Improved Expressions For Anisotropic Scattering In Absorbing Media

Abstract

The diffusion approximation of transport theory can only be applied to light propagation in random media if the absorption cross section is small compared with the effective scattering cross section. In order to obtain more general results, the Boltzmann transport equation was solved numerically in a separate study for the plane symmetry in an unbounded medium for Rayleigh-Gans scattering. Values for the absorption and backscattering coefficients K and S were obtained in this way for the whole range of absorption cross sections. The diffusion pattern within the medium is a part of the rigorous solution of the transport equation. The average photon path length per unit length in the positive direction proves to be different from that in the negative direction. Therefore, the introduction of K+, K-, S+ and S- should be considered. Results for IC' and K- have been obtained. The diffusion pattern has also been used to derive coefficients for reflection of the diffuse radiation at boundaries where the index of refraction changes, assuming that the diffusion pattern of the emerging radiation is the same as in the unbounded medium. Results with this method are compared with results using the diffusion approximation and with Monte Carlo simulations in order to determine the accuracy of calculated values of K and S.