Shadowing effect in clusters of opaque spherical particles

The shadowing effect is studied for clusters of opaque spherical particles. The present modeling allows geometric optics computations of cluster scatt ering phase functions and shadowing effects with internal accuracy better t han 1%. Three types of cluster structures are treated-uniform, ballistic, a nd hierarchical (physical fractal)-and three types of elementary surface sc attering laws are examined-Lambertian, flux-isotropic, and specular. All st ructures investigated give rise to an opposition effect, that is, a nonline ar brightening toward zero phase angle. The amplitude and width of the oppo sition effect depend on the cluster parameters. For uniform dusters, the vo lume fraction and number of particles are the parameters that characterize the shadowing effect. The opposition effect becomes sharper with increasing number of constituent particles and with decreasing particle volume fracti on. For ballistic clusters, the only parameter is the number of particles: when it increases, the opposition effect becomes sharper. For hierarchical clusters, the number of cluster structural levels plays a crucial role. Wit h increasing number of cluster levels, the opposition behavior of brightnes s becomes markedly more nonlinear, mostly due to the decreasing particle vo lume fraction. It is notable, however, that the opposition effects of the h ierarchical clusters and the uniform clusters with the same particle volume fraction differ from each other underscoring the importance of the detaile d cluster structure on shadowing. It is shown that, with reasonable accurac y, the cluster scattering phase functions can be factorized as the products of the corresponding single-particle phase function and the so-called shad owing factor almost independently of the elementary surface scattering law. While the opposition effect due to shadowing is presently confirmed, it is typically wider than the opposition effect due to coherent backscattering, an interference mechanism in multiple scattering. The present work helps u s to understand, e.g., the opposition effects of the Moon, asteroids, and o ther atmosphereless celestial bodies. (C) 2001 Elsevier Science Ltd. All ri ghts reserved.