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In this paper we discuss symmetry properties of the matrices describing the reflection and transmission of polarized radiation by a slab of randomly oriented particles. A complete set of such symmetry relations valid in the common case in which there is no birefringence or dichroism is given. The derivation proceeds via 1) the symmetry properties of the phase matrix describing the scattering in a volume element and 2) the symmetry properties of the reflection and transmission matrices based on single scattering only. Birefringence and dichroism may occur if the particles do not have a plane of symmetry. The study of symmetry relations for this case is not carried beyond the stage of the phase matrix. Possible applications and some errors in the literature are pointed out.
J. W. Hovenier (Thu,) studied this question.