Abstract

An asymptotic analysis of the radiative transfer equation with polarization is developed that leads to a renormalized scalar equation for the total specific intensity of radiation I, the first Stokes parameter, in three-dimensional geometries. The resulting scalar equation can be used without the complexity of performing vector radiative computations since it merely requires an adjustment of the coefficients of the scattering phase matrix. The equation is accurate to first order in the smallness parameter of the asymptotic analysis. Asymptotically consistent quadrature results are obtained for Q, U, and V, the other three Stokes parameters. Numerical results demonstrate the improved accuracy of the renormalized scalar equation for the intensity compared with the usual unpolarized approximation and illustrate that small effects of polarization can be propagated to large optical depths within a medium.

© 1998 Optical Society of America

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