The Problem of Diffuse Reflection in the Case of Redistribution of Radiation by Frequencies and Directions: Complete Simplification of the Solution by means of Decomposition of Resultant Field (DRF) Method

The method of decomposition of the resulting field (DRF) developed by the author is used to further simplify the solution of the diffuse reflection problem (DRP) from a semi-infinite medium in the case of redistribution of radiation by frequencies and directions. Taking into account the presence of a natural combination of frequency and angle of absorption of a quantum makes it possible to bring the solution of the problem to its complete simplification. The search for eigenfunctions and eigenvalues of DRP that depend on three independent variables and satisfy the joint system of integral equations with nonlinearity of the fifth degree and algebraic equations of the second degree is reduced to the determination of two types of new auxiliary functions from the system of nonlinear integral equations. The first type depends on only one argument with the second degree of nonlinearity of the equations, and the second one on three arguments with the third degree of nonlinearity of integral equations. The accompanying systems of algebraic equations that determine the corresponding eigenvalues are also simplified: instead of nonlinearity of the second degree, linear systems are obtained.