Diffusion theory is widely used to describe photon migration in turbid media because it is simple and, in certain cases, can be accurate to within a few percent. However, it neglects the ballistic nature of photon propagation between successive scattering events and hence entirely breaks down for short times and distances, as well as for strong absorption. Here we generalize on the exact two-stream theory of one-dimensional photon migration to obtain a telegrapher equation that accounts for both diffusive and ballistic aspects of propagation in three-dimensional media. At long times and distances the standard diffusion theory is recovered, whereas at short times and distances we find improved predictions for such phenomena as pulse spreading, diffuse photon-density wave dispersion, transmission through a slab, and pulse reflection from a semi-infinite medium. Our theory should be useful for accurately characterizing turbid media, such as biological tissues, and may also aid in improving the spatial resolution of images made with diffuse light.
© 1997 Optical Society of America
D. J. Durian and J. Rudnick, "Photon migration at short times and distances and in cases of strong absorption," J. Opt. Soc. Am. A 14, 235-245 (1997)