Scattering Matrices of Particle Ensembles Analytically Decomposed into Pure Mueller Matrices

Scattering matrices of particle ensembles are analytically decomposed into sums of pure Mueller matrices. The ensembles are assumed to have equal numbers of particles and their mirror particles, both in random orientation. In the general case, there are four pure Mueller matrices in the decomposition. In the present spectral decomposition, of these four matrices, there is a single matrix that qualifies as a scattering matrix, whereas the remaining three matrices represent other classes of pure matrices. For ensembles of spherical particles, there are two pure Mueller matrices in the decomposition. Again, there is a single matrix qualifying as a scattering matrix. The analytical decomposition unveils the explicit dependencies of the pure Mueller matrices on the ensemble-averaged scattering matrix. Applications are identified in scattering by single particles and by random media of particles.