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 phenomenological model of bidirectional reflectance result from a complicated internal structure of planetary regolith particles. This paper tests that hypothesis by theoretically computing asymmetry parameters for isolated 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 that it is essentially impossible to make asymmetry parameters of planetary regolith particles even slightly negative by filling the particles with large numbers of internal inclusions in the form of voids and/or grains with a refractive index substantially different from that of the host medium. Asymmetry parameters are positive even for densely packed composite particles with no internal absorption and extreme values of the internal scattering coefficient. Furthermore, they are sharply increased by even modest absorption inside composite particles, by reducing the refractive index contrast between the inclusions and the host particles, and/or by decreasing the packing density. Thus, the negative asymmetry parameters retrieved with Hapke's model need another explanation 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 approximate solution of the radiative transfer equation which inherently violates the energy conservation law. Therefore, the negative asymmetry parameters are likely to be numerical artefacts resulting from the approximations made in the model. (C) 1997 Elsevier Science Ltd.