The Green’s function for the radiative transport equation in the slab geometry

Abstract The radiative transport equation is solved in the three-dimensional slab geometry by means of the method of rotated reference frames. In this spectral method, the solution is expressed in terms of analytical functions such as spherical harmonics and Wigner d-functions. In addition, the eigenvalues and eigenvectors of a tridiagonal matrix and certain coefficients, which are determined from the boundary conditions, must also be computed. The Green’s function for the radiative transport equation is computed and the results are compared with diffusion approximation and Monte Carlo simulations. We find that the diffusion approximation is not quite correct inside the slab, even when the light emitted from the slab is well described by the diffusion approximation. The solutions we obtain are especially convenient for solving inverse problems associated with radiative transport.