Multiple Scattering in Homogeneous Plane-Parallel Atmospheres

Steady-state multiple-scattering problems for homogeneous plane-parallel atmospheres have been extensively studied by means of the principles of invariance of Ambartsumian and Chandrasekhar. These nonlinear integral equations have been used for computing intensities of radiation on the faces of the atmosphere. Using linear integral-equation theory, the author shows how to compute the source function interior to an atmosphere with optical depth entering the computation only parametrically. Intensities, throughout the atmosphere, are expressed by nonlinear combinations of the computed source function, giving, on the faces, the familiar scattering and transmission functions. By a reduction developed by Sekera, this analysis is applied to Rayleigh scattering including the effects of polarization. Steady-state multiple-scattering problems for homogeneous plane-parallel atmospheres have been extensively studied by means of the principles of invariance of Ambartsumian and Chandrasekhar. These nonlinear integral equations have been used for computing intensities of radiation on the faces of the atmosphere. Using linear integral-equation theory, the author shows how to compute the source function interior to an atmosphere with optical depth entering the computation only parametrically. Intensities, throughout the atmosphere, are expressed by nonlinear combinations of the computed source function, giving, on the faces, the familiar scattering and transmission functions. By a reduction developed by Sekera, this analysis is applied to Rayleigh scattering including the effects of polarization.