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W.J. Markiewicz (Max-Planck-Institute for Aeronomy, Germany), E.V. Petrova (Space Science Institute, Russia and Max-Planck-Institute for Aeronomy, Germany), H.U. Keller (Max-Planck-Institute for Aeronomy, Germany)
A number of approximate models, and mainly the Hapke bidirectional reflection function, have been widely used to analyze photometric observations of planetary surfaces. Although these models are able to fit the data well with a small number of free parameters, they do not contain explicitly such crucial physical parameters as grain size or refractive index. A direct comparison of the Hapke model results with accurate numerical solutions of the radiative transfer equation for Henyey-Greenstein phase functions has revealed that the errors are small only for almost isotropic scattering when the asymmetry parameter is less than 0.2. However it is known that realistic phase functions of the soil particles are strongly forward scattering.
Using geometric optics approximation, we have found that a single scattering phase function of soil grains can be successfully modeled by a shape mixture of randomly oriented polydisperse spheroids. In order to take into account the effect of packing density in a regolith, we used the so-called static structure factor which depends on the particle size and the filling factor. The main effect of increasing packing density is to suppress the forward scattering diffraction component of the phase function and to increase the surface albedo. We used an accurate radiative transfer technique to compute bidirectional reflectance of a regolith layer composed of particles with specified physical properties (size, refractive index and packing density).
Although the problem of non-unique solution, which is inherent for derivation of the media properties from the measurements of the scattered light intensity, still remains, we would like to stress that the used exact procedure allows us to fit the observation data with a set of real characteristics of the regolith rather than with abstract parameters of the widely used approximations.