Search

It has been shown that the regular part of the solution (RPS) which remains after separating the anisotropic part of the solution (APS) in the small-angle modification of the spherical harmonics method (SHM) is a smooth quasi-isotropic function with individual peaks in the angular distribution. The smooth part of the RPS without peaks can be determined in the two-streaming or diffuse approximation. The first iteration of the angular distribution of the radiance significantly refines the solution and allows one to restore the abovementioned angular peaks. The quasi-diffusion approximation—separation of the APS on the basis of the SHM, the determination of the RPS in the diffusion approximation, and the refinement of the solution on the basis of the first iteration—does not depend on the symmetry of the problem and, therefore, can be generalized to the case of an arbitrary geometry of the medium.

The paper suggests a new improved approach to calculating the anisotropic part of a diffuse light field in a turbid medium. We discuss some specific applications related to specific problems of radiative transfer theory, which demonstrate the accuracy and flexibility of this approach in practice.

The development of the small angle approximation of the radiative transfer equation (RTE) solution for the slab taking into account the photon path distribution function in the forward hemisphere of sighting directions is offered. The solution is based on the Taylor series expansion of the sighting angle cosine up to the 2nd order without the RTE conversion to the diffusion approximation. The obtained solution practically coincides with the exact solution in the forward hemisphere of directions up to the deep regime.