Radiative Transfer Equation Solution for Many Scattering Types

Abstract

The radiative transfer equation is a mathematical equation that accounts for the changes in the number of photons within a specified volume of a medium over time. It encompasses the intricate behavior of photons within the medium, including phenomena like scattering, absorption, and re-emission, which arise due to their interactions with the medium. In this study, the radiative transfer equation is considered for a finite slab which anisotropic scattering in a homogeneous medium. The equation solution is done by Legendre polynomials for linear anisotropic, quadratic and Rayleigh scattering types. The numerical results are displayed in the tables up to the 13th iteration of the Legendre polynomials. Tables are obtained using different scattering coefficients and single scattering albedo values. The results contain a wide range of data obtained from the method of solving the Legendre polynomial of the radiative transfer equation. Thus, with this study, the effect of different scattering types on the solution of the radiative transfer equation has been demonstrated.