Exact description of photon migration in anisotropically scattering media

The aim of the present paper is to deliver a method for exact calculation of the probability of photon migration in an infinite and homogeneous medium scattering photons anisotropically. The phase function is represented as an expansion over spherical harmonics. The probability of photon migration is obtained as an expansion with respect to the number of scatterings with the coefficients depending on the distance-to-time ratio and can be easily calculated from recurrence relations. Up to 30 scatterings are taken into account when computing the migration probabilities, the number of effectively contributing scatterings being strongly dependent on the distance-to-time ratio decreasing when one approaches the propagation front. The important property of the method is its capability to describe exactly migration from the early arriving photons up to the scattering ones. The limits of the approximate description of anisotropic scattering as isotropic with an effective value of the scattering coefficient is analyzed by calculating the best-fit value of the scattering coefficient.