For the reduction of the equations of radiative transfer, the most convenient representation of the state of polarization is by a one-column intensity matrix of the four coherency-matrix elements or their linear combinations, derived from the electric-field components parallel and perpendicular to the plane through the local vertical and the direction of the light beam. A particular law of scattering is then expressed by a four-by-four (Mueller) scattering matrix which connects the intensity matrices of the incident and scattered light. The form of such scattering matrices for various representations of the state of polarization, as well as the corresponding reciprocity relationships, are derived with the use of the matrix formalism recently introduced by Marathay. The reciprocity relationships, i.e., the pertinent relationships when the incident and scattered beams are interchanged or when their directions of propagations are reversed, can be expressed in terms of a transposition of the original scattering matrix accompanied by pre- and post-multiplication by certain diagonal matrices that incorporate the changes in the sign of some elements of the scattering matrix after transposition. The derived reciprocity relationships are new except for those which govern the reversal of directions when the state of polarization is represented by the Stokes parameters and their modifications (used by Chandrasekhar) and which have been given earlier by Chandrasekhar and van de Hulst.
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