Two- and three-dimensional radiative transfer in the diffusion approximation

A 3-D transport code DIF3D, based on the diffusion approximation, is used to model the spatial distribution of radiant energy arising from volumetric isotropic sources. The limits of validity of the diffusion approximation are formulated quantitatively by comparing the results, in the case of a slab geometry, of the diffusion and transport theories. For 3-D geometry, the results are presented in the form of isosurface plots, which give the surfaces of constant energy density. It is shown that as the detector sensitivity decreases, individual sources cannot be spatially distinguished, thus leading to a discrimination problem. Applications of the diffusion approximation to imaging through a medium with isotropic scattering are described. For a periodic distribution of line sources, the image is considerably degraded if the optical depth of the scattering medium is 0.4 or larger.