Abstract

To image objects that are present in a random medium, one needs to know how sensitive measurements are to different kinds of objects and to the position of those objects. Within the diffusion theory we generalize expressions that describe the sensitivity to extra scattering and extra absorption. The sensitivity is influenced by the geometry and by the boundaries of the medium. We describe how sources and detectors at different boundaries have to be handled theoretically. We then compare an unbounded medium, a medium having a black boundary, and a medium having a mirror as a boundary and study the differences in sensitivity. Our results are confirmed by experiments.

© 1998 Optical Society of America

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References

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  1. P. N. den Outer, Th. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
    [CrossRef]
  2. X. D. Zhu, S. Wei, S. C. Feng, B. Chance, “Analysis of a diffuse-photon-density wave in multiple-scattering media in the presence of a small spherical object,” J. Opt. Soc. Am. A 13, 494–499 (1996).
    [CrossRef]
  3. R. C. Haskell, L. O. Svaasand, 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]
  4. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  5. W. M. Star, “Diffusion theory of light transport,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 131–206.
  6. D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
    [CrossRef]
  7. A. Ya Polishchuk, S. Gutman, M. Lax, R. R. Alfano, “Photon-density modes beyond the diffusion approximation: scalar wave-diffusion equation,” J. Opt. Soc. Am. A 14, 230–234 (1997).
    [CrossRef]
  8. K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50, 3634–3640 (1994).
    [CrossRef]
  9. M. Bassani, F. Martelli, G. Zaccanti, D. Contini, “Independence of the diffusion coefficient from absorption: experimental and numerical evidence,” Opt. Lett. 22, 853–855 (1997).
    [CrossRef] [PubMed]
  10. K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).
  11. R. Freyer, U. Hampel, M. Forejtek, C. T. Luu, “Detection of local inhomogeneities in scattering media using tomographic reconstruction techniques,” in Proceedings of Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Müller, A. Katzir, eds., Proc. SPIE2626, 316–327 (1995).
    [CrossRef]
  12. M. R. Ostermeyer, S. L. Jacques, “Perturbation theory for diffuse light transport in complex biological tissues,” J. Opt. Soc. Am. A 14, 255–261 (1997).
    [CrossRef]
  13. 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]
  14. H. Jiang, K. D. Paulsen, U. L. Österberg, “Optical image reconstruction using DC data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
    [CrossRef] [PubMed]
  15. 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, 180–213 (1997).
    [CrossRef] [PubMed]
  16. Y. Yao, Y. Wang, Y. Pei, W. Zhu, R. L. Barbour, “Frequency-domain optical imaging of absorption and scattering distributions by a Born iterative method,” J. Opt. Soc. Am. A 14, 325–342 (1997).
    [CrossRef]
  17. W. Zhu, Y. Wang, Y. Yao, J. Chang, H. L. Graber, R. L. Barbour, “Iterative total least-squares image-reconstruction algorithm for optical tomography by the conjugate-gradient method,” J. Opt. Soc. Am. A 14, 799–807 (1997).
    [CrossRef]
  18. S. Feng, F. Zeng, B. Chance, “Monte Carlo simulations of photon migration path distributions in multiple scattering media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 78–89 (1993).
    [CrossRef]
  19. J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
    [CrossRef] [PubMed]
  20. S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
    [CrossRef] [PubMed]
  21. Th. M. Nieuwenhuizen, M. C. W. van Rossum, “Role of a single scatterer in a multiple scattering medium,” Phys. Lett. A 177, 102–106 (1993).
    [CrossRef]
  22. J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
    [CrossRef] [PubMed]
  23. R. Aronson, “Extrapolation distance for diffusion of light,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 297–305 (1993).
    [CrossRef]
  24. Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
    [CrossRef]
  25. A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48 (March), 34–40 (1995).
    [CrossRef]
  26. S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
    [CrossRef]
  27. D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
    [CrossRef]
  28. 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]
  29. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
  30. S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
    [CrossRef] [PubMed]
  31. S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
    [CrossRef]
  32. M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
    [CrossRef] [PubMed]
  33. M. N. Barber, B. W. Ninham, Random and Restricted Walks (Gordon and Breach, New York, 1970).

1997 (6)

1996 (2)

X. D. Zhu, S. Wei, S. C. Feng, B. Chance, “Analysis of a diffuse-photon-density wave in multiple-scattering media in the presence of a small spherical object,” J. Opt. Soc. Am. A 13, 494–499 (1996).
[CrossRef]

H. Jiang, K. D. Paulsen, U. L. Österberg, “Optical image reconstruction using DC data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

1995 (3)

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48 (March), 34–40 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
[CrossRef] [PubMed]

1994 (5)

S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
[CrossRef]

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

R. C. Haskell, L. O. Svaasand, 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]

1993 (6)

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

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]

P. N. den Outer, Th. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
[CrossRef]

Th. M. Nieuwenhuizen, M. C. W. van Rossum, “Role of a single scatterer in a multiple scattering medium,” Phys. Lett. A 177, 102–106 (1993).
[CrossRef]

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]

J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
[CrossRef] [PubMed]

1992 (1)

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

1991 (1)

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

1989 (1)

’t Hooft, G. W.

Alfano, R. R.

Aronson, R.

R. Aronson, “Extrapolation distance for diffusion of light,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 297–305 (1993).
[CrossRef]

Arridge, S. R.

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]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Barber, M. N.

M. N. Barber, B. W. Ninham, Random and Restricted Walks (Gordon and Breach, New York, 1970).

Barbieri, B.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Barbour, R. L.

Bassani, M.

Boas, D. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Case, K. M.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Chance, B.

X. D. Zhu, S. Wei, S. C. Feng, B. Chance, “Analysis of a diffuse-photon-density wave in multiple-scattering media in the presence of a small spherical object,” J. Opt. Soc. Am. A 13, 494–499 (1996).
[CrossRef]

S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
[CrossRef] [PubMed]

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48 (March), 34–40 (1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

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]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

S. Feng, F. Zeng, B. Chance, “Monte Carlo simulations of photon migration path distributions in multiple scattering media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 78–89 (1993).
[CrossRef]

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

Chang, J.

Colak, S. B.

Contini, D.

Cope, M.

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Delpy, D. T.

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]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

den Outer, P. N.

Durian, D. J.

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[CrossRef]

Fantini, S.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
[CrossRef]

Feng, S.

S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
[CrossRef] [PubMed]

S. Feng, F. Zeng, B. Chance, “Monte Carlo simulations of photon migration path distributions in multiple scattering media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 78–89 (1993).
[CrossRef]

Feng, S. C.

Feng, T.

Forejtek, M.

R. Freyer, U. Hampel, M. Forejtek, C. T. Luu, “Detection of local inhomogeneities in scattering media using tomographic reconstruction techniques,” in Proceedings of Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Müller, A. Katzir, eds., Proc. SPIE2626, 316–327 (1995).
[CrossRef]

Franceschini, M. A.

Franceschini-Fantini, M. A.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Freyer, R.

R. Freyer, U. Hampel, M. Forejtek, C. T. Luu, “Detection of local inhomogeneities in scattering media using tomographic reconstruction techniques,” in Proceedings of Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Müller, A. Katzir, eds., Proc. SPIE2626, 316–327 (1995).
[CrossRef]

Furutsu, K.

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

Gonatas, C. P.

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]

Graber, H. L.

Gratton, E.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
[CrossRef]

Gutman, S.

Hampel, U.

R. Freyer, U. Hampel, M. Forejtek, C. T. Luu, “Detection of local inhomogeneities in scattering media using tomographic reconstruction techniques,” in Proceedings of Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Müller, A. Katzir, eds., Proc. SPIE2626, 316–327 (1995).
[CrossRef]

Haselgrove, J. C.

Haskell, R. C.

Hiraoka, M.

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]

Ishii, M.

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]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Jacques, S. L.

Jiang, H.

H. Jiang, K. D. Paulsen, U. L. Österberg, “Optical image reconstruction using DC data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

Lagendijk, A.

Lax, M.

Leigh, J. S.

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]

J. C. Schotland, J. C. Haselgrove, J. S. Leigh, “Photon hitting density,” Appl. Opt. 32, 448–453 (1993).
[CrossRef] [PubMed]

Luck, J. M.

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

Luu, C. T.

R. Freyer, U. Hampel, M. Forejtek, C. T. Luu, “Detection of local inhomogeneities in scattering media using tomographic reconstruction techniques,” in Proceedings of Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Müller, A. Katzir, eds., Proc. SPIE2626, 316–327 (1995).
[CrossRef]

Maier, J. S.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Martelli, F.

McAdams, M. S.

Melissen, J. B. M.

Miwa, M.

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]

Nieuwenhuizen, Th. M.

Th. M. Nieuwenhuizen, M. C. W. van Rossum, “Role of a single scatterer in a multiple scattering medium,” Phys. Lett. A 177, 102–106 (1993).
[CrossRef]

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

P. N. den Outer, Th. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
[CrossRef]

Ninham, B. W.

M. N. Barber, B. W. Ninham, Random and Restricted Walks (Gordon and Breach, New York, 1970).

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Österberg, U. L.

H. Jiang, K. D. Paulsen, U. L. Österberg, “Optical image reconstruction using DC data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

Ostermeyer, M. R.

Paasschens, J. C. J.

Papaioannou, D. G.

Patterson, M. S.

Paulsen, K. D.

H. Jiang, K. D. Paulsen, U. L. Österberg, “Optical image reconstruction using DC data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

Pei, Y.

Pine, D. J.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Polishchuk, A. Ya

Schomberg, H.

Schotland, J.

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]

Schotland, J. C.

Schweiger, M.

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]

Star, W. M.

W. M. Star, “Diffusion theory of light transport,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 131–206.

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.

van Asten, N. A. A. J.

van der Mark, M. B.

van Rossum, M. C. W.

Th. M. Nieuwenhuizen, M. C. W. van Rossum, “Role of a single scatterer in a multiple scattering medium,” Phys. Lett. A 177, 102–106 (1993).
[CrossRef]

Walker, S. A.

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Wang, Y.

Wei, S.

Weitz, D. A.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Wilson, B. C.

Yamada, Y.

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

Yao, Y.

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48 (March), 34–40 (1995).
[CrossRef]

Yodh, A. G.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Zaccanti, G.

Zeng, F.

S. Feng, F. Zeng, B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995).
[CrossRef] [PubMed]

S. Feng, F. Zeng, B. Chance, “Monte Carlo simulations of photon migration path distributions in multiple scattering media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 78–89 (1993).
[CrossRef]

Zhu, J. X.

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Zhu, W.

Zhu, X. D.

Zweifel, P. F.

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

Appl. Opt. (4)

J. Opt. Soc. Am. A (7)

J. Opt. Soc. Am. B (1)

Med. Phys. (1)

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]

Opt. Eng. (Bellingham) (1)

S. Fantini, M. A. Franceschini-Fantini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry,” Opt. Eng. (Bellingham) 34, 32–42 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

Th. M. Nieuwenhuizen, M. C. W. van Rossum, “Role of a single scatterer in a multiple scattering medium,” Phys. Lett. A 177, 102–106 (1993).
[CrossRef]

Phys. Med. Biol. (2)

H. Jiang, K. D. Paulsen, U. L. Österberg, “Optical image reconstruction using DC data: simulations and experiments,” Phys. Med. Biol. 41, 1483–1498 (1996).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope, D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[CrossRef] [PubMed]

Phys. Rev. A (1)

J. X. Zhu, D. J. Pine, D. A. Weitz, “Internal reflection of diffusive light in random media,” Phys. Rev. A 44, 3948–3959 (1991).
[CrossRef] [PubMed]

Phys. Rev. E (4)

K. Furutsu, Y. Yamada, “Diffusion approximation for a dissipative random medium and the applications,” Phys. Rev. E 50, 3634–3640 (1994).
[CrossRef]

Th. M. Nieuwenhuizen, J. M. Luck, “Skin layer of diffusive media,” Phys. Rev. E 48, 569–588 (1993).
[CrossRef]

D. J. Durian, “Influence of boundary reflection and refraction on diffusive photon transport,” Phys. Rev. E 50, 857–866 (1994).
[CrossRef]

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]

Phys. Today (1)

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48 (March), 34–40 (1995).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffusive photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef]

Other (8)

M. N. Barber, B. W. Ninham, Random and Restricted Walks (Gordon and Breach, New York, 1970).

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

K. M. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).

R. Freyer, U. Hampel, M. Forejtek, C. T. Luu, “Detection of local inhomogeneities in scattering media using tomographic reconstruction techniques,” in Proceedings of Photon Propagation in Tissues, B. Chance, D. T. Delpy, G. J. Müller, A. Katzir, eds., Proc. SPIE2626, 316–327 (1995).
[CrossRef]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

W. M. Star, “Diffusion theory of light transport,” in Optical-Thermal Response of Laser-Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), pp. 131–206.

R. Aronson, “Extrapolation distance for diffusion of light,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 297–305 (1993).
[CrossRef]

S. Feng, F. Zeng, B. Chance, “Monte Carlo simulations of photon migration path distributions in multiple scattering media,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 78–89 (1993).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Schematic view of the geometry used for experiments and theory. (a) For measurements in reflection, the source–detector distance in the xy plane is denoted by ρd. The position of the object is given by its lateral coordinate ρo and its depth d. The dashed line shows the position of the physical boundary when present. The object is moved along the horizontal dotted line for the measurements of Figs. 2 and 4 below and along the vertical dotted line for the measurements of Figs. 3 and 5. The scale of the object corresponds to the black cylinder. (b) For measurements in transmission, L is the thickness of the slab in the z direction. The position of the object is given by ρo and d. The dashed lines show the position of the physical boundaries when present. The object is moved along the vertical dotted line for the measurements of Figs. 6 and 7.

Fig. 2
Fig. 2

Sensitivity to absorption ΔΦq/Φ0=qQ in a reflection measurement as a function of the lateral position ρo. The source–detector distance ρd is 30 mm. The depth d of the object is 10 mm. Squares, an infinite medium; crosses, a semi-infinite medium with reflecting aluminum boundaries; dots, a semi-infinite medium with absorbing boundaries. The solid curves are the corresponding theoretical curves; the dashed curve is the theoretical curve for a reflecting gold mirror.

Fig. 3
Fig. 3

Sensitivity to absorption ΔΦq/Φ0=qQ in a reflection measurement. The parameters are the same as those in Fig. 2, but now the lateral distance ρo is fixed at ρd/2=15 mm and the depth d is varied.

Fig. 4
Fig. 4

Sensitivity to scattering ΔΦp/Φ0 in a reflection measurement as a function of the lateral position ρo, with ρd = 30 mm, as in Fig. 2. Squares, infinite medium (d=15 mm); dots, semi-infinite medium with absorbing boundaries (d=17 mm). The solid curves are the corresponding theoretical curves; the dotted–dashed curve is the theoretical curve for the aluminum mirror; the dashed curve is the theoretical curve for a gold mirror (d=15 mm for both).

Fig. 5
Fig. 5

Sensitivity to scattering ΔΦp/Φ0 in a reflection measurement as a function of the depth d, with ρo=ρd/2 = 15 mm, as in Fig. 3. The solid theoretical curves correspond to the data points. The dotted–dashed curve is for an aluminum mirror; the dashed curve is for a gold mirror.

Fig. 6
Fig. 6

Sensitivity to absorption ΔΦq/Φ0=qQ in a transmission measurement as a function of the depth d, with ρo=15 mm. The solid curves are the theoretical values; the dashed curve is the theoretical curve for a gold mirror. The thickness of the slab is L=50 mm.

Fig. 7
Fig. 7

Sensitivity to scattering ΔΦp/Φ0 in a transmission measurement as a function of the depth d. The thickness of the slab is L=50 mm, as in Fig. 6. For the infinite medium (squares), ρo=19 mm; for the semi-infinite medium (dots), ρo=15 mm. Note that the domain of d for the infinite medium is larger than in Fig. 6. The solid theoretical curves correspond to the data points. The dotted–dashed curve is the theoretical curve for an aluminum mirror; the dashed curve is that for a gold mirror (ρo=15 mm for both).

Fig. 8
Fig. 8

Schematic view of the propagation of the photon density in a reflection measurement, as shown schematically in Fig. 1. The arrows show the average direction of the photon density flow. The two solid arrows show the propagation of light in and just outside the source and detector fiber. The dotted arrows are for an infinite medium, where propagation is direct. The dashed arrows are for a semi-infinite medium with absorbing boundaries, where the propagation avoids the boundary.

Equations (90)

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tΦ(r, t)-·D(r)Φ(r, t)+vμa(r)Φ(r, t)=S(r, t).
μaμs.
S(r, t)=Sω exp(-iωt)δ(r-rs).
-2G(r, r)+κ2G(r, r)=δ(r-r),
Φ0(r)=(Sω/D)G(r, rs).
G(r, r)=G(r, r),
G(r-rs)=(1/4πr)exp(-κr),
Φ(r)=D-1drG(r, r)S(r).
-2Φ(r)+κ2Φ(r)=SωDδ(r-rs)+ΔD(r)D2Φ(r)+D-1[Dobj(r)]·[Φ(r)]-3μsΔμa(r)Φ(r).
Δμa(r)=μa,obj(r)-μa,
ΔD(r)=Dobj(r)-D,
ΔΦ(r)Φ(r)-Φ0(r)
=-3μsdrG(r, r)Δμa(r)Φ(r)
-dr[rG(r, r)]ΔD(r)DrΦ(r).
a|ro-rs|,|ro-r|,|κ|-1.
Φ(r)=Φ0(r)-3μsG(r, ro)ΩdrΔμa(r)Φ(r),
Φ(r)=Φ0(r)[1+qQ(ro; r, rs)],
Q(ro; r, rs)=4πκ0G(r, ro)G(ro, rs)G(r, rs).
q=-κ03μs4πΩdrΔμa(r)×1-3μs4πΩdrΔμa(r)|r-r|(1-).
Φ(r)=Φ0(r)1+i,jpijPij(ro; r, rs).
Pij(ro; r, rs)=-4πκ03ro,iG(r, ro)ro,jG(ro, rs)G(r, rs).
pij=κ034πDΩdr ΔD(r)δij-14πDkΩdr ΔD(r)×r,ir,k1|r-r|(δkj-).
P(r0; r, rs)=iPii(r0; r, rs)=-4πκ03roG(r, ro)·roG(ro, rs)G(r, rs),
Φ(r)Φ0(r)1+oqoQ(ro; rs, rd)
+opoP(ro; rs, rd),
q=-κ03ΩΔμa4πμa,p=0,
p=κ03ΩΔD4πD,q=0.
psphere=(κ0a)3Dobj-DDobj+2D.
Φ(r)=Φ0(r)1-3μsκ04πdro Δμa(ro)Q(ro; r, rs)+3κ034πdroDobj(ro)-DDobj(ro)+2DP(ro; r, r2).
qsphere=-κ0a[1-tanh(κobja)/κobja],p=0.
qblack=-κ0a.
Φ(|r-ro|=a)=0.
Φ+ξextnˆ·Φ|atthesurface=0.
qblack=-κ0a2a+ξext.
Φ(r)=Φ0(r)-(So/D)G(r; ro).
Q=2κ0r,
P=2(κ0r)3(1+κr)2.
ΔΦqΦ0=-Δμa3μa(κ0a)32κ0r,
ΔΦpΦ0=ΔD3D+ΔD(κ0a)32κ03r3(1+κr)2,
Φ=A exp(iφ),
ΔΦ=|ΔΦ|exp(iϑ).
ΔAA0=|ΔΦ|cos(ϑ-φ0)/A0=ReΔΦΦ0,
Δφ=|ΔΦ|sin(ϑ-φ0)/A0=ImΔΦΦ0.
ΔAA0=23ar3-Δμaμa(κ0r)2+ΔD3D+ΔDRe(1+κr)2,
Δφ=23ar3ΔD3D+ΔDIm(1+κr)2.
I(r, sˆ)=v4π[Φ(r)-μs-1sˆ·Φ]v4πΦ(r-μs-1sˆ).
I(rd, -nˆ)v4πΦ(rd+ξinnˆ),
ξext=23μs1+30π/2dθ R(θ)sin θ cos2 θ1+20π/2dθ R(θ)sin θ cos θ,
Φ[(r-rb)·nˆ=ξext]=0.
Gs(ρ, z, zs)=d2q(2π)2exp(iq·ρ)Gs(q, z, zs)=κdα2πJ0(ρα2-κ2)αGs(α; z, zs).
-2z2+α2Gs(α; z, zs)=δ(z-zs).
Gs(α; z, zs)=12αexp(αzmin)-1-aξext1+αξext×exp(-αzmin)exp(-αzmax),
Gs(ρ, z, zs)=κdα4πJ0(ρα2-κ2)×exp(αzmin)-1-αξext1+αξext×exp(-αzmin)exp(-αzmax).
G(ρ, z, zs)=κdα4πJ0(ρα2-κ2)×exp[-α(zmax-zmin)]=14πexp(-κr),
Gs(ρ, z, zs)=14πrexp(-κr)+14πr+exp(-κr+)-2ξext--zsdz14πrexp(-κr)×exp[(z+zs)/ξext],
Gs(α; z, zs)=12α{exp(αzmin)-exp[-α(zmin+2ξext)]}×exp(-αzmax),κξext1.
Gs(ρ, z, zs)=G((z-zs)2+ρ2)-G((z-zs-2ξext)2+ρ2),
z>zs.
GL(0, zs)=ξextzG(z, zs)|z=0,
GL(L, zs)=-ξextzG(z, zs)|z=L
GL(α; z, zs)=[exp(αzmin)-F exp(-αzmin)]{exp[α(L-zmax)]-F exp[-α(L-zmax)]}2α[exp(αL)-F2 exp(-αL)],
F=1-αξext1+αξext.
GL(ρ, z, zs)=κdα4πJ0(α2-κ2ρ)2αGL(α; z, zs).
GL(r, rs)=m=-[G(r, rs+2m(L+2ξext)zˆ)-G(r, σzrs-2ξextzˆ+2m(L+2ξext)zˆ)].
Gs(ρ, z, ξin)2G(ρ, z, ξin),ξ.
Qmirror2Q(reflectionexperiment).
QmirrorQ(transmissionexperiment).
QmirrorQ,PmirrorP,
G(r, rs)-G(r, rs-2ξzˆ)
2ξzˆ·rsG(rd, rs-ξzˆ).
GL(r, rs)=2ξzˆ·r˜smG(r, r˜s+2mLzˆ).
GL(rd, r)=±2ξzˆ·r˜dmG(r˜d+2mLzˆ, r).
ΦL(rd)=SωDGL(rd, rs)+4πqκ0GL(rd, ro)GL(ro, rs)=±2ξ2SωD(zˆ·r˜s)(zˆ·r˜d)×mG(r˜d, r˜s+2mLzˆ)+24πqκ0×mG(r˜d+2mLzˆ, ro)×G(ro, r˜s+2mLzˆ).
Φs(rd)=2ξ2SωD(zˆ·r˜s)(zˆ·r˜d)G(r˜d, r˜s)+8πqκ0G(r˜d, ro)G(ro, r˜s).
Φ(rd)=SωDG(rd, rs)+4πqκ0G(rd; ro)G(ro; rs).
(zˆ·r˜s,d)-ds,d.
r1=ρo2+ds2,r2=(ρo-ρd)2+dd2,
r12=ρd2+(dd-ds)2.
Φ0,=Sω4πD1r12exp(-κr12),
ΔΦ=Sω4πDqκ0r1r2exp[-κ(r1+r2)],
Φ0,s=Sω4πD2ξ21+κr12r123exp(-κr12),
ΔΦs=Sω4πD4qξ2d2(1+κr1)(1+κr2)κ0r13r23×exp[-κ(r1+r2)].
Q=r12κr1r2exp[-κ0(r1+r2-r12)],
Qs=2(1+κr1)(1+κr2)1+κr12d2r122r12r22Q.
Φ0,Φ0,s=2ξr122(1+κr12)(inreflection),
Q=Lκ0r1r2,
Qslab=L2r1r2(1+κr1)(1+κr2)2+2κL+κ2L2Q,
P=(1+κr1)(1+κr2)Lκ03r12r22,
Pslab=(2+2κr1+κ2r12)(2+2κr2+κ2r22)L3(2+2κL+κ2L2)κ03r13r23.
ΦslabΦ=ξL2(2+2κL+κ2L2)(intransmission).

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