Shadow-hiding effect in inhomogeneous layered particulate media

Abstract

Shadow hiding is studied for particulate media consisting of opaque, spherical particles with Lambertian scattering phase functions. The present computer modeling allows geometric optics calculations of the photometric characteristics of layered particulate media with accuracies better than 1%. For statistically homogeneous particulate media, packing density is the single parameter that characterizes the opposition effect due to shadow hiding. The opposition effects become sharper with decreasing packing density both for monodisperse and polydisperse particulate media. There are no differences between the phase curves of monodisperse and polydisperse media with equal packing densities. A monolayer of hemispherical particles placed randomly on a plane-parallel, Lambertian background medium always produces phase curves that are convex upward. A monolayer of spherical particles can give almost linear phase curves in the phase angles of 0–40°. In a double-layer model, an optically thin layer of small particles can sharpen the opposition effect, but that depends strongly on the method of conjugation of the two layers. A dependence of the opposition effect on the size of the upper-layer particles really exists (Hillier's effect), but it is rather small at about 5% according to our calculations. Sparsely distributed large particles on a plane-parallel dusty surface can also produce sharpening of the phase function near opposition.