APPLICATION OF THE EIGENFUNCTIONS METHOD AND AMBARTSUMYAN INVARIANCE-PRINCIPLE TO THE PROBLEM OF SMALL-ANGLE LIGHT-REFLECTION FROM MEDIA WITH LARGE-SCALE SCATTERING CENTERS

The process of small-angle reflection of radiation under grazing incid ence of a light beam upon a flat surface of a semi-infinite material l ayer with large-scale scattering centers is considered. The most impor tant practical case is analyzed when the scattering phase function dec reases with the increase of the single-scattering angle gamma slower t han gamma(4), which precludes the use of the Fokker-Planck approximati on for the description of light reflection. Two alternative approaches are considered: the ''invariant embedding'' method proposed by Ambart sumyan for small-angle light reflection and the method of eigenfunctio ns, which allows one to obtain a linear equation for the reflection fu nction. Using the reflection function obtained in the framework of qua si-diffusion approximation with respect to photon scattering angles, t he influence of the ratio of the angle of grazing incidence zeta(0) to the effective single-scattering angle gamma(ef) on the process of lig ht reflection is investigated with the help of the Ambartsumyan equati on. If zeta(0)/gamma(ef)(l) greater than or similar to 5, the quasi-di ffusion approximation is shown to describe the process of backward sca ttering with high accuracy. Thorough analysis of the role of linear an d nonlinear terms in the Ambartsumyan equation is made. It is shown th at the nonlinear term in this equation can be neglected in the case of small-angle reflection.