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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 1 — Jan. 1, 2003
  • pp: 92–98

Light propagation in biological tissue

Arnold D. Kim and Joseph B. Keller  »View Author Affiliations


JOSA A, Vol. 20, Issue 1, pp. 92-98 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000092


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Abstract

Biological tissue scatters light mainly in the forward direction where the scattering phase function has a narrow peak. This peak makes it difficult to solve the radiative transport equation. However, it is just for forward-peaked scattering that the Fokker–Planck equation provides a good approximation, and it is easier to solve than the transport equation. Furthermore, the modification of the Fokker–Planck equation by Leakeas and Larsen provides an even better approximation and is also easier to solve. We demonstrate the accuracy of these two approximations by solving the problem of reflection and transmission of a plane wave normally incident on a slab composed of a uniform scattering medium.

© 2003 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(290.4210) Scattering : Multiple scattering

Citation
Arnold D. Kim and Joseph B. Keller, "Light propagation in biological tissue," J. Opt. Soc. Am. A 20, 92-98 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-1-92


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References

  1. W-F. Cheong, S. A. Prahl, and A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
  2. C. L. Leakeas and E. W. Larsen, “Generalized Fokker–Planck approximations of particle transport with highly forward-peaked scattering,” Nucl. Sci. Eng. 137, 236–250 (2001).
  3. G. C. Pomraning, “The Fokker–Planck operator as an asymptotic limit,” Math. Models Methods Appl. Sci. 2, 21–36 (1992).
  4. E. W. Larsen, “The linear Boltzmann equation in optically thick systems with forward-peaked scattering,” Prog. Nucl. Energy 34, 413–423 (1999).
  5. A. D. Kim, J. B. Keller, and M. Moscoso, Department of Mathematics, Stanford University, Stanford, Calif. 94305–2125 are preparing a manuscript to be called “Point-spread functions in scattering media.”
  6. A. D. Kim and M. Moscoso, “Radiative transfer computations for optical beams,” J. Comput. Phys. (to be published).
  7. M. Moscoso, J. B. Keller, and G. Papanicolaou, “Depolarization and blurring of optical images by biological tissue,” J. Opt. Soc. Am. A 18, 948–960 (2001).
  8. A. Y. Polishchuk, M. Zevallos, F. Liu, and R. R. Alfano, “Generalization of Fermat’s principle for photons in random media: the least mean square curvature of paths and photon diffusion on the velocity sphere,” Phys. Rev. E 53, 5523–5526 (1996).
  9. J. B. Keller and H. F. Weinberger, “Boundary and initial boundary-value problems for separable backward–forward parabolic problems,” J. Math. Phys. 38, 4343–4353 (1997).
  10. L. M. Delves and J. L. Mohamed, Computational Methods for Integral Equations (Cambridge U. Press, Cambridge, UK, 1985).
  11. L. N. Trefethen, Spectral Methods in Matlab (Society for Industrial and Applied Mathematics, Philadephia, Pa., 2000).
  12. A. D. Kim and A. Ishimaru, “Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer,” Appl. Opt. 37, 5313–5319 (1998).

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