Normalization for Ultrafast Radiative Transfer Analysis With Collimated Irradiation

Normalization of the scattering phase function is applied to the transient discrete ordinates method for ultrafast radiative transfer analysis in a turbid medium subject to a normal collimated incidence. Previously, the authors have developed a normalization technique which accurately conserves both scattered energy and phase function asymmetry factor after directional discretization for the Henyey-Greenstein phase function approximation in steady-state diffuse radiative transfer analysis. When collimated irradiation is considered, additional normalization must be applied to ensure that the collimated phase function also satisfies both scattered energy and asymmetry factor conservation. The authors’ technique is applied to both the diffuse and collimated components of scattering using the general Legendre polynomial phase function approximation for accurate and efficient ultrafast radiative transfer analysis. The impact of phase function normalization on both predicted heat fluxes and overall energy deposition in a model tissue cylinder is investigated for various phase functions and optical properties. A comparison is shown between the discrete ordinates method and the finite volume method. It is discovered that a lack of conservation of asymmetry factor for the collimated component of scattering causes over-predictions in both energy deposition and heat flux for highly anisotropic media.