Separation of Frequency Variables in the Problem of Diffuse Reflection from a Semi-Infinite Medium under Isotropic Scattering with a General Law of Radiation Redistributionby Frequencies - Pikichyan, H. V.
In the presented work, with the help of a new approach previously proposed by the author, the problem of diffuse reflection of radiation from a plane-parallel semi-infinite medium under isotropic scattering in the case of the general law of radiation redistribution by frequencies is solved. Resulting solution implements the possibility of separating a pair of independent variables (namely, the frequency and direction of the quantum) of entering the medium quanta from the same pair of exiting quanta. The advantage of this approach in relation to the known methods is that the separation of the explanatory variables is achieved without the need to solve the additional problem of separation or any special representation of the characteristics of a single act of scattering. Here, in an expanded form is sought namely the solution of the modified initial problem, instead of a preliminary decomposition of the characteristics of a single act of scattering. As a result, the unknown function of the four explanatory variables is expressed explicitly through a system of auxiliary functions that depend on only two variables. For this purpose, a problem for eigenvalues and eigenfunctions is formulated for a specially selected and previously unknown kernel. Bilateral relationships between the solutions of the new and traditionally used methods are obtained, which makes it possible to directly compare their accuracy and efficiency. The general scheme of the organization of calculations is also discussed.
Keywords: Astrometry; Space Sciences; Archaeoastronomy and Astronomy in Culture