Radiative Transfer in a Rayleigh-Scattering Atmosphere with True Absorption

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Abstract
The singular‐eigenfunction‐expansion technique is used to solve the equation of transfer for partially polarized light in a Rayleigh‐scattering atmosphere with true absorption. The normal modes for the considered nonconservative vector equation of transfer are established; two discrete eigenvectors and two linearly independent continuum solutions are thus derived. Further, the necessary full‐range completeness and orthogonality theorems are proved, so that all expansion coefficients can be determined explicitly, and, in order to illustrate the technique, an exact analytical solution for the infinite‐medium Green's function is developed. Finally, a numerical tabulation of the required discrete eigenvalue, as a function of the single‐scatter albedo, is given.