Isotropization length for random walk models of photon migration in turbid media

Abstract Analyses of photon transport in multiply scattering media are often formulated in terms of diffusion theory. Recently Gandjbakhche et al. have taken forward scattering into account by calculating the mean-squared displacement of an anisotropic random walk as a function of the step number and calculating a diffusion constant in terms of parameters that take anisotropy into account. This cannot yield accurate results at very short times when the motion is ballistic rather than diffusive. We translate the calculation of Gandjbakhche et al. into continuous time. As expected, the short-time behaviour of the mean squared displacement is proportional to t 2 while at longer times it switches over to being proportional to t. The long-time limit of these results provides an isotropization length for the corresponding diffusion approximation.