A discussion of the reduction of the equations of radiative transfer when the phase matrix is "separable." A separable matrix is one that can be expressed as the product of two matrices, one whose elements depend on the directional parameters of the incident beam alone, and the other whose elements depend on the directional parameters of the scattered and incident beams and each term of this series is separable, the radiative transfer equations have "series" solutions with each term of this series is separable, the radiative transfer equations have "series" solutions with each term in these series being given by a product of three matrices; one of these is azimuth-independent, the other two, which post- and pre-multiply this matrix, are the same matrices whose product forms the corresponding term in the phase matrix.
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