Light scattering by randomly oriented crystals

Karri Muinonen; Kari Lumme; Jouni Peltoniemi; William M. Irvine

doi:10.1364/AO.28.003051

Applied Optics
Vol. 28,
Issue 15,
pp. 3051-3060
(1989)
•https://doi.org/10.1364/AO.28.003051

Light scattering by randomly oriented crystals

Karri Muinonen, Kari Lumme, Jouni Peltoniemi, and William M. Irvine

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Karri Muinonen, Kari Lumme, Jouni Peltoniemi, and William M. Irvine, "Light scattering by randomly oriented crystals," Appl. Opt. 28, 3051-3060 (1989)

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Abstract

The scattering phase function and the degree of linear polarization for small crystals oriented randomly in space have been computed using the geometric ray tracing theory and assuming that the crystals are homogeneous and isotropic. Calculations have been carried out for the main crystal geometries. Detection of halos from crystals other than hexagonal water ice is briefly discussed. The crystal size and shape parameters have also been averaged over some simple distributions in order to examine general light scattering properties of sharp-edged particles. A scalar physical optics correction has been developed for the geometric optics phase functions. Results can be applied to light scattering from regoliths and planetary rings, and possibly also to atmospheric halos. Retroreflecting crystals in the regolith would cause an opposition spike, a phenomenon observed for many bright satellites.

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Crystals	Ice plate	Ice column	Ice cube	Orthoclase	Anorthite	Enstatite	Forsterite	Augite
M	1.31	1.31	1.31	1.52	1.58	1.66	1.66	1.71
c:2a,a:b:c	1:5	5:1	1:1:1	5:1:2	5:1:5	1:1:1	2:2:1	1:1:1
α					93.17			100.99
β				116.02	115.85	91.80		100.99
γ					91.22			85.13
Features	22,46,180	22,46,180	46,180	44,136,180	52,136	172,176,180	180	10,18,44,140
P₁₁(0°)	7.3 × 10³	4.3 × 10³	4.3 × 10³	6.6 × 10³	7.6 × 10³	5.5 × 10³	5.8 × 10³	5.4 × 10³
P₁₁(180°)	1.9 × 10⁰	1.9 × 10⁰	1.1 × 10²	5.1 × 10⁰	2.6 × 10⁻¹	7.2 × 10⁰	1.9 × 10²	4.7 × 10⁻¹
P_min	−0.40	−0.16	−0.54	−0.33	−0.02	−0.25	−0.45	−0.11
P_max	0.16	0.21	0.13	0.24	0.34	0.27	0.28	0.23
B	0.068	0.112	0.046	0.120			0.114
C			0.016				0.028
T	0.017	0.019	0.023	0.043			0.075
g	0.75	0.72	0.48	0.60	0.66	0.47	0.50	0.52
g_s	0.78	0.78	0.78	0.64	0.60	0.56	0.56	0.53

n	n′ka	$\tilde{ω}$ ₀	P₁₁(0°)	P₁₁(180°)	P_min	P_max	g
1.71	0.00	1.00	5.4 × 10³	4.7 × 10⁻¹	−0.11	0.23	0.52
1.71	0.25	0.53	5.9 × 10³	2.0 × 10⁻¹	−0.09	0.39	0.59
1.71	1.00	0.20	3.3 × 10³	4.0 × 10⁻¹	0.00	0.75	0.50

m	Δa:a₀	α₀,Δα	P₁₁(0°)	P₁₁(180°)	P_min	P_max	g	g_s
1.31	0.20	90.0,2.0	4.4 × 10³	3.1 × 10⁰	−0.25	0.13	0.48	0.78
1.31	0.20	,10.0	4.3 × 10³	5.8 × 10⁻¹	−0.04	0.13	0.49	0.78
1.31	0.20	,30.0	3.9 × 10³	4.2 × 10⁻¹	−0.02	0.08	0.54	0.78
1.55	0.20	90.0,2.0	5.3 × 10³	4.4 × 10°	−0.24	0.23	0.46	0.62
1.55	0.20	,10.0	5.3 × 10³	5.3 × 10⁻¹	−0.08	0.19	0.49	0.62
1.55	0.20	,30.0	4.7 × 10³	9.2 × 10⁻¹	0.00	0.19	0.40	0.62

Crystals	Ice plate	Ice column	Ice cube	Orthoclase	Anorthite	Enstatite	Forsterite	Augite
M	1.31	1.31	1.31	1.52	1.58	1.66	1.66	1.71
c:2a,a:b:c	1:5	5:1	1:1:1	5:1:2	5:1:5	1:1:1	2:2:1	1:1:1
α					93.17			100.99
β				116.02	115.85	91.80		100.99
γ					91.22			85.13
Features	22,46,180	22,46,180	46,180	44,136,180	52,136	172,176,180	180	10,18,44,140
P₁₁(0°)	7.3 × 10³	4.3 × 10³	4.3 × 10³	6.6 × 10³	7.6 × 10³	5.5 × 10³	5.8 × 10³	5.4 × 10³
P₁₁(180°)	1.9 × 10⁰	1.9 × 10⁰	1.1 × 10²	5.1 × 10⁰	2.6 × 10⁻¹	7.2 × 10⁰	1.9 × 10²	4.7 × 10⁻¹
P_min	−0.40	−0.16	−0.54	−0.33	−0.02	−0.25	−0.45	−0.11
P_max	0.16	0.21	0.13	0.24	0.34	0.27	0.28	0.23
B	0.068	0.112	0.046	0.120			0.114
C			0.016				0.028
T	0.017	0.019	0.023	0.043			0.075
g	0.75	0.72	0.48	0.60	0.66	0.47	0.50	0.52
g_s	0.78	0.78	0.78	0.64	0.60	0.56	0.56	0.53

n	n′ka	$\tilde{ω}$ ₀	P₁₁(0°)	P₁₁(180°)	P_min	P_max	g
1.71	0.00	1.00	5.4 × 10³	4.7 × 10⁻¹	−0.11	0.23	0.52
1.71	0.25	0.53	5.9 × 10³	2.0 × 10⁻¹	−0.09	0.39	0.59
1.71	1.00	0.20	3.3 × 10³	4.0 × 10⁻¹	0.00	0.75	0.50

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Applied Optics