On the property of ”statistical identity” of solutions to some classical problems of the radiative transfer theory

Abstract

A probabilistic interpretation of the classical solution of the diffuse reflection problem (DRP) of radiation from a semi-infinite homogeneous scattering-absorbing medium on the language of random events in the simple case of monochromatic and isotropic scattering is constructed. A certain property of the so-called ”statistical identity” is specially defined. By using these two circumstances, it is possible to construct a simple symbolic scheme for the direct transformation of the solution mentioned above in the particular case of DRP into solutions to more general cases of DRP, which taking into account the anisotropy and incoherence of scattering, as well as the temporal dependence of the task on the act of absorption. Moreover, some generalization of the primary scheme makes it possible to directly obtain solutions of the DRP also for nonhomogeneous media and for general case of time dependence (on absorption acts and free flights between them) for the quanta diffusion process. At the same time, both the well-known results of the DRP decisions and some new ones were obtained.