Coherent backscattering and radiative transfer inembedded particulate planetary media

Scattering and absorption of light in macroscopic discrete random media of densely packed particles (e.g., planetary regoliths) constitutes a computational challenge in electromagnetics described by the Maxwell equations. There are differing physics cases that must be tackled separately. Exact solutions are typically available only for systems with maximum sizes of only a few wavelengths. 
  
We consider a radiative-transfer coherent-backscattering (RT-CB) approximation for embedded discrete random media of particles. The first case (Case I) concerns wavelength-scale particles within a half space of optically isotropic and homogeneous material described by a complex refractive index (host medium). In comparison to a semi-infinite discrete random medium in free space, Case I introduces an interface between free space and host medium and particle scattering and absorption properties must be computed in relation to the host medium. In RT-CB, interaction paths always include refractions into and out of the host medium, as well as any internal reflections that take place at the interface. Numerical Monte Carlo computation largely resembles that for semi-infinite random media in free space. In the UV-Vis-NIR part of the spectrum (wavelengths of 0.1-2.5 microns), Case I is relevant for planetary-regolith particles large compared to the wavelength with inhomogeneous internal composition. The internal inhomogeneities can derive from agglomerated minerals or voids. In the microwave part of the spectrum relevant for radars (wavelengths of 1-100 mm), Case I is relevant by the very definition of the radar scattering problem. 
  
Case II concerns a finite layer of wavelength-scale particles in free space on a half space of optically isotropic and homogeneous material (host medium). In comparison to a semi-infinite discrete random medium in free space, Case II thus introduces an interface in the bottom of the finite layer of particles. In RT-CB, interaction paths including a refraction into the host medium do not contribute to the scattering by the medium: refracted radiation is considered to be entirely absorbed. The interaction paths can include reflections from the interface and, from the point of view of RT-CB, the paths fall into different categories. The categories include the following cases: 
(i) the interaction path is a pure reflection process at the interface;
(ii) the interaction path includes particle scattering processes but no reflection processes;
(iii) the interaction path includes reflection processes but, in the RT path, the first and final interactions are particle scattering processes;
(iv) the first interaction is a reflection process and the last interaction is a particle scattering process;
(v) the first interaction is a particle scattering process and the last interaction is a reflection process;
(vi) the first and last interactions are reflection processes.    

We highlight a number of applications in scattering and absorption by airless Solar System objects in the UV-Vis-NIR and microwave spectral ranges (see Leppälä et al. and Pentikäinen et al., present conference). For UV-Vis-NIR, we apply the RT-CB computations to the case of a layer of wavelength-scale amorphous ice particles on the surface of crystalline ice particles large compared to the wavelength. For radar, we carry out a computation for absorbing particles within pure, crystalline water ice.