Multiple Light Scattering by Spherical Dielectric Particles*

David H. Woodward

doi:10.1364/JOSA.54.001325

Journal of the Optical Society of America
Vol. 54,
Issue 11,
pp. 1325-1331
(1964)
•https://doi.org/10.1364/JOSA.54.001325

Multiple Light Scattering by Spherical Dielectric Particles

David H. Woodward

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David H. Woodward, "Multiple Light Scattering by Spherical Dielectric Particles*," J. Opt. Soc. Am. 54, 1325-1331 (1964)

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Abstract

The general multiple light-scattering theory due to Hartel for the angular scattering from high concentrations of spherical scattering particles has been calculated for the case of large spheres. Experimental data for the multiple scattering for various volume concentrations of monodisperse polystyrene latex particles are compared with calculations of the theory. The results indicate that the theory as generalized in this paper is a valid general multiple light-scattering theory for fairly high concentrations of spherical scattering particles.

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n	A_n	C_n⁽²⁾	C_n⁽³⁾	C_n⁽⁴⁾	C_n⁽⁵⁾	C_n⁽⁶⁾	C_n⁽⁸⁾	C_n⁽¹⁰⁾	C_t⁽¹⁵⁾	C_n⁽²⁰⁾	C_n⁽⁴⁰⁾
1	2.62307	2.29350	2.00534	1.75338	1.53316	1.34053	1.02484	0.78349	0.40040	0.20463	0.03189
2	3.88407	3.01720	2.34380	1.82070	1.41435	1.09868	0.66299	0.40007	0.13594	0.03445	0.00091
3	4.67930	3.12798	2.09097	1.39733	0.97496	0.65174	0.29123	0.13014	0.01737	0.00232
4	5.12149	2.91441	1.65846	0.94375	0.53705	0.26135	0.08463	0.02741	0.00164
5	5.33099	2.58359	1.25210	0.60681	0.29408	0.14252	0.03348	0.00780	0.00020
6	5.44700	2.28229	0.95628	0.40068	0.18541	0.07034	0.01235	0.00217
7	5.45219	1.98176	0.72033	0.26260	0.09517	0.03459	0.00457	0.00060
8	5.49056	1.77331	0.57273	0.18498	0.05973	0.01930	0.00201
9	5.51080	1.59836	0.46359	0.13446	0.03871	0.01123	0.00094
10	5.57966	1.48251	0.39390	0.10709	0.02781	0.00739	0.00053
11	5.67306	1.39929	0.34514	0.08513	0.02100	0.00519	0.00032
12	5.80354	1.34724	0.31275	0.07260	0.01685	0.00391	0.00021
13	5.95407	1.31300	0.28954	0.06385	0.01408	0.00331	0.00015
14	6.12348	1.29300	0.27302	0.05765	0.01221	0.00258	0.00011
15	6.31511	1.28647	0.26764	0.05339	0.01088	0.00221	0.00009
16	6.46042	1.26476	0.24760	0.04847	0.00949	0.00186
17	6.66804	1.27036	0.24202	0.04611	0.00879	0.00167
18	6.75580	1.23354	0.22523	0.04113	0.00751	0.00138
19	6.88411	1.21515	0.21449	0.03786	0.00668	0.00118
20	6.91103	1.11649	0.19636	0.03310	0.00558	0.00094
21	6.86203	1.09506	0.17475	0.02809	0.00482	0.00072
22	6.69058	0.99475	0.14790	0.02199	0.00327	0.00049
23	6.41904	0.87668	0.11992	0.01635	0.00223	0.00031
24	5.90379	0.71132	0.08570	0.01033	0.00124	0.00015
25	5.29298	0.54933	0.05688	0.00592	0.00061	0.00006
26	4.42007	0.36862	0.03074	0.00256	0.00021	0.00002
27	3.39337	0.20936	0.01292	0.00081	0.00005
28	2.22537	0.08688	0.00339	0.00013
29	1.19944	0.02438	0.00050	0.00001
30	0.69085	0.00782	0.00009
31	0.25484	0.00110
32	0.08876	0.00012
33	0.02758	0.00001
34	0.00770
35	0.00194
36	0.00043
37	0.00008
38	0.00001

	C₀ = 5×10⁻⁴	C₀ = 1×10⁻³	C₀ = 2×10⁻³	C₀ = 3×10⁻³	C₀ = 5×10⁻³
(FNx)	0.287	0.574	1.148	1.722	2.87
Q₁	0.215 (86.3%)	0.323 (74%)	0.364 (53.3%)	0.308 (37.5%)	0.1635 (17.25%)
Q₂	0.031 (12.4%)	0.0930 (21.2%)	0.209 (32.7%)	0.265 (32.2%)	0.2345 (24.85%)
Q₃	0.003 (1.2%)	0.0177 (4.1%)	0.080 (8.5%)	0.152 (18.5%)	0.224 (23.65%)
Q₄		0.0025 (0.6%)	0.0228 (3.0%)	0.0655 (8.0%)	0.161 (17.00%)
Q₅			0.0052 (0.8%)	0.0226 (2.75%)	0.0925 (9.76%)
Q₆				0.0065 (0.79%)	0.0443 (4.57%)
Q₇				0.0016 (0.20%)	0.0182 (1.92%)
Q₈					0.0065 (0.69%)
Q₉					0.0021 (0.22%)
Q₁₀					0.0006 (0.06%)
T	0.249	0.435	0.683	0.820	0.937

δ/R	C₀
10⁻⁴	34.8
10⁻⁵	75
4.2×10⁻⁶	100
10⁻⁶	163

n	A_n	C_n⁽²⁾	C_n⁽³⁾	C_n⁽⁴⁾	C_n⁽⁵⁾	C_n⁽⁶⁾	C_n⁽⁸⁾	C_n⁽¹⁰⁾	C_t⁽¹⁵⁾	C_n⁽²⁰⁾	C_n⁽⁴⁰⁾
1	2.62307	2.29350	2.00534	1.75338	1.53316	1.34053	1.02484	0.78349	0.40040	0.20463	0.03189
2	3.88407	3.01720	2.34380	1.82070	1.41435	1.09868	0.66299	0.40007	0.13594	0.03445	0.00091
3	4.67930	3.12798	2.09097	1.39733	0.97496	0.65174	0.29123	0.13014	0.01737	0.00232
4	5.12149	2.91441	1.65846	0.94375	0.53705	0.26135	0.08463	0.02741	0.00164
5	5.33099	2.58359	1.25210	0.60681	0.29408	0.14252	0.03348	0.00780	0.00020
6	5.44700	2.28229	0.95628	0.40068	0.18541	0.07034	0.01235	0.00217
7	5.45219	1.98176	0.72033	0.26260	0.09517	0.03459	0.00457	0.00060
8	5.49056	1.77331	0.57273	0.18498	0.05973	0.01930	0.00201
9	5.51080	1.59836	0.46359	0.13446	0.03871	0.01123	0.00094
10	5.57966	1.48251	0.39390	0.10709	0.02781	0.00739	0.00053
11	5.67306	1.39929	0.34514	0.08513	0.02100	0.00519	0.00032
12	5.80354	1.34724	0.31275	0.07260	0.01685	0.00391	0.00021
13	5.95407	1.31300	0.28954	0.06385	0.01408	0.00331	0.00015
14	6.12348	1.29300	0.27302	0.05765	0.01221	0.00258	0.00011
15	6.31511	1.28647	0.26764	0.05339	0.01088	0.00221	0.00009
16	6.46042	1.26476	0.24760	0.04847	0.00949	0.00186
17	6.66804	1.27036	0.24202	0.04611	0.00879	0.00167
18	6.75580	1.23354	0.22523	0.04113	0.00751	0.00138
19	6.88411	1.21515	0.21449	0.03786	0.00668	0.00118
20	6.91103	1.11649	0.19636	0.03310	0.00558	0.00094
21	6.86203	1.09506	0.17475	0.02809	0.00482	0.00072
22	6.69058	0.99475	0.14790	0.02199	0.00327	0.00049
23	6.41904	0.87668	0.11992	0.01635	0.00223	0.00031
24	5.90379	0.71132	0.08570	0.01033	0.00124	0.00015
25	5.29298	0.54933	0.05688	0.00592	0.00061	0.00006
26	4.42007	0.36862	0.03074	0.00256	0.00021	0.00002
27	3.39337	0.20936	0.01292	0.00081	0.00005
28	2.22537	0.08688	0.00339	0.00013
29	1.19944	0.02438	0.00050	0.00001
30	0.69085	0.00782	0.00009
31	0.25484	0.00110
32	0.08876	0.00012
33	0.02758	0.00001
34	0.00770
35	0.00194
36	0.00043
37	0.00008
38	0.00001

	C₀ = 5×10⁻⁴	C₀ = 1×10⁻³	C₀ = 2×10⁻³	C₀ = 3×10⁻³	C₀ = 5×10⁻³
(FNx)	0.287	0.574	1.148	1.722	2.87
Q₁	0.215 (86.3%)	0.323 (74%)	0.364 (53.3%)	0.308 (37.5%)	0.1635 (17.25%)
Q₂	0.031 (12.4%)	0.0930 (21.2%)	0.209 (32.7%)	0.265 (32.2%)	0.2345 (24.85%)
Q₃	0.003 (1.2%)	0.0177 (4.1%)	0.080 (8.5%)	0.152 (18.5%)	0.224 (23.65%)
Q₄		0.0025 (0.6%)	0.0228 (3.0%)	0.0655 (8.0%)	0.161 (17.00%)
Q₅			0.0052 (0.8%)	0.0226 (2.75%)	0.0925 (9.76%)
Q₆				0.0065 (0.79%)	0.0443 (4.57%)
Q₇				0.0016 (0.20%)	0.0182 (1.92%)
Q₈					0.0065 (0.69%)
Q₉					0.0021 (0.22%)
Q₁₀					0.0006 (0.06%)
T	0.249	0.435	0.683	0.820	0.937

Abstract

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Figures (4)

Tables (3)

Equations (29)

Journal of the Optical Society of America