The vectorial radiative transfer equation problem in the small angle modification of the spherical harmonics method with the determination of the solution smooth part

Abstract

The paper deals with the vectorial radiative transfer equation (VRTE) problem for a homogeneous strongly anisotropic scattering slab illuminated by a plain unidirectional source of light with an arbitrary angle of irradiance and polarization state. The problem is a theoretical base for the polarized satellite remote sensing (POLDER, PARASOL and others). The VRTE boundary problem decomposition allows reducing to the nonreflecting bottom with subsequent including its polarization properties. We give the complete analysis for the solution smooth non-small angle part for the vectorial small angle modification of the spherical harmonics method (VMSH) built upon the smoothness of the spatial spectrum of the light field distribution vector-function caused by mathematical singularities of the top-boundary condition for the VRTE boundary problem and the anisotropy of many natural scattering media (clouds, ocean). The VMSH itself is described as well.