Light scattering by randomly oriented particles into solid angles

L. E. Paramonov

doi:10.1364/JOSAA.11.001360

Journal of the Optical Society of America A
Vol. 11,
Issue 4,
pp. 1360-1369
(1994)
•https://doi.org/10.1364/JOSAA.11.001360

Light scattering by randomly oriented particles into solid angles

L. E. Paramonov

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L. E. Paramonov, "Light scattering by randomly oriented particles into solid angles," J. Opt. Soc. Am. A 11, 1360-1369 (1994)

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Abstract

Light scattering by a macroscopically isotropic volume element consisting of randomly oriented particles is considered. The expansion of scattering-matrix elements in a series of generalized spherical functions is used to develop a rigorous analytical method for computing scattered flux into any solid angle for incoherent parallel, convergent, or divergent incident beams. Some illustrative numerical results are reported.

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Equations (129)

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ρ	m_r

	1.005	1.01	1.03	1.05	1.07
5	$\frac{0.53540}{8.6846 \times 10^{- 4}}$	$\frac{0.53622}{8.6096 \times 10^{- 4}}$	$\frac{0.53929}{8.4124 \times 10^{- 4}}$	$\frac{0.54207}{8.4006 \times 10^{- 4}}$	$\frac{0.54451}{8.5852 \times 10^{- 4}}$
10	$\frac{0.51513}{2.1179 \times 10^{- 4}}$	$\frac{0.51622}{2.1852 \times 10^{- 4}}$	$\frac{0.51983}{2.4967 \times 10^{- 4}}$	$\frac{0.52226}{2.8789 \times 10^{- 4}}$	$\frac{0.52345}{3.3467 \times 10^{- 4}}$
25	$\frac{0.50663}{2.7798 \times 10^{- 5}}$	$\frac{0.50752}{2.9808 \times 10^{- 5}}$	$\frac{0.50719}{4.7111 \times 10^{- 5}}$	$\frac{0.49932}{9.0433 \times 10^{- 5}}$	$\frac{0.48026}{1.8805 \times 10^{- 4}}$
50	$\frac{0.50451}{6.9871 \times 10^{- 6}}$	$\frac{0.50396}{7.4884 \times 10^{- 6}}$	$\frac{0.48327}{1.7138 \times 10^{- 5}}$	$\frac{0.40122}{9.7854 \times 10^{- 5}}$	$\frac{0.20250}{6.6049 \times 10^{- 4}}$
100	$\frac{0.50200}{1.8558 \times 10^{- 6}}$	$\frac{0.49472}{2.3080 \times 10^{- 6}}$	$\frac{0.30434}{2.1217 \times 10^{- 5}}$	$\frac{0.33268}{2.0979 \times 10^{- 4}}$	$\frac{0.21694}{1.1229 \times 10^{- 3}}$

θ (deg)	υ₀′ (deg)

	0	1	5	10
0	1244.47	1115.15	194.653	63.5498
10	11.4185	10.6873	11.0933	32.9132
20	7.4857	6.9108	5.2298	4.7707
30	2.7400	2.6691	2.4212	2.5052
40	1.3182	1.3262	1.3913	1.3932
50	5.3715 × 10⁻¹	5.6773 × 10⁻¹	6.2692 × 10⁻¹	6.7099 × 10⁻¹
60	3.1315 × 10⁻¹	2.9714 × 10⁻¹	2.7958 × 10⁻¹	2.9123 × 10⁻¹
70	7.9112 × 10⁻²	9.1897 × 10⁻²	1.2395 × 10⁻¹	1.3325 × 10⁻¹
80	9.5857 × 10⁻²	8.6855 × 10⁻²	6.9060 × 10⁻²	6.8799 × 10⁻²
90	2.4729 × 10⁻²	2.6769 × 10⁻²	3.1185 × lO⁻²	3.3793 × lO⁻²
100	1.5454 × 10⁻²	1.7173 × 10⁻²	1.9872 × 10⁻²	2.1067 × 10⁻²
110	5.3954 × 10⁻³	9.7174 × 10⁻³	2.0474 × 10⁻²	2.6725 × 10⁻²
120	2.9420 × 1O⁻²	3.8324 × 10⁻²	5.0236 × 10⁻²	4.4059 × 10⁻²
130	3.6384 × 10⁻²	4.2941 × 10⁻²	7.6172 × 10⁻²	8.9185 × 10⁻²
140	2.4656 × 10⁻¹	2.2934 × 10⁻¹	2.1549 × 10⁻¹	1.8985 × 10⁻¹
150	1.2251 × 10⁻¹	1.2867 × 10⁻¹	1.6019 × 10⁻¹	1.7927 × 10⁻¹
160	7.0569 × 10⁻²	8.1240 × 10⁻²	1.1140 × 10⁻¹	1.3792 × 10⁻¹
170	1.3890 × lO⁻¹	1.4444 × 10⁻¹	1.6607 × 10⁻¹	1.7916 × 10⁻¹
180	2.0617 × 10⁻¹	1.8442 × 10⁻¹	3.3477 × 10⁻¹	2.0714 × 10⁻¹

ρ	υ₀′

	0	1	2	3	4	5
10	$\frac{0.5181}{0.2332 \times 10^{- 3}}$	$\frac{0.5169}{0.2330}$ ^b	$\frac{0.5131}{0.2325}$	$\frac{0.5070}{0.2316}$	$\frac{0.4985}{0.2304}$	$\frac{0.4878}{0.2289}$
20	$\frac{0.5101}{0.5624 \times 10^{- 4}}$	$\frac{0.5052}{0.5622}$	$\frac{0.4908}{0.5619}$	$\frac{0.4679}{0.5615}$	$\frac{0.4379}{0.5615}$	$\frac{0.4029}{0.5621}$
30	$\frac{0.5064}{0.2493 \times 10^{- 4}}$	$\frac{0.4954}{0.2501}$	$\frac{0.4644}{0.2522}$	$\frac{0.4177}{0.2552}$	$\frac{0.3619}{0.2581}$	$\frac{0.3035}{0.2607}$
40	$\frac{0.5026}{0.1485 \times 10^{- 4}}$	$\frac{0.4834}{0.1485}$	$\frac{0.4341}{0.1488}$	$\frac{0.3588}{0.1490}$	$\frac{0.2819}{0.1494}$	$\frac{0.2133}{0.1500}$
50	$\frac{0.4979}{0.9975 \times 10^{- 5}}$	$\frac{0.4685}{0.9947}$	$\frac{0.3924}{0.9898}$	$\frac{0.2974}{0.9886}$	$\frac{0.2109}{0.9935}$	$\frac{0.1466}{1.0016}$
75	$\frac{0.4803}{0.5352 \times 10^{- 5}}$	$\frac{0.4183}{0.5373}$	$\frac{0.2847}{0.5409}$	$\frac{0.1682}{0.5438}$	$\frac{0.1014}{0.5475}$	$\frac{0.06728}{0.5524}$

ρ	m_r

	1.005	1.01	1.03	1.05	1.07
5	$\frac{0.53540}{8.6846 \times 10^{- 4}}$	$\frac{0.53622}{8.6096 \times 10^{- 4}}$	$\frac{0.53929}{8.4124 \times 10^{- 4}}$	$\frac{0.54207}{8.4006 \times 10^{- 4}}$	$\frac{0.54451}{8.5852 \times 10^{- 4}}$
10	$\frac{0.51513}{2.1179 \times 10^{- 4}}$	$\frac{0.51622}{2.1852 \times 10^{- 4}}$	$\frac{0.51983}{2.4967 \times 10^{- 4}}$	$\frac{0.52226}{2.8789 \times 10^{- 4}}$	$\frac{0.52345}{3.3467 \times 10^{- 4}}$
25	$\frac{0.50663}{2.7798 \times 10^{- 5}}$	$\frac{0.50752}{2.9808 \times 10^{- 5}}$	$\frac{0.50719}{4.7111 \times 10^{- 5}}$	$\frac{0.49932}{9.0433 \times 10^{- 5}}$	$\frac{0.48026}{1.8805 \times 10^{- 4}}$
50	$\frac{0.50451}{6.9871 \times 10^{- 6}}$	$\frac{0.50396}{7.4884 \times 10^{- 6}}$	$\frac{0.48327}{1.7138 \times 10^{- 5}}$	$\frac{0.40122}{9.7854 \times 10^{- 5}}$	$\frac{0.20250}{6.6049 \times 10^{- 4}}$
100	$\frac{0.50200}{1.8558 \times 10^{- 6}}$	$\frac{0.49472}{2.3080 \times 10^{- 6}}$	$\frac{0.30434}{2.1217 \times 10^{- 5}}$	$\frac{0.33268}{2.0979 \times 10^{- 4}}$	$\frac{0.21694}{1.1229 \times 10^{- 3}}$

θ (deg)	υ₀′ (deg)

	0	1	5	10
0	1244.47	1115.15	194.653	63.5498
10	11.4185	10.6873	11.0933	32.9132
20	7.4857	6.9108	5.2298	4.7707
30	2.7400	2.6691	2.4212	2.5052
40	1.3182	1.3262	1.3913	1.3932
50	5.3715 × 10⁻¹	5.6773 × 10⁻¹	6.2692 × 10⁻¹	6.7099 × 10⁻¹
60	3.1315 × 10⁻¹	2.9714 × 10⁻¹	2.7958 × 10⁻¹	2.9123 × 10⁻¹
70	7.9112 × 10⁻²	9.1897 × 10⁻²	1.2395 × 10⁻¹	1.3325 × 10⁻¹
80	9.5857 × 10⁻²	8.6855 × 10⁻²	6.9060 × 10⁻²	6.8799 × 10⁻²
90	2.4729 × 10⁻²	2.6769 × 10⁻²	3.1185 × lO⁻²	3.3793 × lO⁻²
100	1.5454 × 10⁻²	1.7173 × 10⁻²	1.9872 × 10⁻²	2.1067 × 10⁻²
110	5.3954 × 10⁻³	9.7174 × 10⁻³	2.0474 × 10⁻²	2.6725 × 10⁻²
120	2.9420 × 1O⁻²	3.8324 × 10⁻²	5.0236 × 10⁻²	4.4059 × 10⁻²
130	3.6384 × 10⁻²	4.2941 × 10⁻²	7.6172 × 10⁻²	8.9185 × 10⁻²
140	2.4656 × 10⁻¹	2.2934 × 10⁻¹	2.1549 × 10⁻¹	1.8985 × 10⁻¹
150	1.2251 × 10⁻¹	1.2867 × 10⁻¹	1.6019 × 10⁻¹	1.7927 × 10⁻¹
160	7.0569 × 10⁻²	8.1240 × 10⁻²	1.1140 × 10⁻¹	1.3792 × 10⁻¹
170	1.3890 × lO⁻¹	1.4444 × 10⁻¹	1.6607 × 10⁻¹	1.7916 × 10⁻¹
180	2.0617 × 10⁻¹	1.8442 × 10⁻¹	3.3477 × 10⁻¹	2.0714 × 10⁻¹

Abstract

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Figures (1)

Tables (3)

Equations (129)

Journal of the Optical Society of America A