Coherent backscattering in discrete random media of particle ensembles

We consider radiative transfer and coherent backscattering (RT-CB) in a discrete random medium of particles. The elementary scattering matrix of the medium conforms to the ensemble-averaged scattering matrix for nonspherical particles and their mirror particles, both in random orientation. We express the ensemble-averaged matrix, via spectral decomposition, as a linear superposition of four pure Mueller matrices, and enable RT-CB computations via an independent treatment of the pure matrices. We validate the method for sparsely and densely packed random media of spherical particles. For the case of sparse packing, we compare two different RT-CB approaches, one with explicit input of polydisperse spherical-particle characteristics and the other with input by decomposing the ensemble-averaged scattering matrix. The results are in agreement and reproduce markedly well the asymptotically exact results from the Fast Superposition $T$-Matrix Method (FaSTMM). For the cases of dense packing, we compare the RT-CB to the FaSTMM by invoking the ensemble-averaged incoherent scattering matrix of volume elements as input for the RT-CB. For non-absorbing particles, the RT-CB agrees well with the FaSTMM. For strongly absorbing particles, there are deviations that underscore the need for further method development. In order to demonstrate the potential of the RT-CB, we compute multiple scattering for a sparsely packed spherical medium of nonspherical feldspar particles by utilizing their experimentally measured ensemble-averaged scattering phase matrix. Finally, we discuss future prospects for the RT-CB.