Complete simplification of the solution of the diffuse reflection problem by the method of “decomposition of resultant field” (DRF) - Pikichyan, H. V.
The classical diffuse reflection problem (DRP) of radiation from a plane-parallel semi-infinite medium under isotropic scattering in the case of the general law r (x, x′) of radiation redistribution by frequencies in the elementary act of scattering is considered. It is shown that the solution of the DRP ρ ( x, μ;x ′ , μ ′) , which depends on four independent variables, with the help of author’s recently developed method of ”decomposition of the resultant field-DRF” it is possible to express explicitly through auxiliary functions Gi (z) , Qi (x) that depend on only one independent variable. A significant difference between this DRF method and the widely used traditional approach of ”decomposition of a single act - DSA” of scattering is that it no longer requires any decomposition or a special representation of the characteristics of a single act of scattering (in the case under consideration, the function of redistribution of radiation by frequencies - r (x, x′)) . In DRF, the resulting field of multiply scattered radiation itself is searched directly in the decomposed form. It is obvious that after each successive single act of scattering, the resulting radiation field in the medium becomes more and more smoother, so that with the same required accuracy, its decomposition will contain fewer terms than the decomposition of the characteristic of a single act of scattering. This circumstance makes the DRF method especially effective in relation to the DSA approach in cases where the latter requires taking into account a large number of terms of the decomposition of the frequency redistribution function r (x, x′) . Explicit analytical expressions of the two-way relationship are also obtained between the desired values of the traditional and the methods proposed by the author.
Keywords: Radiative transfer