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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.
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.
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
James A. Lock
Raymond L. Lee Jr
Waldemar H. Lehn
David K. Lynch
Siebren van der Werf
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
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 Free download
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
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.
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
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 Free download
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.
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
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
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.
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.
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
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 Free download
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
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 Free download
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
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 Free download
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
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 Free download
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.
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
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
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 Free download
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 Free download
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
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
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 Free download
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
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.
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 Free download
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 Free download
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 Free download
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
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
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?
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 Free download
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
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.
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 [Appl. Opt. 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 Free download
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 Free download
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. [Appl. Opt. 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
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
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.
N.B. see related articles:Halo Observations Provide Evidence of Airborne Cubic Ice in the Earth's AtmosphereSunset 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
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
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 Free download
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.
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, Appl. Opt. 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., Appl. Opt. 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
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
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
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
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
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
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
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.
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
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
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 [Appl. Opt. 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.
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
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
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.
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
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
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
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.
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