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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

  • Editor: Steven A. Burns
  • Vol. 24, Iss. 9 — Sep. 1, 2007
  • pp: 2902–2910

Scaling property of the diffusion equation for light in a turbid medium with varying refractive index

Margarita L. Shendeleva and John A. Molloy  »View Author Affiliations


JOSA A, Vol. 24, Issue 9, pp. 2902-2910 (2007)
http://dx.doi.org/10.1364/JOSAA.24.002902


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Abstract

A spatially varying refractive index leads to the bending of photon paths in a medium, which complicates the Monte Carlo modeling of a photon random walk. We show that the process of photon diffusion in a turbid medium with varying refractive index and curved photon paths can be mapped to the diffusion process in a medium with straight photon paths and modified optical properties. Specifically, the diffusion coefficient, the absorption, and the refractive index of the second medium should differ from the corresponding properties of the first medium by the factor of the squared refractive index of the first medium. The specific intensity of light in the second medium will then be equal to the specific intensity in the first medium divided by the same factor, which also means that the photon density distributions in the two media will be identical. In a Monte Carlo simulation the scaling property suggests that two different algorithms can be used to obtain the photon density distribution, namely, the algorithm with curved photon paths and given optical properties and the algorithm with straight photon paths and modified optical properties.

© 2007 Optical Society of America

OCIS Codes
(030.5620) Coherence and statistical optics : Radiative transfer
(080.2710) Geometric optics : Inhomogeneous optical media
(170.5280) Medical optics and biotechnology : Photon migration
(290.1990) Scattering : Diffusion

ToC Category:
Scattering

History
Original Manuscript: January 23, 2007
Revised Manuscript: May 10, 2007
Manuscript Accepted: May 11, 2007
Published: August 22, 2007

Virtual Issues
Vol. 2, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Margarita L. Shendeleva and John A. Molloy, "Scaling property of the diffusion equation for light in a turbid medium with varying refractive index," J. Opt. Soc. Am. A 24, 2902-2910 (2007)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-9-2902


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References

  1. S. A. Alexandrov, A. V. Zvyagin, K. K. M. B. D. Silva, and D. D. Sampson, "Bifocal optical coherence refractometry of turbid media," Opt. Lett. 28, 117-199 (2003). [CrossRef] [PubMed]
  2. A. V. Zvyagin, K. K. M. B. D. Silva, S. A. Alexandrov, T. R. Hillman, and J. J. Armstrong, "Refractive index tomography of turbid media by bifocal optical coherence refractometry," Opt. Express 11, 3503-3517 (2003). [CrossRef] [PubMed]
  3. T. Khan and H. Jiang, "A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive indices," J. Opt. A, Pure Appl. Opt. 5, 137-141 (2003). [CrossRef]
  4. L. Martí -López, J. Bouza-Domínguez, J. C. Hebden, S. R. Arridge, and R. A. Martínez-Celorio, "Validity conditions for the radiative transfer equation," J. Opt. Soc. Am. A 20, 2046-2056 (2003). [CrossRef]
  5. J.-M. Tualle and E. Tinet, "Derivation of the radiative transfer equation for scattering media with a spatially varying refractive index," Opt. Commun. 228, 33-38 (2003). [CrossRef]
  6. M. L. Shendeleva, "Radiative transfer in a turbid medium with a varying refractive index: comment," J. Opt. Soc. Am. A 21, 2464-2468 (2004). [CrossRef]
  7. M. Premaratne, E. Premaratne, and A. J. Lowery, "The photon transport equation for turbid biological media with spatially varying isotropic refractive index," Opt. Express 13, 389-399 (2005). [CrossRef] [PubMed]
  8. G. Bal, "Radiative transfer equations with varying refractive index: a mathematical perspective," J. Opt. Soc. Am. A 23, 1639-1644 (2006). [CrossRef]
  9. H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, "The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach," Phys. Med. Biol. 48, 2713-2727 (2003). [CrossRef] [PubMed]
  10. H. Dehghani, B. A. Brooksby, B. W. Pogue, and K. D. Paulsen, "Effects of refractive index on near-infrared tomography of the breast," Appl. Opt. 44, 1870-1878 (2005). [CrossRef] [PubMed]
  11. T. Khan and A. Thomas, "Inverse problem in refractive index based optical tomography," Inverse Probl. 22, 1121-1137 (2006). [CrossRef]
  12. X. Liang, Q. Zhang, and H. Jiang, "Quantitative reconstruction of refractive index distribution and imaging of glucose concentration by using diffusing light," Appl. Opt. 45, 8360-8365 (2006). [CrossRef] [PubMed]
  13. L. Wang, S. Jacques, and L. Zheng, "MCML--Monte Carlo modeling of light transport in multi-layered tissues," Comput. Methods Programs Biomed. 47, 131-146 (1995). [CrossRef] [PubMed]
  14. M. L. Shendeleva and J. A. Molloy, "Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry," Appl. Opt. 45, 7018-7025 (2006). [CrossRef] [PubMed]
  15. M. Born and E. Wolf, Principles of Optics, 4th ed. (Pergammon, 1970).

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