Use of two scaling relations in the study of multiple-scattering effects on the transmittance of light beams through a turbid atmosphere

E. Battistelli; P. Bruscaglioni; A. Ismaelli; G. Zaccanti

doi:10.1364/JOSAA.2.000903

Journal of the Optical Society of America A
Vol. 2,
Issue 6,
pp. 903-912
(1985)
•https://doi.org/10.1364/JOSAA.2.000903

Use of two scaling relations in the study of multiple-scattering effects on the transmittance of light beams through a turbid atmosphere

E. Battistelli, P. Bruscaglioni, A. Ismaelli, and G. Zaccanti

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E. Battistelli, P. Bruscaglioni, A. Ismaelli, and G. Zaccanti, "Use of two scaling relations in the study of multiple-scattering effects on the transmittance of light beams through a turbid atmosphere," J. Opt. Soc. Am. A 2, 903-912 (1985)

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Abstract

Monte Carlo methods, used in calculations of the received power in transmissions of collimated light beams through a turbid atmosphere in a multiple-scattering regime, present a shortcoming because of the length of computer time necessary to obtain reliable results. We show how the introduction of two scaling formulas makes a substantial reduction of calculation time possible, since situations differing through the values of some geometrical parameters do not require separate treatment. Two versions of the scaling formulas are presented. The simpler one can be applied when the scattering function of the medium has a high forward peak, so that one can assume that only small scattering angles are important. The second form of the scaling formula can be applied in cases when small-angle assumption is not adequate.

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D(m)	σ = 0.04 m⁻¹				σ = 0.06 m⁻¹				σ = 0.08 m⁻¹

	α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad

	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀
50	0.13	0.13	0.71	0.71	0.19	0.20	0.11	0.11	0.26	0.26	0.14	0.14
	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻¹	10⁻¹	10⁻²	10⁻²	10⁻¹	10⁻¹
100	0.13	0.13	0.71	0.72	0.19	0.22	0.11	0.11	0.26	0.26	0.14	0.15
	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻¹	10⁻¹	10⁻²	10⁻²	10⁻¹	10⁻¹
200	0.14	0.15	0.782	0.82	0.21	0.22	0.12	0.14	0.29	0.37	0.15	^a
	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻¹	10⁻¹	10⁻²	10⁻²	10⁻¹

D(m)	σ = 0.04 m⁻¹				σ = 0.06 m⁻¹				σ = 0.08 m⁻¹

	α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad

	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀
50	0.23	0.25	0.37	0.40	0.35	0.38	0.56	0.62	0.47	0.53	0.75	0.86
	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹
100	0.23	0.25	0.37	0.40	0.35	0.39	0.56	0.64	0.47	0.56	0.75	0.99
	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹
200	0.26	0.29	0.41	0.51	0.39	0.54	0.62	0.15	0.52	^a	0.82	^a
	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹		10⁻¹		10⁻¹

D(m)	σ = 0.04 m⁻¹				σ = 0.06 m⁻¹				σ = 0.08 m⁻¹

	α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad

	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀
50	0.13	0.13	0.71	0.71	0.19	0.20	0.11	0.11	0.26	0.26	0.14	0.14
	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻¹	10⁻¹	10⁻²	10⁻²	10⁻¹	10⁻¹
100	0.13	0.13	0.71	0.72	0.19	0.22	0.11	0.11	0.26	0.26	0.14	0.15
	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻¹	10⁻¹	10⁻²	10⁻²	10⁻¹	10⁻¹
200	0.14	0.15	0.782	0.82	0.21	0.22	0.12	0.14	0.29	0.37	0.15	^a
	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻²	10⁻¹	10⁻¹	10⁻²	10⁻²	10⁻¹

D(m)	σ = 0.04 m⁻¹				σ = 0.06 m⁻¹				σ = 0.08 m⁻¹

	α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad		α = 40 mrad		α = 400 mrad

	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀	R₁	R₁₀
50	0.23	0.25	0.37	0.40	0.35	0.38	0.56	0.62	0.47	0.53	0.75	0.86
	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹
100	0.23	0.25	0.37	0.40	0.35	0.39	0.56	0.64	0.47	0.56	0.75	0.99
	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹
200	0.26	0.29	0.41	0.51	0.39	0.54	0.62	0.15	0.52	^a	0.82	^a
	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹	10⁻¹		10⁻¹		10⁻¹

Abstract

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Figures (12)

Tables (2)

Equations (20)

Journal of the Optical Society of America A