Diffusion Boundary Conditions for Photon Waves

R. Aronson (1997)

Summary

The use of diffusion theory in calculations on photon waves necessitates a new look at boundary conditions, since the standard boundary conditions have been derived under static conditions. When the underlying process satisfies the transport equation, the proper boundary conditions are obtained by solving the Milne problem. This paper presents benchmark–quality values for extrapolation distances calculated by transport theory, for various values of absorption and three models of the phase function—isotropic, linearly anisotropic and Henyey-Greenstein scattering. The results show that the static boundary conditions are perfectly adequate up to photon wave frequencies of 1 GHz or even more. Specifically, the quantity Σ'trd, where Σ'trd = Σtrd - ik, where Σtr is the macroscopic transport cross section and k the wave number in the medium and d the linear extrapolation distance, is essentially independent of frequency over this range. We have also examined the ratio of the diffusion length as given by transport theory to that given by diffusion theory itself. This is extremely insensitive to frequency, but for substantial absorption, using the diffusion theory result can lead to substantial errors in thick media, especially for Henyey–Greenstein scattering.