Scattering and absorption of light in planetary regoliths: Holistic modeling

We consider scattering and absorption of light in planetary regoliths composed of nonspherical particles, striving towards a holistic theoretical model. For the particles, we incorporate size and refractive index distributions and generate sample regolith geometries using varying packing algorithms. In order to ensure feasibility for the computations, we make use of average elementary scattering and absorption properties of the particles available from experimental and numerical studies. In so doing, we make use of empirical parameterizations for the elementary scattering matrices.

We start by considering radiative transfer and coherent backscattering (RT-CB) in discrete random media of particles, where the scattering phase matrix has the symmetry corresponding to an ensemble of nonspherical particles and their mirror particles, both in random orientation. Using the Cloude spectral decomposition, we present the ensemble-averaged scattering phase matrices as a linear superposition of four pure Mueller matrices (Muinonen & Penttilä, JQSRT, submitted, 2024). The pure Mueller matrices enable RT-CB computations based on the assumption of independence of the four contributing components. We validate the RT-CB decomposition method for sparsely and densely packed random media of polydisperse spherical particles (Muinonen et al., in preparation). For the case of sparse packing, we compare two different RT-CB approaches, one based on explicit input of different spherical-particle characteristics and the other based on the decomposition of the ensemble-averaged scattering phase matrix. The results agree closely.  

For the cases of dense packing, the so-called incoherent volume elements of particles need to be invoked. Consequently, we compare the RT-CB results to exact results using the Fast Superposition T-matrix Method (FaSTMM; Markkanen & Yuffa, JQSRT 189, 181, 2017) for equivalent media, invoking the decomposed ensemble-averaged scattering phase matrix of wavelength-scale incoherent volume elements as input for RT-CB. For non-absorbing particles, the RT-CB results are seen to agree well with the exact FaSTMM results, whereas, for absorbing particles, the agreement remains satisfactory. Here it is possible to introduce size distributions of particle clusters that are large compared to the wavelength, resulting in mutual shadowing of such clusters. The overall volume density then derives from voids within the clusters and those in between the clusters.

In order to facilitate an efficient use of the RT-CB method, we have devised an empirical parameterization of the ensemble-averaged scattering matrix (Muinonen & Leppälä, in preparation). Combined with spectral decomposition, this provides a straightforward pathway to RT-CB computations using arbitrary scattering phase matrices. In particular, such matrices can derive from experimental measurements or numerical computations.

Fractional-Brownian-motion statistics (fBm) provide a realistic model for surface roughness, that is, the interface between the regolith and the free space (see, e.g., Björn et al., present meeting). The fBm statistics are described by two parameters: the Hurst exponent related to the fractal dimension and describing the horizontal variegation and the amplitude describing the vertical variegation. The fBm interfaces can be utilized by intersecting numerically generated particulate regolith geometries with sample fBm interfaces, removing the particles residing above the interface. 

Finally, we discuss future modeling prospects for the RT-CB decomposition method, paying special attention to the modelling of photometric opposition effects, degrees of linear polarization for unpolarized incident light, and spectral phase effects. The holistic modelling can be applied in studies of airless Solar System objects, such as the Moon, Mercury, asteroids, and icy planetary satellites (e.g., Leppälä et al., Björn et al., and Penttilä et al., present meeting).