ISOTROPIZATION LENGTH FOR RANDOM-WALK MODELS OF PHOTON MIGRATION IN TURBID MEDIA

Analyses of photon transport in multiply scattering media are often fo rmulated in terms of diffusion theory. Recently Gandjbakhche et al. ha ve taken forward scattering into account by calculating the mean-squar ed displacement of an anisotropic random walk as a function of the ste p number and calculating a diffusion constant in terms of parameters t hat take anisotropy into account. This cannot yield accurate results a t very short times when the motion is ballistic rather than diffusive. We translate the calculation of Gandjbakhche et ad. into continuous t ime. As expected, the short-time behaviour of the mean squared displac ement is proportional to t(2) while at longer times it switches over t o being proportional to t. The long-time limit of these results provid es an isotropization length for the corresponding diffusion approximat ion.