PHOTON PATH-LENGTH DISTRIBUTION FUNCTION .2. RAYLEIGH-CABANNES SCATTERING

The determination of the photon path-length distribution function (PLDF) in a semi-infinite plane-parallel homogeneous atmosphere is discussed while the atmosphere scatters radiation according to the 2 x 2 Rayleigh-Cabannes phase matrix. The Piessens-Huysmans method of numerically inverting the Laplace transform which proved to be successful for the non-polarized radiation works in this special case as well. To employ this method we had to define the complex H-matrix and to find a fast method to determine its numerical values. For determining the average path-lengths and the dispersion we set up a system of integral equations the solution of which gave us the H-matrix and its first two derivatives with respect to the albedo of single scattering. The influence of different parameters characterizing the interaction of the polarized radiation with the atmosphere on the PLDF and the average path-length is studied in detail and a sample of average path-lengths is given in Table I.