Petrov D. Photometrical properties of surfaces and particles with pre-fractal structure.

Object of study: the particles having complex hierarchical structure, for example, powders or lunar soil, and surfaces of complex hierarchical structure, for example, lunar surface.Aim: the theoretical description of shadowing effect concerning with surfaces and particles with random hierarchical structure.Methods: the solving of differential equations by known methods and numerical simulation of lightscattering by hierarchical structure is suggested in this work.Results, novelty: It was at first time the theoretical description of shadowing effect on pre-fractal statistically rough surfaces with any quantity of hierarchical structure levels with finite value of root-mean-square slope on each level. At first time the shadowing effect is described, when the surface on each hierarchical level is single-valued with gaussian heights distribution. At first time the equations, which describe the shadow effect for wide class of discrete random media with arbitrary shape particles density gradient, are obtained. At first time the influence of multiple scattering on the determination of multiscale rough surface parameters is estimated. At first time the area of permanent shading sections of lunar surface near the poles is estimated in the branches of two-scale model, when crater relief is complicated by random relief. Field of implementation: optics, planetology.