Abstract
Many current and proposed programs of satellite remote sensing of the Earth and other celestial bodies rely upon measurements of the intensity and polarization of light scattered by these bodies. These measurement data are interpreted by searching for the best fits to light-scattering characteristics precalculated with some theoretical models. For regolith-like surfaces, i.e., discrete densely packed random media, the light-scattering models are still under development and they work under different approaches. Here, to estimate the difference between the reflectance characteristics yielded by these procedures, we compare the results of simulations performed according to five frequently used approximate models of a semi-infinite particulate medium. Special attention is paid to taking into account the weak-localization effect. The models differ by the scattering matrixes of a volume element and the dependence of the imaginary part of the effective refractive index on the filling factor. The volume element is an individual spherical particle or a randomly oriented cluster of particles. The cases of modifying the scattering matrix by the static structure factor correction or by subtracting the contribution of the mean field are also considered. The values for the size parameter of particles or monomers in the clusters and the refractive index were assumed at 1.76 and 1.50 + i0.0001, respectively; and two values for the filling factor (defined as a volume fraction occupied by particles in the medium), 20 and 10%, were considered. Our analysis shows that the angular dependences of the intensity and the linear polarization degree obtained with the considered models are rather close to each other. Moreover, they agree with the corresponding characteristics for a large cloud of particles (N is equal to or exceeds 106) with the filling factor up to 20%, which were obtained by approximate methods but well follow the trends found in rigorous simulations for smaller ensembles of particles (Penttilä et al., J. Quant. Spectrosc. Radiat. Transfer, 2021, 262, 107524). Hence, these approximate models are equally acceptable to the interpretation of the results of observations.
Highlights
For many celestial bodies, the surfaces of which are covered with a regolith—a powder-like material composed of grains of different sizes and packing density—the interpretation of the results of observations in terms of the sizes, refractive index, and packing density of regolith particles requires the use of an adequate model to determine the characteristics of electromagnetic radiation reflected from a densely packed discrete random medium
While the description of the light scattering by densely packed media in terms of the ladder and cyclic diagrams has been considerably improved in recent years [see (Tishkovets et al, 2011; Doicu and Mishchenko, 2019b; Doicu and Mishchenko, 2019c) and references therein], the contribution of the diagrams corresponding to the interference of waves of different scattering orders has not been taken into account yet
To solve the radiative transfer and weak localization equations, the scattering matrix of a volume element of the medium is usually presented as a series expansion in generalized spherical functions (Mishchenko et al, 2006)
Summary
To gain insight into the nature, origin, and evolution of various bodies in the Solar System, including the Earth, photometric and polarimetric data obtained in space-borne and ground-based observations are widely used. The matter is that, as distinct from sparse media, densely packed media exhibit the effects, which cannot be described only by contributions of the ladder and cyclic diagrams to the scattered radiation, since these effects are caused by the interference of inhomogeneous waves of different scattering orders. The interference of this kind manifests itself in the mutual shadowing and may considerably influence the opposition effects (Tishkovets et al, 2013). While the description of the light scattering by densely packed media in terms of the ladder and cyclic diagrams has been considerably improved in recent years [see (Tishkovets et al, 2011; Doicu and Mishchenko, 2019b; Doicu and Mishchenko, 2019c) and references therein], the contribution of the diagrams corresponding to the interference of waves of different scattering orders has not been taken into account yet
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