The transport equation in optically thick media

The photon transport equation is transformed into a new form by considering the deviation of the specific intensity from the local equilibrium field. We call the new form of the equations the difference formulation. It is rigorously equivalent to the original transport equation. The difference formulation is particularly suited for thick media, where the radiation field approaches local equilibrium and the deviations from the Planck distribution are small. The difference formulation for photon transport also clarifies the diffusion limit. Preliminary results confirm our expectations of a substantial advantage for accurate numerical calculations in optically thick media.