<title>Effective computational method of the light fields in three-dimensional medium with an anisotropic scattering</title>

Abstract

Practically all the real problems of the atmospheric and oceanic optics are based on the solution of the radiative transfer equation (RTE) for three-dimensional (3D) medium area with a strong anisotropic scattering. In case of the flat medium geometry the most effective method of the RTE solution is the approach, when the difference between the exact solution and the solution of RTE in the small angle approximation (SAA) is determined. As SAA contains all the singularities of the exact solution, the indicated difference is a smooth angle function that essentially simplifies its determination by any numerical method. The most general SAA form is the small angle modification of the spherical harmonics method (MSH), an analytic form of which is a series on surface harmonic. It determined the choice of the spherical harmonics (SH) method for the definition of the indicated difference. However at the transition to 3D medium geometry the SH method loses its efficiency because of the huge difficulties of the statement of the boundary conditions. At the same time an analytic form of SAA allows easily to calculate the scattering integral in RTE and to determinate the source function. In this case the rest can be determined by the discrete ordinates method (DOM). In DOM RTE is exchanged to a set of the ordinary differential equations for the directions fixed in space (rays) that essentially simplifies a statement of both arbitrary boundary conditions, and accommodation to the complex 3D medium geometry. Such approach is similar to SHDOM, but exceeds it at the convergence rate.