Development of the small angle approximation of the radiative transfer theory taking into account the photon path distribution function

Abstract

The development of the small angle approximation of the radiative transfer equation (RTE) solution for the slab taking into account the photon path distribution function in the forward hemisphere of sighting directions is offered. The solution is based on the Taylor series expansion of the sighting angle cosine up to the 2nd order without the RTE conversion to the diffusion approximation. The obtained solution practically coincides with the exact solution in the forward hemisphere of directions up to the deep regime.