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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 26 — Dec. 24, 2007
  • pp: 18168–18175

Heuristic Green’s function of the time dependent radiative transfer equation for a semi-infinite medium

Fabrizio Martelli, Angelo Sassaroli, Antonio Pifferi, Alessandro Torricelli, Lorenzo Spinelli, and Giovanni Zaccanti  »View Author Affiliations


Optics Express, Vol. 15, Issue 26, pp. 18168-18175 (2007)
http://dx.doi.org/10.1364/OE.15.018168


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Abstract

The Green’s function of the time dependent radiative transfer equation for the semi-infinite medium is derived for the first time by a heuristic approach based on the extrapolated boundary condition and on an almost exact solution for the infinite medium. Monte Carlo simulations performed both in the simple case of isotropic scattering and of an isotropic point-like source, and in the more realistic case of anisotropic scattering and pencil beam source, are used to validate the heuristic Green’s function. Except for the very early times, the proposed solution has an excellent accuracy (>98% for the isotropic case, and >97% for the anisotropic case) significantly better than the diffusion equation. The use of this solution could be extremely useful in the biomedical optics field where it can be directly employed in conditions where the use of the diffusion equation is limited, e.g. small volume samples, high absorption and/or low scattering media, short source-receiver distances and early times. Also it represents a first step to derive tools for other geometries (e.g. slab and slab with inhomogeneities inside) of practical interest for noninvasive spectroscopy and diffuse optical imaging. Moreover the proposed solution can be useful to several research fields where the study of a transport process is fundamental.

© 2007 Optical Society of America

OCIS Codes
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5280) Medical optics and biotechnology : Photon migration
(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics
(170.7050) Medical optics and biotechnology : Turbid media

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: October 31, 2007
Revised Manuscript: December 7, 2007
Manuscript Accepted: December 17, 2007
Published: December 19, 2007

Virtual Issues
Vol. 3, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Fabrizio Martelli, Angelo Sassaroli, Antonio Pifferi, Alessandro Torricelli, Lorenzo Spinelli, and Giovanni Zaccanti, "Heuristic Green’s function of the time dependent radiative transfer equation for a semi-infinite medium," Opt. Express 15, 18168-18175 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-26-18168


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