Mathematical Model of a Surface Radiance Factor

Abstract

The article is devoted to the creation of a surface radiance factor mathematical model. The basis of the model is the solution of the boundary value problem of the radiative transfer equation (RTE). The surface is considered as a structure consisting of several turbid layers, each of which is characterized by its optical parameters. The top of the structure is randomly rough, uncorrelated, Fresnel. The lower boundary reflects perfectly diffusely. The complexity of solving the RTE boundary value problem for real layers is due to the fact that the suspended particles in each layer are always much longer than the wavelength. This leads to a strong anisotropy of the radiance angular distribution according to Mie theory. The solution comes down to a system of equations by the discrete ordinates method that consists of several hundred of differential equations. Subtraction of the anisotropic part from the solution based on an approximate analytical solution of the RTE allows avoiding this problem. The approximation is based on a slight decrease in the anisotropic part of the angular spectrum. The matrix-operator method determines the general solution for a complex multilayer structure. The calculation speed can be increased without compromising the accuracy of the solution with the help of the synthetic iterations method. The method consists of two stages: the first one repeats the described one with a small number of ordinates; on the second one the iteration of it is performed. The model is realised in the Matlab software.