Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer

The scattering of radiation from collimated irradiation is accurately treated via normalization of phase function. This approach is applicable to any numerical method with directional discretization. In this study it is applied to the transient discrete-ordinates method for ultrafast collimated radiative transfer analysis in turbid media. A technique recently developed by the authors, which conserves a phasefunction asymmetry factor as well as scattered energy for the Henyey-Greenstein phase function in steady- state diffuse radiative transfer analysis, is applied to the general Legendre scattering phase function in ultrafast collimated radiative transfer. Heat flux profiles in a model tissue cylinder are generated for various phase functions and compared to those generated when normalization of the collimated phase function is neglected. Energy deposition in the medium is also investigated. Lack of conservation of scattered energy and the asymmetry factor for the collimated scattering phase function causes overpredictions in both heat flux and energy deposition for highly anisotropic scattering media. In addition, a discussion is presented to clarify the time-dependent formulation of divergence of radiative heat flux.