An adjoint Monte Carlo treatment of the equations of radiative transfer for polarized light

Abstract

The equation of radiative transfer for a Stokes' intensity vector is used to define a four-vector Green's function. The physical quantities of interest are represented by a response vector which is found by integrating the product of a suitable response matrix and the Stokes' intensity vector over phase space. Equations adjoint to those for the Stokes' intensity vector and for the Green's function vector are given. The response vector is then expressed in terms of the adjoint vector Green's function. A Monte Carlo sampling procedure is given for the adjoint Green's function vector equation. When the adjoint source vector is given by a Dirac delta function in phase space, the response vector is the Stokes' intensity vector and the “backward Monte Carlo method” of Collins and Wells (Report RRA-T74, Radiation Research Associates, Inc.) obtains.