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Optical Engineering

Similarity relations for anisotropic scattering in absorbing media
Author(s): Reindert Graaff; Jan G. Aarnoudse; Frits F. M. de Mul; Henk W. Jentink
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Paper Abstract

The validity of the similarity parameter ∑'s ≡ ∑s(1 - g), the reduced scattering coefficient, where g is the average cosine of the scattering phase function is investigated. Attenuation coefficients α and diffusion patterns are obtained from solutions of the transport equation for isotropic scattering and Rayleigh-Gans scattering, applied to infinite media. Similarity is studied for the attenuation coefficient α, as well as for the Kubelka-Munk absorption and backscattering coefficients in the positive and negative directions, and for predictions of the internal reflection at interfaces. Similarity between solutions of the Boltzmann equation for highly forward scattering and isotropic scattering (g = 0) exist only when ∑a << ∑s(l - g). However, because similarity between results, both with g > 0.9, is independent of the value of the absorption coefficient, it is advantageous to simulate highly forward scattering media like biological tissues with g > 0.9, e.g., by Monte Carlo simulations, instead of using isotropic scattering or diffusion theory. Monte Carlo simulations on slabs confirm the deviations from the diffusion approximation and show the behavior near boundaries. Application of similarity may save calculation time in Monte Carlo simulations, because simulation with a lower value for g will increase the mean free path.

Paper Details

Date Published: 1 February 1993
PDF: 9 pages
Opt. Eng. 32(2) doi: 10.1117/12.60735
Published in: Optical Engineering Volume 32, Issue 2
Show Author Affiliations
Reindert Graaff, Univ. of Groningen (Netherlands)
Jan G. Aarnoudse, Univ. of Groningen (Netherlands)
Frits F. M. de Mul, Univ. of Twente (Netherlands)
Henk W. Jentink, Univ. of Twente (Netherlands)

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