Eigenvalue Shifting - A New Analytical-Computational Method in Radiative Transfer Theory

Abstract

Linear integral functional relations holding for the leading regular eigenmodes are employed to transform the radiative transfer equation for polarized light in plane-parallel homogeneous media into an equivalent transfer equation of the same form with a modified scattering integral (pseudo-scattering). In its general form, this transformation incorporates two free function vectors. On specifying them appropriately, the effective single-scattering albedo for the transformed transfer equation can be reduced substantially. This drastically accelerates the convergence of iterative computational approaches. As a particular case, it is demonstrated how to employ the F- and K-integrals to transform the original transfer equation for conservative isotropic scattering into an equivalent transfer equation for nonconservative pseudo-scattering. A general method of transforming the transfer equation is described for the azimuthally averaged I,Q-component of the transfer equation for polarized radiation. Simple formulae are derived that express the original albedo matrix and surface Green’s function matrix in terms of the corresponding function matrices related to the transformed transfer equation. It is shown that the transformation described here selectively affects the asymptotic eigenmodes of the transfer equation and shifts the leading pair of discrete eigenvalues.