Statistics
Scientific paper
Nov 1976
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976jqsrt..16..973d&link_type=abstract
Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 16, Nov. 1976, p. 973-982.
Statistics
3
Fredholm Equations, Green'S Functions, Linear Equations, Radiative Transfer, Stokes Law Of Radiation, Albedo, Eigenvalues, Eigenvectors, Kernel Functions, Milne Method, Normalizing (Statistics)
Scientific paper
Linear Fredholm integral equations for the Stokes vector of polarized radiation emergent from a scattering plane-parallel semiinfinite medium are derived by means of the full-range orthogonality and completeness properties of Case's (1967) eigensolutions. A renormalization concerning the eigenmode with the greatest discrete eigenvalue is applied which permits one to obtain an integral equation for the zeroth Fourier component of the radiation field. The kernel of the integral equations is given in terms of Case's eigenfunctions or of the Green's function matrix for an infinite medium. For isotropic scattering, it is shown that the integral equation can be solved by means of a very rapidly convergent Neumann series. Physical arguments lead to the conclusion that the renormalized Fredholm integral equations are also well suited for arbitrary phase matrices.
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