Abstract

Diffuse Optical Tomography is rapidly developing as a new imaging modality for characterizing the spatially varying optical properties of media which strongly scatter light (e.g. tissue). Numerous imaging algorithms exist, and more are being developed. Many of these algorithms rely on assumptions which linearize the relationship between the optical contrast and the perturbed signal. We show that this linear approximation makes quantitative imaging of spatially varying optical properties impossible. The explanation for this result is presented and the implication for Diffuse Optical Tomography is discussed.

©1997 Optical Society of America

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References

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  1. B. Chance, Photon Migration in Tissues (Plenum Press, New York, 1988).
  2. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).
  3. A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum Press, New York, 1995).
  4. A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48,34–40 (1995).
    [Crossref]
  5. S. R. Arridge and J. C. Hebden, “Optical Imaging in Medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42:841–854 (1997).
    [Crossref]
  6. R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).
  7. S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11, 35–64 (1993).
  8. D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
    [Crossref]
  9. M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20,426–428 (1995).
    [Crossref] [PubMed]
  10. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, “Optical image reconstruction using frequency-domain data: Simulations and experiments,” J. Opt. Soc. Am. A 13,253–266 (1996).
    [Crossref]
  11. Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, “Frequency-domain optical imaging of absorption andscattering distributions using a born iterative method,” J. Opt. Soc. Am. A 14,325–342 (1997).
    [Crossref]
  12. A. IshimaruWave Propagation and Scattering in Random Media (Academic Press, Inc., San Diego, 1978).
  13. M. S. Patterson, B. Chance, and 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]
  14. M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69,2658–2661 (1992).
    [Crossref] [PubMed]
  15. J. B. Fishkin and E. Gratton, “Propagation of photon density waves in strongly scattering media containing an absorbing ‘semi-infinite’ plane bounded by a straight edge,” J. Opt. Soc. Am. A 10,127–140 (1993).
    [Crossref] [PubMed]
  16. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47,R2999 (1993).
    [Crossref]
  17. P. N. den Outer, T. M. Nieuwenhuizen, and A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10,1209–1218 (1993).
    [Crossref]
  18. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
    [Crossref] [PubMed]
  19. S. Feng, F. Zeng, and B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34,3826–3837 (1995).
    [Crossref] [PubMed]
  20. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Detection and characterization of opticalinhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36,75–92 (1997).
    [Crossref] [PubMed]
  21. A. C. Kak and M. SlaneyPrinciples of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
  22. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and 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]
  23. M. R. Ostermeyer and S. L. Jacques, “Perturbation theory for diffuse light transport in complex biological tissues,” J. Opt. Soc. Am. A 14,255–261 (1997).
    [Crossref]
  24. W. L. BriggsA Multigrid Tutorial (Society for Industrial and Applied Mathematics, Philadelphia, 1987).

1997 (4)

1996 (1)

1995 (4)

1994 (2)

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

D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
[Crossref]

1993 (5)

R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).

S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11, 35–64 (1993).

J. B. Fishkin and E. Gratton, “Propagation of photon density waves in strongly scattering media containing an absorbing ‘semi-infinite’ plane bounded by a straight edge,” J. Opt. Soc. Am. A 10,127–140 (1993).
[Crossref] [PubMed]

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47,R2999 (1993).
[Crossref]

1992 (1)

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69,2658–2661 (1992).
[Crossref] [PubMed]

1989 (1)

Alfano, R.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

Aronson, R.

R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).

Arridge, S.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

Arridge, S. R.

S. R. Arridge and J. C. Hebden, “Optical Imaging in Medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42:841–854 (1997).
[Crossref]

S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11, 35–64 (1993).

Barbour, R. L.

Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, “Frequency-domain optical imaging of absorption andscattering distributions using a born iterative method,” J. Opt. Soc. Am. A 14,325–342 (1997).
[Crossref]

R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).

Benaron, D. A.

D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
[Crossref]

Beuthan, J.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

Boas, D. A.

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Detection and characterization of opticalinhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36,75–92 (1997).
[Crossref] [PubMed]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20,426–428 (1995).
[Crossref] [PubMed]

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47,R2999 (1993).
[Crossref]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69,2658–2661 (1992).
[Crossref] [PubMed]

Briggs, W. L.

W. L. BriggsA Multigrid Tutorial (Society for Industrial and Applied Mathematics, Philadelphia, 1987).

Chance, B.

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Detection and characterization of opticalinhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36,75–92 (1997).
[Crossref] [PubMed]

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

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20,426–428 (1995).
[Crossref] [PubMed]

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

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47,R2999 (1993).
[Crossref]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69,2658–2661 (1992).
[Crossref] [PubMed]

M. S. Patterson, B. Chance, and 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]

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

B. Chance, Photon Migration in Tissues (Plenum Press, New York, 1988).

Chang, J.

R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).

den Outer, P. N.

Feng, S.

Fishkin, J. B.

Graber, H. L.

R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).

Gratton, E.

J. B. Fishkin and E. Gratton, “Propagation of photon density waves in strongly scattering media containing an absorbing ‘semi-infinite’ plane bounded by a straight edge,” J. Opt. Soc. Am. A 10,127–140 (1993).
[Crossref] [PubMed]

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

Hebden, J. C.

S. R. Arridge and J. C. Hebden, “Optical Imaging in Medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42:841–854 (1997).
[Crossref]

Ho, D. C.

D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
[Crossref]

Ishimaru, A.

A. IshimaruWave Propagation and Scattering in Random Media (Academic Press, Inc., San Diego, 1978).

Jacques, S. L.

Jiang, H.

Kak, A. C.

A. C. Kak and M. SlaneyPrinciples of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Kaschke, M.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

Lagendijk, A.

Masters, B.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

Muller, G.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

Nieuwenhuizen, T. M.

O'Leary, M. A.

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Detection and characterization of opticalinhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36,75–92 (1997).
[Crossref] [PubMed]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20,426–428 (1995).
[Crossref] [PubMed]

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47,R2999 (1993).
[Crossref]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69,2658–2661 (1992).
[Crossref] [PubMed]

Osterberg, U. L.

Ostermeyer, M. R.

Patterson, M. S.

Paulsen, K. D.

Pei, Y.

Pogue, B. W.

Slaney, M.

A. C. Kak and M. SlaneyPrinciples of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

Spilman, S.

D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
[Crossref]

Stevenson, D. K.

D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
[Crossref]

Svanberg, S.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

van der Zee, P.

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

van Gemert, M. J. C.

A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum Press, New York, 1995).

Van Houten, J. P.

D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
[Crossref]

Wang, Y.

Y. Yao, Y. Wang, Y. Pei, W. Zhu, and R. L. Barbour, “Frequency-domain optical imaging of absorption andscattering distributions using a born iterative method,” J. Opt. Soc. Am. A 14,325–342 (1997).
[Crossref]

R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).

Welch, A. J.

A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum Press, New York, 1995).

Wilson, B. C.

Yao, Y.

Yodh, A.

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

Yodh, A. G.

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Detection and characterization of opticalinhomogeneities with diffuse photon density waves: a signal-to-noise analysis,” Appl. Opt. 36,75–92 (1997).
[Crossref] [PubMed]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20,426–428 (1995).
[Crossref] [PubMed]

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

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47,R2999 (1993).
[Crossref]

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69,2658–2661 (1992).
[Crossref] [PubMed]

Zeng, F.

Zhu, W.

Adv. Exp. Med. Biol. (1)

D. A. Benaron, D. C. Ho, S. Spilman, J. P. Van Houten, and D. K. Stevenson, “Tomographic time-of-flight optical imaging device,” Adv. Exp. Med. Biol. 361,609–617 (1994).
[Crossref]

Appl. Opt. (3)

J. Opt. Soc. Am. A (5)

Opt. Lett. (2)

Phys. Med. Biol. (1)

S. R. Arridge and J. C. Hebden, “Optical Imaging in Medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42:841–854 (1997).
[Crossref]

Phys. Rev. E (1)

D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47,R2999 (1993).
[Crossref]

Phys. Rev. Lett. (1)

M. A. O'Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69,2658–2661 (1992).
[Crossref] [PubMed]

Phys. Today (1)

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

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

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

Proc. SPIE (2)

R. L. Barbour, H. L. Graber, Y. Wang, J. Chang, and R. Aronson, “Perturbation approach for optical diffusiontomography using continuous-wave and time-resolved data,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11,87–120 (1993).

S. R. Arridge, “Forward and inverse problems in time-resolved infrared imaging,” in Medical Optical Tomography: Functional Imaging and Monitoring, ed. G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Proc. SPIE IS11, 35–64 (1993).

Other (6)

B. Chance, Photon Migration in Tissues (Plenum Press, New York, 1988).

G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, and P. van der Zee, Medical Optical Tomography: Functional Imaging and Monitoring, Proc. SPIEIS11 (1993).

A. J. Welch and M. J. C. van Gemert, Optical-Thermal Response of Laser-Irradiated Tissue (Plenum Press, New York, 1995).

A. IshimaruWave Propagation and Scattering in Random Media (Academic Press, Inc., San Diego, 1978).

A. C. Kak and M. SlaneyPrinciples of Computerized Tomographic Imaging (IEEE Press, New York, 1988).

W. L. BriggsA Multigrid Tutorial (Society for Industrial and Applied Mathematics, Philadelphia, 1987).

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Figures (6)

Fig. 1
Fig. 1 The geometry used for calculating the scattered DPDW (see text).

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Fig. 2
Fig. 2 Comparison of the first order Born approximation with the exact solution for a 1 cm diameter absorbing object with different absorption coefficients.

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Fig. 3
Fig. 3 Comparison of the first order Born approximation with the exact solution for an absorbing object with an absorption coefficient of 0.3 cm-1 and different radii.

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Fig. 4
Fig. 4 Comparison of the Rytov approximation with the exact solution for a 1 cm diameter absorbing object with different absorption coefficients.

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Fig. 5
Fig. 5 Comparison of the Rytov approximation with the exact solution for an absorbing object with and absorption coefficient of 0.3 cm-1 and different radii.

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Fig. 6
Fig. 6 This is a view of the interactive applet for browsing the four dimensional data set. The data here is for an absorber with a 0.6 cm diameter. Click on the figure to start the applet. [Media 1]

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Equations (7)

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( − D ∇ 2 + v μ a + ∂ ∂ t ) Φ ( r , t ) = vS ( r , t ) .
Φ l = 0 ( r s , r d ) = v S A C exp ( i k r s ) 4 π D r s exp ( i k r d ) 4 π r d [ 4 π a 3 3 ] [ − v δ μ a D ]
Φ l = 1 ( r s , r d ) = v S A C exp ( i k r s ) 4 π D r s exp ( i k r d ) 4 π r d [ i k − 1 r s ] [ i k − 1 r d ] [ 4 π a 3 D ] [ − 3 cos θ δ μ s ' 3 μ s ' + 2 δ μ s ' ]
Φ l = 2 ( r s , r d ) = v S A C exp ( i k r s ) 4 π D r s exp ( i k r d ) 4 π r d [ k 2 + 3 ik r s − 3 r s 2 ] [ k 2 + 3 ik r d − 3 r d 2 ]
[ 3 cos 2 θ − 1 ] [ 4 π a 5 45 ] [ δ μ s ' 5 μ s ' + 3 δ μ ' ]
Φ s c ( r s , r d ) = − ∫ Φ inc ( r s , r d ) L ( r ) G ( r s , r d ) d r .
Φ s c ( r s , r d ) = − 1 Φ inc ( r s , r d ) ∫ Φ inc ( r s , r d ) L ( r ) G ( r s , r d ) d r .

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