### Abstract

Forward-peaked and large-angle scattering approximations of the radiative transport equation give rise to generalized Fokker-PIanck equations whose main feature is the replacement of the integral scattering operator with differential operators in the direction-space variables. Using the P_{N} method, an appraisal of generalized Fokker-PIanck equations due to González- Rodriguez 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-PIanck equations and the transport equation with Henyey-Greenstein phase function for anisotropies ranging from 0 to 1. Generalized Fokker-PIanck 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.

Original language | English (US) |
---|---|

Pages (from-to) | 229-241 |

Number of pages | 13 |

Journal | Applied Optics |

Volume | 48 |

Issue number | 2 |

DOIs | |

State | Published - Jan 10 2009 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Applied Optics*,

*48*(2), 229-241. https://doi.org/10.1364/AO.48.000229

**On the accuracy of generalized fokker-planck transport equations in tissue optics.** / Phillips, Kevin G.; Lancellotti, Carlo.

Research output: Contribution to journal › Article

*Applied Optics*, vol. 48, no. 2, pp. 229-241. https://doi.org/10.1364/AO.48.000229

}

TY - JOUR

T1 - On the accuracy of generalized fokker-planck transport equations in tissue optics

AU - Phillips, Kevin G.

AU - Lancellotti, Carlo

PY - 2009/1/10

Y1 - 2009/1/10

N2 - Forward-peaked and large-angle scattering approximations of the radiative transport equation give rise to generalized Fokker-PIanck equations whose main feature is the replacement of the integral scattering operator with differential operators in the direction-space variables. Using the PN method, an appraisal of generalized Fokker-PIanck equations due to González- Rodriguez 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-PIanck equations and the transport equation with Henyey-Greenstein phase function for anisotropies ranging from 0 to 1. Generalized Fokker-PIanck 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.

AB - Forward-peaked and large-angle scattering approximations of the radiative transport equation give rise to generalized Fokker-PIanck equations whose main feature is the replacement of the integral scattering operator with differential operators in the direction-space variables. Using the PN method, an appraisal of generalized Fokker-PIanck equations due to González- Rodriguez 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-PIanck equations and the transport equation with Henyey-Greenstein phase function for anisotropies ranging from 0 to 1. Generalized Fokker-PIanck 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.

UR - http://www.scopus.com/inward/record.url?scp=60849133341&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60849133341&partnerID=8YFLogxK

U2 - 10.1364/AO.48.000229

DO - 10.1364/AO.48.000229

M3 - Article

C2 - 19137033

AN - SCOPUS:60849133341

VL - 48

SP - 229

EP - 241

JO - Applied Optics

JF - Applied Optics

SN - 0003-6935

IS - 2

ER -