OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 27, Iss. 7 — Jul. 1, 2010
  • pp: 1521–1528

Influence of boundary conditions on photon diffusion through an interface between two turbid media with different refractive indices

Margarita L. Shendeleva  »View Author Affiliations


JOSA A, Vol. 27, Issue 7, pp. 1521-1528 (2010)
http://dx.doi.org/10.1364/JOSAA.27.001521


View Full Text Article

Enhanced HTML    Acrobat PDF (336 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The photon migration in two semi-infinite highly scattering media with different refractive indices is studied in the diffusion approximation for two sets of boundary conditions at the interface. In commonly used boundary conditions, the ratio of the intensity (fluence rate) to the squared refractive index is assumed continuous across an interface and the normal component of flux is required to be continuous. However, a more rigorous approach shows that the boundary condition for the intensity may be different. As was shown by Aronson [J. Opt. Soc. Am. A 12, 2532 (1995)] , the ratio of the intensity to the squared refractive index undergoes a jump across an interface that is proportional to the diffuse flux. A diffusion model with an instantaneous point source that can be solved analytically for both sets of boundary conditions is considered. The analytical solutions are derived and compared with the results of Monte Carlo simulations that take into account the reflections and refractions at the interface according to Fresnel’s formulas. It is shown that the analytical solutions with the Aronson boundary condition for intensity match the Monte Carlo results better than the solutions with a continuous ratio of the intensity to the squared refractive index.

© 2010 Optical Society of America

OCIS Codes
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.5280) Medical optics and biotechnology : Photon migration
(290.1990) Scattering : Diffusion
(290.7050) Scattering : Turbid media

ToC Category:
Scattering

History
Original Manuscript: October 12, 2009
Revised Manuscript: May 4, 2010
Manuscript Accepted: May 5, 2010
Published: June 2, 2010

Virtual Issues
Vol. 5, Iss. 11 Virtual Journal for Biomedical Optics

Citation
Margarita L. Shendeleva, "Influence of boundary conditions on photon diffusion through an interface between two turbid media with different refractive indices," J. Opt. Soc. Am. A 27, 1521-1528 (2010)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-27-7-1521


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Planck, The Theory of Heat Radiation (Blakiston’s Son & Co., 1914).
  2. M. Keijzer, W. M. Star, and P. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988). [CrossRef] [PubMed]
  3. R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994). [CrossRef]
  4. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995). [CrossRef]
  5. G. W. Faris, “Diffusion equation boundary conditions for the interface between turbid media: a comment,” J. Opt. Soc. Am. A 19, 519–520 (2002). [CrossRef]
  6. J. S. Cassell and M. M. R. Williams, “Radiation transport and internal reflection in a two region, turbid sphere,” J. Quant. Spectrosc. Radiat. Transf. 104, 400–427 (2007). [CrossRef]
  7. J. Bouza-Dominguez, “Light propagation at interfaces of biological media: boundary conditions,” Phys. Rev. E 78, 031926 (2008). [CrossRef]
  8. J. M. Schmitt, G. X. Zhou, E. C. Walker, and R. T. Wall, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990). [CrossRef] [PubMed]
  9. F. Martelli, S. D. Bianco, and G. Zaccanti, “Effect of the refractive index mismatch on light propagation through diffusive layered media,” Phys. Rev. E 70, 011907 (2004). [CrossRef]
  10. J.-M. Tualle, E. Tinet, J. Prat, and S. Avrillier, “Light propagation near turbid-turbid planar interfaces,” Opt. Commun. 183, 337–346 (2000). [CrossRef]
  11. J.-M. Tualle, J. Prat, E. Tinet, and S. Avrillier, “Real space Green’s function calculation for the solution of the diffusion equation in stratified turbid media,” J. Opt. Soc. Am. A 17, 2046–2055 (2000). [CrossRef]
  12. M. L. Shendeleva, “One-dimensional time-domain Green functions for diffuse light in two adjoining turbid media,” Opt. Commun. 235, 233–245 (2004). [CrossRef]
  13. M. L. Shendeleva, “Time-domain Green functions for diffuse light in two adjoining turbid half-spaces,” Appl. Opt. 46, 1641–1649 (2007). [CrossRef] [PubMed]
  14. J. Ripoll and M. Nieto-Vesperinas, “Index mismatch for photon density waves at both flat and rough diffuse-diffuse interfaces,” J. Opt. Soc. Am. A 16, 1947–1957 (1999). [CrossRef]
  15. M.Abramovitz and I.A.Stegun, eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th ed. (Dover, 1970).
  16. S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, 1988).
  17. L. Wang, S. L. Jacques, and L. Zeng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995). [CrossRef] [PubMed]
  18. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, 1986).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited