Single-scattering solutions to radiative transfer in infinite turbid media

Abstract

An instantaneous point source generating a light field in an infinite turbid medium with anisotropic individual scatterers is considered. Single-scattering solutions are sought as the first term of a series expansion of the solution of the radiative transfer equation in successive scattering orders. A simple formula for a single-scattering solution in media with an arbitrary axially symmetric phase function is derived. Applications of this formula are shown for the Henyey-Greenstein phase function, an ellipsoidal phase function, and a linear phase function. In addition, the single-scattering term of the RTE solution derived by Kholin [Zh. Vych. Mat. i Mat. Fys.4, 1126 (1964)] for media with a phase function represented by a finite series in Legendre polynomials is considered in more detail.