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

  • Vol. 17, Iss. 9 — Sep. 1, 2000
  • pp: 1671–1681

Boundary conditions for light propagation in diffusive media with nonscattering regions

Jorge Ripoll, Manuel Nieto-Vesperinas, Simon R. Arridge, and Hamid Dehghani  »View Author Affiliations


JOSA A, Vol. 17, Issue 9, pp. 1671-1681 (2000)
http://dx.doi.org/10.1364/JOSAA.17.001671


View Full Text Article

Enhanced HTML    Acrobat PDF (413 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The diffusion approximation proves to be valid for light propagation in highly scattering media, but it breaks down in the presence of nonscattering regions. We present a compact expression of the boundary conditions for diffusive media with nonscattering regions, taking into account small-index mismatch. Results from an integral method based on the extinction theorem boundary condition are contrasted with both Monte Carlo and finite-element-method simulations, and a study of its limit of validity is presented. These procedures are illustrated by considering the case of the cerebro-spinal fluid in the brain, for which we demonstrate that for practical situations in light diffusion, these boundary conditions yield accurate results.

© 2000 Optical Society of America

OCIS Codes
(170.5270) Medical optics and biotechnology : Photon density waves
(290.1990) Scattering : Diffusion

History
Original Manuscript: November 2, 1999
Revised Manuscript: May 8, 2000
Manuscript Accepted: May 8, 2000
Published: September 1, 2000

Citation
Jorge Ripoll, Manuel Nieto-Vesperinas, Simon R. Arridge, and Hamid Dehghani, "Boundary conditions for light propagation in diffusive media with nonscattering regions," J. Opt. Soc. Am. A 17, 1671-1681 (2000)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-17-9-1671


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. B. de Haller, “Time-resolved transillumination and optical tomography,” J. Biomed. Opt. 1, 7–17 (1996). [CrossRef] [PubMed]
  2. A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today, March1995, pp. 38–40.
  3. See related studies in Advances in Optical Imaging and Photon Migration, J. Fujimoto, M. S. Patterson, eds., Vol. 21 of Trends in Optics and Photonic Series (Optical Society of America, Washington, D.C., 1998).
  4. S. R. Arridge, P. van der Zee, M. Cope, D. T. Delpy, “Reconstruction methods for near infra-red absorption imaging,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, A. Katzir, eds., Proc. SPIE1431, 204–215 (1991). [CrossRef]
  5. M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995). [CrossRef] [PubMed]
  6. C. P. Gonatas, M. Ishii, J. S. Leigh, J. C. Schotland, “Optical diffusion imaging using a direct inversion method,” Phys. Rev. E 52, 4361–4365 (1995). [CrossRef]
  7. Ch. L. Matson, N. Clark, L. McMackin, J. S. Fender, “Three-dimensional tumor localization in thick tissue with the use of diffuse photon-density waves,” Appl. Opt. 36, 214–220 (1997). [CrossRef] [PubMed]
  8. X. D. Li, T. Durduran, A. G. Yodh, B. Chance, D. N. Pattanayak, “Diffraction tomography for biochemical imaging with diffuse-photon density waves,” Opt. Lett. 22, 573–575 (1997). [CrossRef] [PubMed]
  9. S. A. Walker, S. Fantini, E. Gratton, “Image reconstruction by backprojection from frequency-domain optical measurements in highly scattering media,” Appl. Opt. 36, 170–179 (1997). [CrossRef] [PubMed]
  10. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, M. S. Patterson, “Simultaneous reconstruction of optical absorption and scattering maps in turbid media from near-infrared frequency-domain data,” Opt. Lett. 20, 2128–2130 (1995). [CrossRef] [PubMed]
  11. S. B. Colak, D. G. Papaioannou, G. W.’t Hooft, M. B. van der Mark, H. Schomberg, J. C. J. Paasschens, J. B. M. Melissen, N. A. A. J. van Asten, “Tomographic image reconstruction from optical projections in light-diffusing media,” Appl. Opt. 36, 181–213 (1997). [CrossRef]
  12. P. N. den Outer, Th. M. Nieuwenbuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993). [CrossRef]
  13. S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 35, 3826–3836 (1995). [CrossRef]
  14. S. R. Arridge, J. C. Hebden, “Optical imaging in medicine: II. Modeling and reconstruction,” Phys. Med. Biol. 42, 841–853 (1997). [CrossRef] [PubMed]
  15. J. C. Schotland, “Continuous-wave diffusion imaging,” J. Opt. Soc. Am. A 14, 275–279 (1997). [CrossRef]
  16. S. J. Norton, T. Vo-Dinh, “Diffraction tomographic imaging with photon density waves: an explicit solution,” J. Opt. Soc. Am. A 15, 2670–2677 (1998). [CrossRef]
  17. S. A. Walker, D. A. Boas, E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935–1944 (1998). [CrossRef]
  18. S. Fantini, S. A. Walker, M. A. Franceschini, M. Kaschke, P. M. Schlag, K. T. Moesta, “Assessment of the size, position, and optical properties of breast tumor in vivo by noninvasive optical methods,” Appl. Opt. 37, 1982–1989 (1998). [CrossRef]
  19. J. C. Hebden, F. E. W. Schmidt, M. E. Fry, M. Schweiger, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, “Simultaneous reconstruction of absorption and scattering images by multichannel measurement of purely temporal data,” Opt. Lett. 24, 534–536 (1999). [CrossRef]
  20. S. R. Arridge, “Optical tomography in medical imaging,” Topical Rev. Inverse Probl. 15, R41–R93 (1999). [CrossRef]
  21. M. Firbank, S. R. Arridge, M. Schweiger, D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol. 41, 767–783 (1996). [CrossRef] [PubMed]
  22. S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite element model for the propagation of light in scattering media: a direct method for domains with non-scattering regions,” Med. Phys. 27, 252–264 (2000). [CrossRef] [PubMed]
  23. S. Takahashi, D. Imai, Y. Yamada, “Fundamental 3D FEM analysis of light propagation in head model toward 3D optical tomography,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model and Human Studies II, Proc. SPIE2979, 130–138 (1997).
  24. S. Takahashi, Y. Yamada, “Simulation of 3D light propagation in a layered head model including a clear CSF layer,” in Advances in Optical Imaging and Photon Migration, J. Fujimoto, M. S. Patterson eds., Vol. 21 of Trends in Optics and Photonic Series (Optical Society of America, Washington, D.C., 1998).
  25. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989). [CrossRef] [PubMed]
  26. N. G. Chen, J. Bai, “Monte Carlo approach to modeling of boundary conditions for the diffusion equation,” Phys. Rev. Lett. 80, 5321–5324 (1998). [CrossRef]
  27. C. P. Gonatas, M. Miwa, M. Ishii, J. Schotland, B. Chance, J. S. Leigh, “Effects due to geometry and boundary conditions in multiple light scattering,” Phys. Rev. E 48, 2212–2216 (1993). [CrossRef]
  28. I. Freund, “Surface reflections and boundary conditions for diffusive photon transport,” Phys. Rev. A 45, 8854–8858 (1992). [CrossRef] [PubMed]
  29. K. Furutsu, “Boundary conditions of the diffusion equation and applications,” Phys. Rev. A 39, 1386–1401 (1989). [CrossRef] [PubMed]
  30. J. Wu, F. Partovi, M. S. Field, R. P. Rava, “Diffuse reflectance from turbid media: an analytical model of photon migration,” Appl. Opt. 32, 1115–1121 (1993). [CrossRef] [PubMed]
  31. S. Ito, “Diffusion of collimated, narrow beam waves in discrete random media,” Appl. Opt. 34, 7106–7112 (1995). [CrossRef] [PubMed]
  32. R. C. Haskell, L. O. Vaasand, T. Tsay, T. Feng, M. S. McAdams, B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 11, 2727–2741 (1994). [CrossRef]
  33. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995). [CrossRef]
  34. D. J. Durian, J. Rudnick, “Spatially resolved backscattering: implementation of extrapolation boundary condition and exponential source,” J. Opt. Soc. Am. A 16, 837–844 (1999). [CrossRef]
  35. A. D. Kim, 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). [CrossRef]
  36. F. Martinelli, A. Sassaroli, G. Zaccanti, Y. Yamada, “Properties of the light emerging from a diffusive medium: angular dependence and flux at the external boundary,” Phys. Med. Biol. 44, 1257–1275 (1999). [CrossRef]
  37. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. I.
  38. J. Ripoll, M. Nieto-Vesperinas, “Scattering integral equations for diffusive waves. Detection of objects buried in diffusive media in the presence of rough interfaces,” J. Opt. Soc. Am. A 16, 1453–1465 (1999). [CrossRef]
  39. J. A. Sánchez-Gil, M. Nieto-Vesperinas, “Light scattering from random rough dielectric surfaces,” J. Opt. Soc. Am. A 8, 1270–1286 (1991). [CrossRef]
  40. A. A. Maradudin, T. Michel, A. R. McGurn, E. R. Méndez, “Enhanced backscattering of light from a random grating,” Ann. Phys. (N.Y.) 203, 255–307 (1990). [CrossRef]
  41. S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993). [CrossRef] [PubMed]
  42. M. Schweiger, S. R. Arridge, M. Hirakoa, D. T. Delpy, “The finite element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995). [CrossRef] [PubMed]
  43. S. R. Arridge, “Photon-measurement density functions. Part I: Analytical forms,” Appl. Opt. 34, 7395–7409 (1995). [CrossRef] [PubMed]
  44. J. Ripoll, M. Nieto-Vesperinas, “Index mismatch for diffuse photon density waves at both flat and rough diffuse–diffuse interfaces,” J. Opt. Soc. Am. A 16, 1947–1957 (1999). [CrossRef]
  45. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1993).
  46. G. B. Arfken, H. J. Weber, Mathematical Methods for Physicists, 4th ed. (Academic, New York, 1995).
  47. M. Nieto-Vesperinas, Scattering and Diffraction in Physical Optics (Wiley-Interscience, New York, 1991).
  48. C. A. Brebbia, J. Dominguez, Boundary Elements, An Introductory Course (Computational Mechanics Publications, McGraw-Hill, New York, 1989).
  49. L. H. Wang, S. L. Jacques, L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multilayered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995). [CrossRef] [PubMed]
  50. R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstra, A. C. M. Dassel, J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–434 (1993). [CrossRef] [PubMed]

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