An analytical solution of the radiative transfer equation for the radiance caused by an isotropic source which is located in an infinitely extended medium was derived using the $P_N$ method. The results were compared with Monte Carlo simulations and excellent agreement was found. In addition, the radiance of the ${\mathit{SP}}_N$ approximation for the same geometry was derived. Comparison with Monte Carlo simulations showed that the ${\mathit{SP}}_N$ radiance, although being more exact than the radiance derived from diffusion theory, has relatively large errors in many relevant cases.

• Received 14 October 2010

DOI:https://doi.org/10.1103/PhysRevE.83.036605