Time-domain solution to the radiative transfer equation in an infinite turbid medium with linearly anisotropic...

A time-dependent solution of the transport equation with an instantaneous point source is considered by the multiple collision method developed by Kholin [Zh. Vych. Mat. i Mat. Fys.4, 1126 (1964)]. For a linear phase function, Kholin's solution is found to be considerably simplified and can be expressed through a single integral. The shape of the time-dependent angle-averaged scattering intensity is shown to depend on the distance from the source. For short distances, the angle-averaged scattering intensity decays monotonically with time. For longer distances, the angle-averaged intensity exhibits two peaks. The first infinite peak occurs at the wavefront and is followed by a narrow decaying tail. The second peak occurs at approximately the position of the diffusion peak but is higher than the diffusion peak. At large distances, the shape of the intensity after the wavefront arrival is well approximated by the diffusion shape. Good agreement with Monte Carlo simulation is demonstrated.