw
Applied Optics Vol. 17, 2, p. 272 January 1978 OSA Optics InfoBase
This paper describes a radiative transfer model for estimating the brightness or radiance of the sky during a total solar eclipse. The model is approximate; it only considers sunlight that diffuses into the umbra by first- and second-order scattering processes. It nevertheless correctly predicts the major observed features of the eclipsed sky including reddening of the horizon and lowering of zenith radiance over the normal day value by approximately 4 orders of magnitude. The calculated absolute zenith radiance at blue wavelength is about 20% lower than observed during the 1973 African solar eclipse. The model predicts, and observations confirm, that the zenith has the highest blue-red ratio (color temperature) and lowest brightness of any place in the sky during totality.


Optical backscattering from near-spherical water, ice, and mixed phase drops
Kenneth Sassen
Applied Optics Vol. 16, 5, p. 1332 May 1977 OSA Optics InfoBase
An experimental assessment of the scattering behavior of freely falling artificial raindrops and mechanically suspended drops in the ice and mixed phase has been undertaken with a device which simultaneously measures the parallel and cross polarized components of backscattered linearly polarized laser light (6328 A). Among the findings are that linear depolarization ratios (D) are generally <0.01 for raindrops up to nearly 6 mm diam, near 0.5 for regularly shaped frozen drops, and between 0.35 and 1.0 for more irregular ice particles. Anomalous scattering behavior has been observed during the liquid to solid drop phase transition (D > 1.0) and in the relatively great amounts of parallel polarized energy returned from raindrops > 4 mm. Backscattered signal variations produced during drop melting reveal that D values tend to remain near the initial ice value until most of the ice has changed phase. The details of the variations aid in the determination of the dominant scattering mechanisms responsible for the backscatter from large, near-spherical particles. The results are shown to have some bearing on measurements of atmospheric hydrometeors obtained by lidar.

Solutions of the refraction and extinction integrals for use in inversions and image formation
Alistair B. Fraser
Applied Optics Vol. 16, 1, p. 160 January 1977 OSA Optics InfoBase
Analytic solutions to the refraction and extinction integrals are presented for the case of a horizontally or spherically stratified medium. These solutions are not only useful for the calculation of the images that would be seen through a lens with a continuously varying index of refraction, such as the atmosphere, they also provide a solution to the inverse problem of determining the refractive structure from measurements of the image. A remarkably simple inversion scheme is presented for determining the refractive (temperature) structure of the earth's atmosphere by observations of the setting sun. The same scheme works for determination of vertical profiles of the extinction coefficient.

Geometrical optics of inhomogeneous particles: glory ray and the rainbow revisited
C. L. Brockman, Jr., and N. G. Alexopoulos
Applied Optics Vol. 16, 1, p. 166 January 1977 OSA Optics InfoBase
The glory ray and the rainbow are analyzed by considering the scattering of light from inhomogeneous particles. It is shown that melting ice crystals may be strong contributors to the glory ray. Geometrical optics is used to investigate and catalog a wide variety of particle inhomogeneities which support rainbow and glory rays.


Sky color near the horizon during a total solar eclipse
Stanley David Gedzelman
Applied Optics Vol. 14, 12, p. 2831 (December 1975) OSA Optics InfoBase
A theory for the color of the sky near the horizon for an observer in the umbral region of a total solar eclipse is presented. The model uses a Rayleigh scattering atmosphere, and the light reaching the observer is a beam of singly scattered sunlight, which, in turn, has suffered depletion by scattering in its passage from outside the shadow region. The model predicts both the red color observed in the lowest 8° of the sky for the total solar eclipse of 30 June 1973 and the enriched blue color of the sky at any elevation angle greater than the solar elevation angle. The model is also adapted to explain the reddening of the horizon sky observed during such times as when a dark cloud passes overhead or when the light from a large city is seen from the distance at night.

Sky brightness during eclipses: a review
S. M. Silverman and E. G. Mullen
Applied Optics Vol. 14, 12, p. 2838 (December 1975) OSA Optics InfoBase
This paper is abstracted from the introductory section of "Sky Brightness During Eclipses: A Compendium from the Literature," AFCRL-TR-74-0363, Special Reports 180, Air Force Cambridge Research Laboratories, Hanscom AFB, Massachusetts 01731. This report should be consulted for fuller details and tables.

Sky Brightness and Polarization During the 1973 African Eclipse
Glenn E. Shaw
Applied Optics Vol. 14, 2, p. 388 (February 1975) OSA Optics InfoBase
The absolute intensity, color, and polarization of the sky were measured during the eclipse of 30 June 1973 in Northern Kenya. Zenith sky radiance during totality decreased by a factor of 104 from the normal day sky value. The distribution of sky intensity with angle on the celestial hemisphere was approximately symmetrical about the local zenith, with this point having the minimum intensity value. The spectral distribution of zenithal diffuse skylight shifted toward the blue during totality, but the horizon reddened. The polarization ratio P decreased from a normal day value of 0.45 to 0.04. There is evidence that the distribution of polarization ratio is strongly affected by variations in surface albedo. The major results are compatible with predictions based on a radiative transfer model that considers double-scattering processes only.


Summary of Sky Brightness Measurements During Eclipses of the Sun
W. E. Sharp, S. M. Silverman, and J. W. F. Lloyd
Applied Optics Vol. 10 , 6, p. 1207 (June 1971) OSA Optics InfoBase
A selected group of measurements of the sky brightness during total solar eclipses is used to determine a standard light curve during the period from no obscuration to totality. It is found that the sky light may be considered as attenuated sunlight up to at least 99.8% obscuration. During totality, the sky light consists of multiply scattered light from outside the umbral region. The effects of solar elevation angle, cloud cover, and albedo and the variability of the light curve during totality are discussed.

Zenith Sky Brightness and Color Change During the Total Solar Eclipse of 12 November 1966 at Santa Ines, Peru
D. A. Velasquez
Applied Optics Vol. 10 , 6, p. 1211 (June 1971) OSA Optics InfoBase
This paper reports observations of the zenith sky brightness around totality at 5580 i and 6300 during the eclipse of 12 November 1966. The observations were carried out at Santa Ines, Huancavelica, Peru, using interference filter photometers. The color change and the variation of the sky brightness at zenith were determined and are presented.

Measurements of the Zenith Sky Intensity and Spectral Distribution During the Solar Eclipse of 12 November 1966 at Bage, Brazil, and on an Aircraft
J. W. F. Lloyd and S. M. Silverman
Applied Optics Vol. 10 , 6, p. 1215 (June 1971) OSA Optics InfoBase
Measurements of the zenith sky intensity and spectral distribution during the solar eclipse of 12 November 1966 at Bage, Brazil, and on an aircraft over the Atlantic are reported. These, together with measurements reported elsewhere from Santa Ines, Peru, and Quehua, Bolivia, are used to define the intensities and changes in spectral distribution during totality and to discuss the dependence of these on such factors as height and terrain.

Day Sky Brightness and Polarization During the Total Solar Eclipse of 7 March 1970
B. S. Dandekar and J. P. Turtle
Applied Optics Vol. 10 , 6, p. 1220 (June 1971) OSA Optics InfoBase
Zenith sky brightness at totality was observed to be about four orders of magnitude lower than that for a normal day sky. The spectral distributions in terms of an effective blackbody temperature for the range 4100-8000 A were 5000 K, 9000 K, and 11,000 K for the twilight, control day sky, and totality, respectively, indicating a shift toward the shorter wavelength at totality. The polarization measured in the sun's vertical plane 90° away from the sun was 4% and 0.6% at 4750 i and 6000 A, respectively. Both colors showed a change in the plane of polarization of about 500 at the time of totality. From the change in the plane of polarization it is estimated from the primary component reduced by about an order of magnitude at totality of the eclipse.

Spectral Changes in the Zenith Skylight During Total Solar Eclipses
W. N. Hall
Applied Optics Vol. 10 , 6, p. 1225 (June 1971) OSA Optics InfoBase
The relative spectral intensity of the zenith sky was measured with an optical scanning spectrometer at Nantucket Island, Massachusetts, during the total solar eclipse of 7 March 1970. The spectral ratios I(5100 A)/I(4300 A) and I(5900 A)/I(5100 A) at Nantucket remained unchanged for 96% or less obscuration of the sun by the moon. The results are compared with other recent relative spectral intensity measurements made during total solar eclipses. Comparison with other eclipse measurements for solar elevation angle at totality less than 45° shows a blue color shift consistent with rayleigh scattering. Eclipses with solar elevation angles at totality greater than 45° do not show consistent color shifts. This inconsistency may be due to difficulty in establishing a suitable reference spectrum for comparison with the spectral distribution of the zenith sky at totality. Selection of a suitable reference spectrum is discussed.


Unusual or Neglected Optical Phenomena in the Landscape
M. G. J. Minnaert
J. Opt. Soc. Am., Vol. 58, No. 3, pp. 297-303 (March 1968) OSA Optics InfoBase
As examples of unusual optical phenomena, some observations of multiple suns and moons are described. They are corroborated by photography; older observations now appear to be genuine. A number of examples are further quoted: shadows, reflections, green flash, halo phenomena, rainbows, iridescent clouds, colors in thin sheets of ice, accidental double refraction. Then some observations are made about physiological optics, relating to contrast and to the perception of flicker and colors.

Der Regenbogen in Wissenschaft und Kunst
S. Rosch
Applied Optics Vol. 7, 2, p. 233 (February 1968) OSA Optics InfoBase
New ideas and calculations about angles are presented, particularly about the degree of polarization of the first twenty rainbows, and it is proved why never more than two rainbows can be seen in the sky. The general sky brightness of the rainbow neighborhood is calculated with the Fresnel reflection formulas. It is shown that for certain refraction indices the first one or each of the higher rainbows can be polarized completely and that with a rising n there is an upper limit of existence for each one of them. This is clearly shown by diagrams. The standard of the exact color finding on rainbows is described with special emphasis on the fact that the loss of saturation, due to light reflected by waterdrops, must be considered. Some special features of rainbows mentioned in literature are pointed out and the importance of this phenomenon in constructive art, folklore, and religion is discussed.


Direct observation of surface waves on droplets
T. S. Fahlen and H. C. Bryant
J. Opt. Soc. Am., Vol. 56, No. 11, pp. 1635–1636 (November 1966)
The explanation of the glory phenomenon, or the pronounced backscattering of light from water droplets, requires that a toroidal wavefront be introduced having an exegisis beyond the scope of geometrical optics. This toroidal wavefront is supposed to be due to "surface" or "creeping" waves which travel around the droplet, perhaps through many circumferences, sending off tangential rays all along, which are in phase and unidirectional, however, only in the direct forward and backward directions. Recent calculations, based on the Mie theory, have confirmed the importance of surface waves in producing the glory phenomenon.

Mie Theory and the Glory
H. C. Bryant and A. J. Cox
J. Opt. Soc. Am., Vol. 56, No. 11, pp. 1529-1532 (November 1966)
Results are presented of the predictions of Mie's series solution to the scattering of an electromagnetic plane wave from a dielectric sphere of index 1.333. Cases of size parameters near 200 and 500 are examined in detail in an attempt to understand the mechanism responsible for the backscattering of light. These calculations demonstrate that the backscattering is due mainly to the last few significant terms in the Mie expansion, which can be associated with geometrical rays grazing the droplet surface, or "surface waves." Sharp periodic spikes in the dependence of the backscattered intensity are shown to be associated with very slightly damped surface waves of both polarizations involving hundreds of circumvolutions. The geometrically computed axial contribution to the backscattered light is shown to be present in the Mie results.

Zenith Skylight Intensity and Color during the Total Solar Eclipse of 20 July 1963
William E. Sharp, John W. F. Lloyd and S. M. Silverman
Applied Optics Vol. 5, 5, p. 787 (May 1966) OSA Optics InfoBase
The zenith skylight intensity was measured, with a resolution of 10 A, over the wavelength range from 5200 A to 6400 A during a total solar eclipse at Hermon, Maine. The intensity was found to change by about two orders of magnitude in the 2-min period before totality and reached a minimum during totality of 19.5 kR/A at 5200 A. The spectral distribution remained that of the day sky until the sun was more than 99.8% obscured. During totality, the shorter wavelengths were enhanced, indicating a shift to the blue in sky color. Comparisons with an independent measurement from an aircraft show that the intensity scale height of the secondary scattered component, predominating at totality, is significantly less than that of the day sky. The measurements are compared with the day and twilight sky.


Sky Brightness as a Function of Altitude
J. V. Hughes
Applied Optics Vol. 3, 10, p. 1135 (October 1964) OSA Optics InfoBase
It is shown that the preponderance of experimental evidence supports the theoretical prediction based on Rayleigh scattering for the variation of sky brightness with altitude. Curves indicating the limits of sky brightness as a function of altitude are given.

Rayleigh Scattering
Victor Twersky
Applied Optics Vol. 3, 10, p. 1150 (October 1964) OSA Optics InfoBase
This paper discusses Rayleigh's contributions to scattering theory in eight categories: (1) “tenuous scatterers” (relative physical parameters near unity); (2) series solutions for cylinders and spheres (“partial waves”); (3) “small scatterers” (significant dimensions small compared to wavelength); (4) large apertures (applications of Kirchhoff approximations); (5) periodic planar arrays (diffraction gratings); (6) periodic volume arrays and stratified regions; (7) random planar distributions (rough surfaces); (8) random volume distributions (blue sky). Some related topics are also touched on.

Optics of the Lower Atmosphere
F. Möller
Applied Optics Vol. 3, 2, p. 157 (February 1964) OSA Optics InfoBase
A brief survey of the problems of optics and atmospheric radiation arising from the influence of the lower atmosphere on the solar radiation and from emission absorption of radiation within the atmosphere is given. Theoretical deductions as well as detailed quantitative results are omitted.

Optics of the Upper Atmosphere
D. M. Hunten
Applied Optics Vol. 3, 2, p. 167 (February 1964) OSA Optics InfoBase
Present knowledge of the upper atmosphere is reviewed, and the various absorption and emission phenomena are discussed. Topics included are: chemical composition, ionization, temperatures, aurora, night airglow, and twilight and day airglow. A short bibliography lists the standard reference works on this material

Scattering and Polarization Properties of Water Clouds and Hazes in the Visible and Infrared
D. Deirmendjian
Applied Optics Vol. 3, 2, p. 187 (February 1964) OSA Optics InfoBase
The extinction coefficient, albedo of single scattering, and differential scattering and polarization properties of water clouds and hazes in the visible and infrared have been computed using the complete Mie series. The results with three types of size distributions are presented and compared with observations. These show a strong dependence of angular intensity and polarization patterns on the size distribution, the size range, and the dielectric and absorbing properties of water droplets at each wavelength. A peculiarity of scattering at angles near 45°, observed experimentally and independently by two authors, is corroborated by the numerical results. Prominent observational features characteristic of natural fog, such as an extremely bright and narrow aureole, cloudbows, and glories, are reproduced in a model cloud of spherical water droplets, with a wide distribution in droplet radius and a maximum concentration at a 4 µm radius.

The Scattering of Infrared Radiation from Clouds
Ernest Bauer
Applied Optics Vol. 3, 2, p. 197 (February 1964) OSA Optics InfoBase
The scattering of infrared radiation from clouds composed of spherical water droplets has been calculated by Mie theory. For wavelengths in the range from 2.5 to 6 µm and for large angle scattering, the effective reflectivity is due to single rather than multiple scattering by water droplets. This is a consequence of the rather large absorption cross section and of the forward peak in the differential scattering cross section. The effective diffuse reflectivity under these conditions is of the order of 2% at λ = 2.7 µm and 15% at λ= 4.3 µm for scattering through angles θ > 60°.


Low Sun Phenomena
W. A. Feibelman
Applied Optics Vol. 2, 2, p. 199 (February 1963) OSA Optics InfoBase
Of the many natural effects of atmospheric optics, none seems to have been given as much attention as the "Green Flash." 2 Lately, a man-made effect has been added to the list of phenomena: artificial prominences of the sun caused by airplanes crossing the sun. Because of the increasing importance of observations of solar flares and prominences, discrimination between natural and artificial effects is desirable.


Astronomical Refraction - Some History and Theories
A. I. Mahan
Applied Optics Vol. 1, 4, p. 497 (July 1962) OSA Optics InfoBase
Astronomical refraction has had a long and fascinating history. Cleomedes (100 A.D.) and Ptolemy (200 A.D.) were aware of its existence and understood in a qualitative way some of its properties. Alhazen (1100 A.D.) quite correctly suggested that the flattening of the sun's disk near the horizon was due to astronomical refraction. Tycho Brahe in 1587, however, was the first to make direct measurements of the magnitude of the refraction. The first theory of astronomical refraction based on Snell's law was that of Cassini, who in 1656 looked upon the earth's atmosphere as being of constant refractive index up to its upper limit at which all the refraction took place. Extensive investigations of the physical properties of the atmosphere modified these ideas and led to the "concentric spherical shell model" and the "plane parallel layer model," the latter being an approximation for the former. Attempts to evaluate the "refraction integral" for the concentric spherical shell model have led to the theories of Bessel, Bradley, Gylden, Ivory, Laplace, Mayer, Simpson, Young, and others. At the beginning of the twentieth century, investigations on the physical properties of the atmosphere extended to higher elevations, and new physical properties appeared which were not anticipated by the earlier workers. This led to the celebrated work of Harzer, who for the first time was able to compute the astronomical refraction purely from meteorological measurements. Harzer also made the first detailed investigation of the applicability of the spherical shell model, which is used almost universally by workers in this field. Harzer's work has served as a source of inspiration, but much remains to be done. This paper attempts to give a brief chronological description of some of the more significant theories of astronomical refraction for the purpose of pointing out the types of problems which have existed, how these problems were attacked, and the problems which still remain. It also gives adequate references for those wishing additional information.


The Colors of Distant Objects
W. E. Knowles Middleton
J. Opt. Soc. Am., Vol. 40, No. 6, p. 373 June 1950 OSA Optics InfoBase
A general expression is developed for the apparent color of an object of any intrinsic color, seen through a given thickness of an atmosphere of any specified optical properties. In deriving this expression, the author has made use of modern theories of the alteration of contrast by the atmosphere. Some examples of the application of this theory are given, and in conclusion it is shown that the visual range of colored objects differs little from that of achromatic objects of the same luminance factor.


A Theory of the Anti-Coronae
H.C. van de Hulst
J. Opt. Soc. Am., Vol. 37, No. 1, p. 16 January 1947 OSA Optics InfoBase
The anti-coronae, or luminous rings around the anti-solar point, are explained as a peculiar diffraction phenomenon in small water drops. The optical and the electromagnetic theories give results in agreement with each other and with the observations. The most important features are those which relate to the polarization.

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