Simulation of shadings in systems of opaque particles

Results of computer simulation of the shading effect in systems of opaque spherical particles scattering light in accordance with the Lambert law are presented. Two types of systems are studied: a semi-infinite medium and statistically uniform clusters of a finite number of particles. The simulation makes it possible to obtain photometric characteristics of systems with an accuracy better than 1%. The phase dependence of the shading effect is shown to become steeper as the packing density of particles in clusters decreases and their number increases. For statistically uniform media, the following relation takes place: The lower the packing density, the more pronounced the shadow decrease in brightness with an increasing phase angle.