Radiative scattering cross sections: comparison of experiment and theory

H. F. Nelson

doi:10.1364/AO.20.000500

Applied Optics
Vol. 20,
Issue 3,
pp. 500-504
(1981)
•https://doi.org/10.1364/AO.20.000500

Radiative scattering cross sections: comparison of experiment and theory

H. F. Nelson

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H. F. Nelson, "Radiative scattering cross sections: comparison of experiment and theory," Appl. Opt. 20, 500-504 (1981)

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Abstract

By comparing experimental and theoretical values of the radiative scattering cross sections of spherical particles over a wavelength range of 0.40–0.70 μm, both the scattering particle distribution function and concentration as well as the scattering coefficient are obtained. The experimental cross sections are derived from transmission data by using monodispersed polystyrene latex particles immersed in distilled water and a standard spectrophotometer. A discrete bimodal particle size distribution is used to account for coagulation. It is adjusted to yield the correct distribution function by making the difference between the experimental and theoretical cross section essentially constant with wavelength. The constant difference is proportional to the measurement error in the particle volume concentration and is easily eliminated by correcting the concentration. In addition, the scattering coefficient for the medium is obtained as a function of wavelength.

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Diameter (μm)	Standard deviation (μm)
0.109	0.0027
0.481	0.0018
1.011	0.0054

Particle =	D = 0.109 μm		D = 0.481 μm		D = 1.011 μm
Distribution =	f(D) = 1		f(D₁) = 0.97, f(D₂) = 0.03		f(D₁) = 0.95, f(D₂) = 0.05

λ₀ (μm)	x	$c_{the}^{'} (1 / cm)$	x	$c_{the}^{'} (1 / cm)$	x	$c_{the}^{'} (1 / cm)$
0.40	1.15	8599	5.22	62,600	11.19	42,700
0.42	1.09	7125	4.97	57,550	10.65	42,680
0.44	1.04	5944	4.74	53,070	10.15	42,500
0.46	1.00	4992	4.53	49,020	9.70	41,930
0.48	0.95	4220	4.34	45,190	9.29	41,410
0.50	0.91	3589	4.16	41,770	8.91	40,590
0.52	0.88	3070	4.00	38,660	8.56	39,870
0.54	0.85	2640	3.85	35,900	8.24	38,890
0.56	0.82	2282	3.71	33,370	7.94	38,050
0.58	0.79	1982	3.58	30,970	7.66	37,230
0.60	0.76	1730	3.46	28,770	7.40	36,230
0.62	0.74	1516	3.34	26,800	7.16	35,270
0.64	0.71	1335	3.24	25,010	6.94	34,320
0.66	0.69	1179	3.14	23,390	6.72	33,470
0.68	0.67	1045	3.05	21,930	6.52	32,500
0.70	0.65	930	2.96	20,620	6.34	31,480

Diameter (μm)	Standard deviation (μm)
0.109	0.0027
0.481	0.0018
1.011	0.0054

Particle =	D = 0.109 μm		D = 0.481 μm		D = 1.011 μm
Distribution =	f(D) = 1		f(D₁) = 0.97, f(D₂) = 0.03		f(D₁) = 0.95, f(D₂) = 0.05

λ₀ (μm)	x	$c_{the}^{'} (1 / cm)$	x	$c_{the}^{'} (1 / cm)$	x	$c_{the}^{'} (1 / cm)$
0.40	1.15	8599	5.22	62,600	11.19	42,700
0.42	1.09	7125	4.97	57,550	10.65	42,680
0.44	1.04	5944	4.74	53,070	10.15	42,500
0.46	1.00	4992	4.53	49,020	9.70	41,930
0.48	0.95	4220	4.34	45,190	9.29	41,410
0.50	0.91	3589	4.16	41,770	8.91	40,590
0.52	0.88	3070	4.00	38,660	8.56	39,870
0.54	0.85	2640	3.85	35,900	8.24	38,890
0.56	0.82	2282	3.71	33,370	7.94	38,050
0.58	0.79	1982	3.58	30,970	7.66	37,230
0.60	0.76	1730	3.46	28,770	7.40	36,230
0.62	0.74	1516	3.34	26,800	7.16	35,270
0.64	0.71	1335	3.24	25,010	6.94	34,320
0.66	0.69	1179	3.14	23,390	6.72	33,470
0.68	0.67	1045	3.05	21,930	6.52	32,500
0.70	0.65	930	2.96	20,620	6.34	31,480

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Equations (17)

Applied Optics