Analysing the corona
(using the Debye series)

Fig. 1  Corona: Mie calculation of scattering by a water drop of radius r = 10 µm of red light of wavelength λ = 0.65 µm

Fig. 1 shows scattering of red light by a water droplet with a radius r = 10 µm.   The maximum around 3° corresponds to a ring of the corona, which is often seen as concentric coloured rings around a cloud-covered moon.   Noting that the vertical axis of Fig. 1 has a logarithmic scale, the intensity of the corona is only about 3% of the intensity in the forward direction (θ → 0°).   Coronas also appear around the sun, but are generally not visible because our eyes are dazzled by the brightness of the sun.

The corona is usually attributed to diffraction, but Fig. 1 does not show the regular scattering pattern normally associated with diffraction.

Fig. 2   Corona:  Various calculations of scattering by a water drop of radius r = 10 µm of red light of wavelength λ = 0.65µm (perpendicular polarisation)

Fig. 2 shows that the Debye p = 0 contribution is dominant in the forward-scattering zone (scattering angles below 5°).   As noted above, the p = 0 term includes both diffraction effects and external reflection.  The blue curve in Fig. 2 represents the diffraction process: it has been calculated using the following equations:

For scattering angles θ below about 6°, the maxima for the p = 0 term coincide with the maxima of the diffraction term.   The minima are much shallower for the p = 0 term than for the diffraction term (because the p = 0 term includes reflection from the exterior of the sphere).   However, note that the minima calculated using Mie theory do not coincide with the minima of the diffraction pattern.

Fig. 3  Corona: Debye series calculation of scattering by a water drop of radius r = 10 µm of red light of wavelength λ = 0.65 µm (perpendicular polarisation)

The sharp minimum of the Mie curve at θ ≈ 4.3° in Fig. 2. can be explained by Fig. 3.   This minimum occurs where the red and the magenta curves cross each other.   The red curve represents the contribution from p = 0 scattering (external reflection & diffraction) whilst the magenta curve represents p = 1 sacttering (direct transmission).   The black curve, which represents the vector sum of the p = 0 and p = 1 contributions, has a deep minimum at θ ≈ 4.3°.   This indicates that, in this direction, the p = 0 and p = 1 contributions are of equal amplitude but with a phase difference approaching 180°.   As the black curve is almost identical to the Mie curve in Fig. 2, it is also clear that the p = 0 and p = 1 contributions are dominant in the forward scattering zone.

MiePlot offers the option of using the Debye series.

Page updated on 10 November 2002