Forward-peaked and large-angle scattering approximations of the radiative transport equation give rise to generalized Fokker–Planck equations whose main feature is the replacement of the integral scattering operator with differential operators in the direction-space variables. Using the method, an appraisal of generalized Fokker–Planck equations due to González-Rodríguez and Kim [Appl. Opt. 47, 2599–2609 (2008)], Leakeas and Larsen [Nucl. Sci. Eng. 137, 236–250 (2001), and J. Opt. Soc. Am. A 20, 92–98 (2003)], and Pomraning [Math. Models Meth. Appl. Sci. 2, 21–36 (1992)] is carried out by computing the relative error between the backscattered and transmitted surface flux predicted by the generalized Fokker–Planck equations and the transport equation with Henyey–Greenstein phase function for anisotropies ranging from 0 to 1. Generalized Fokker–Planck equations whose scattering operators incorporate large-angle scattering and possess eigenvalues similar to the integral scattering operator with Henyey–Greenstein phase function are found to minimize the relative error in the limit of unit anisotropy.
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Eleanor P. Zege, losif L. Katsev, and Igor N. Polonsky
Appl. Opt. 32(15) 2803-2812 (1993)
Arnold D. Kim and Joseph B. Keller
J. Opt. Soc. Am. A 20(1) 92-98 (2003)
Anabela da Silva, Mady Elias, Christine Andraud, and Jacques Lafait
J. Opt. Soc. Am. A 20(12) 2321-2329 (2003)