ASYMMETRY PARAMETERS OF THE PHASE FUNCTION FOR ISOLATED AND DENSELY PACKED SPHERICAL-PARTICLES WITH MULTIPLE INTERNAL INCLUSIONS IN THE GEOMETRIC OPTICS LIMIT

Since large, homogeneous dielectric particles have positive asymmetry parameters even when they are densely packed, it has been hypothesized that negative asymmetry parameters retrieved with Hapke's phenomenolo gical model of bidirectional reflectance result from a complicated int ernal structure of planetary regolith particles. This paper tests that hypothesis by theoretically computing asymmetry parameters for isolat ed and densely packed composite spherical particles with size typical of regolith grains. It is assumed that the wavelength of the scattered light is much smaller than the particle size, and that particles are filled with large numbers of small inclusions. The computations show t hat it is essentially impossible to make asymmetry parameters of plane tary regolith particles even slightly negative by filling the particle s with large numbers of internal inclusions in the form of voids and/o r grains with a refractive index substantially different from that of the host medium. Asymmetry parameters are positive even for densely pa cked composite particles with no internal absorption and extreme value s of the internal scattering coefficient. Furthermore, they are sharpl y increased by even modest absorption inside composite particles, by r educing the refractive index contrast between the inclusions and the h ost particles, and/or by decreasing the packing density. Thus, the neg ative asymmetry parameters retrieved with Hapke's model need another e xplanation rather than assuming that they are real and are the result of a complicated internal structure of regolith particles. Besides the opposition-effect term, Hapke's model is nothing more than an approxi mate solution of the radiative transfer equation which inherently viol ates the energy conservation law. Therefore, the negative asymmetry pa rameters are likely to be numerical artefacts resulting from the appro ximations made in the model. (C) 1997 Elsevier Science Ltd.