Mathematical model of polarized light reflection by turbid medium slab with an anisotropic scattering

Abstract

The registration of the reflected radiation polarization at the remote sensing allows gaining all the information available to optical methods about the observed object. Mathematically it gives a boundary-value problem of the vectorial radiative transfer equation (VRTE). The natural media of the radiative transfer have strongly anisotropic light scattering. Because of their singularities the solution of the boundary-value problem of VRTE for such media is a mathematically illconditioned problem. The classical method (S.Chandrasekhar) of the elimination of this problem is based on the subtraction of the nonscattered component from the solution. However under the conditions of strong anisotropy a diffusion part is not distinguished enough from the nonscattered part that gives heavy oscillations in the numerical solution. In this paper it is offered to subtract from the required solution of VRTE its solution in a small angle approximation (SAA), which besides nonscattered component contains all the anisotropic part. The rest of the solution is a smooth function, which can be easily found by any numerical method. As SAA it is offered to take a small angle modification of a spherical harmonics method (MSH), presenting the generalization of Goudsmit-Saunderson's solution for the case of VRTE.