# 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*'*_{tr}d, where Σ*'*_{tr}d = Σ_{tr}d
- *ik*, where Σ_{tr} 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.