Relations between the elements of the phase matrix for scattering

Abstract

The process of scattering of radiation is usually characterized by a 4 × 4 transformation matrix which relates the radiation field vector incident on the scatterer to the scattered field vector. The nine relations between the 16 elements of this phase matrix for scattering are derived explicitly for the three most commonly used representations of the intensity vector, viz., Wolf's coherency matrix formalism, Chandrasekhar's and Stokes's representations. The invariance of these relations under the action of any optical train containing one or more elements characterized by their Jones representation is demonstrated. These relations should be useful in the theory of polarization optics. The same relations are also shown to hold after rotation of the axes of reference for the electric vectors in the incident and scattered beams. Since such a transformation is required in the formulation of the theory of radiative transfer, the relations derived here may find use in multiple scattering problems as well.