Abstract

Diffusing photons provide information about the optical properties of turbid media. In biological tissues these optical properties may be correlated to physiological parameters, enabling one to probe effectively the physiological states of tissue for abnormalities such as tumors and hemorrhages. We show that positional uncertainty in the source and detector lead to significant random errors that degrade the optical information available from diffusing photons. We investigate the limits for the detection, localization, and characterization of optical inhomogeneities by using diffusing photons as a probe. Although detection is sufficient for tumor screening, full characterization of the optical properties is desirable for specification of the tumor. Our findings in model breast systems with realistic signal-to-noise ratios indicate that tumors as small as 0.3 cm in diameter can be unambiguously detected; however, simultaneous determination of tumor size and optical properties is possible only if its diameter is of the order of 1.0 cm or larger. On the other hand, if a priori information about the size (optical properties) is available, then the optical properties (size) of tumors as small as 0.3 cm in diameter can be determined.

© 1997 Optical Society of America

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  1. B. Chance, ed., Photon Migration in Tissues (Plenum, New York, 1988).
  2. A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
    [CrossRef]
  3. B. J. Tromberg, L. O. Svaasand, T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
    [CrossRef] [PubMed]
  4. 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]
  5. E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
    [CrossRef] [PubMed]
  6. B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
    [CrossRef]
  7. J. B. Fishkin, 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]
  8. M. A. O’Leary, D. A. Boas, B. Chance, A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
    [CrossRef] [PubMed]
  9. B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
    [CrossRef] [PubMed]
  10. F. F. Jobsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
    [CrossRef]
  11. S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
    [CrossRef] [PubMed]
  12. H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
    [CrossRef] [PubMed]
  13. V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
    [CrossRef] [PubMed]
  14. A table of published optical properties compiled by L. Wang, S. Jacques, is available from ftp://laser.mda.uth.tmc.edu/pub/tissue/Cheong1990.msw or ftp://laser.mda.uth.tmc.edu/pub/tissue/Cheong1990.ps.
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    [CrossRef]
  16. D. A. Boas, M. A. O’Leary, B. Chance, 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]
  17. P. N. den Outer, T. M. Nieuwenhuizen, A. Lagendijk, “Location of objects in multiple-scattering media,” J. Opt. Soc. Am. A 10, 1209–1218 (1993).
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  18. 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]
  19. J. M. Schmitt, A. Knuttel, J. R. Knutson, “Interference of diffusive light waves,” J. Opt. Soc. Am. A 9, 1832–1843 (1992).
    [CrossRef] [PubMed]
  20. B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
    [CrossRef] [PubMed]
  21. J. Maier, E. Gratton, “Frequency domain methods in optical tomography: Detection of localized absorbers and a backscattering reconstruction scheme,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 440–451 (1993).
    [CrossRef]
  22. A. Knuttle, J. M. Schmitt, J. R. Knutson, “Spatial localization of absorbing bodies by interfering diffusive photon density waves,” Appl. Opt. 32, 381–389 (1993).
    [CrossRef]
  23. D. Pattanayuk, “Resolution of optical images formed by diffusive waves in highly scattering media,” (General Electric, Schenectady, N.Y., 1992).
  24. J. A. Moon, J. Reintjes, “Image resolution by use of multiply scattered light,” Opt. Lett. 19, 521–523 (1994).
    [CrossRef] [PubMed]
  25. A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
    [CrossRef] [PubMed]
  26. M. Essenpreis, C. E. Elwell, M. Cope, P. van der Zee, S. R. Arridge, D. T. Delpy, “Spectral dependence of temporal point spread functions in human tissues,” Appl. Opt. 32, 418–425 (1993).
    [CrossRef] [PubMed]
  27. D. G. Papaioannou, G. W. ’t Hooft, J. J. M. Baselmans, M. J. C. van Gemert, “Image quality in time-resolved transillumination of highly scattering media,” Appl. Opt. 34, 6144–6157 (1995).
    [CrossRef] [PubMed]
  28. D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).
    [CrossRef] [PubMed]
  29. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).
  30. Y. Yao, Y. Wang, R. L. Barbour, H. L. Graber, J. Chang, “Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 291–303 (1995).

1995 (6)

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[CrossRef] [PubMed]

D. G. Papaioannou, G. W. ’t Hooft, J. J. M. Baselmans, M. J. C. van Gemert, “Image quality in time-resolved transillumination of highly scattering media,” Appl. Opt. 34, 6144–6157 (1995).
[CrossRef] [PubMed]

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 (4)

J. A. Moon, J. Reintjes, “Image resolution by use of multiply scattered light,” Opt. Lett. 19, 521–523 (1994).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, 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]

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

1993 (7)

1992 (3)

J. M. Schmitt, A. Knuttel, J. R. Knutson, “Interference of diffusive light waves,” J. Opt. Soc. Am. A 9, 1832–1843 (1992).
[CrossRef] [PubMed]

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

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

1991 (1)

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

1990 (1)

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

1989 (1)

1977 (1)

F. F. Jobsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef]

’t Hooft, G. W.

Arridge, S. R.

Barbour, R. L.

Y. Yao, Y. Wang, R. L. Barbour, H. L. Graber, J. Chang, “Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 291–303 (1995).

Baselmans, J. J. M.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Boas, D. A.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, 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]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

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

Bonner, R. F.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Campbell, L. E.

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[CrossRef] [PubMed]

Chance, B.

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]

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, 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]

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

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

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

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]

Chang, J.

Y. Yao, Y. Wang, R. L. Barbour, H. L. Graber, J. Chang, “Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 291–303 (1995).

Cooper, C. E.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

Cope, M.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

M. Essenpreis, C. E. Elwell, M. Cope, P. van der Zee, S. R. Arridge, D. T. Delpy, “Spectral dependence of temporal point spread functions in human tissues,” Appl. Opt. 32, 418–425 (1993).
[CrossRef] [PubMed]

Delpy, D. T.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

M. Essenpreis, C. E. Elwell, M. Cope, P. van der Zee, S. R. Arridge, D. T. Delpy, “Spectral dependence of temporal point spread functions in human tissues,” Appl. Opt. 32, 418–425 (1993).
[CrossRef] [PubMed]

den Outer, P. N.

Elwell, C. E.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

M. Essenpreis, C. E. Elwell, M. Cope, P. van der Zee, S. R. Arridge, D. T. Delpy, “Spectral dependence of temporal point spread functions in human tissues,” Appl. Opt. 32, 418–425 (1993).
[CrossRef] [PubMed]

Essenpreis, M.

Feng, S.

Fishkin, J. B.

Frank, G. L.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Gandjbakhche, A. H.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Graber, H. L.

Y. Yao, Y. Wang, R. L. Barbour, H. L. Graber, J. Chang, “Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 291–303 (1995).

Gratton, E.

J. B. Fishkin, 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]

J. Maier, E. Gratton, “Frequency domain methods in optical tomography: Detection of localized absorbers and a backscattering reconstruction scheme,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 440–451 (1993).
[CrossRef]

Haskell, R. C.

He, L.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Jobsis, F. F.

F. F. Jobsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef]

Kang, K.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Knutson, J. R.

Knuttel, A.

Knuttle, A.

Lagendijk, A.

Leigh, J.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Liu, H.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Maier, J.

J. Maier, E. Gratton, “Frequency domain methods in optical tomography: Detection of localized absorbers and a backscattering reconstruction scheme,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 440–451 (1993).
[CrossRef]

Maris, M.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Matcher, S. J.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

Moon, J. A.

Nieuwenhuizen, T. M.

Nioka, S.

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Nossal, R.

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, 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]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

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

Papaioannou, D. G.

Pattanayuk, D.

D. Pattanayuk, “Resolution of optical images formed by diffusive waves in highly scattering media,” (General Electric, Schenectady, N.Y., 1992).

Patterson, M. S.

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

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]

Peters, V. G.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Pogue, B. W.

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

Reintjes, J.

Schmitt, J. M.

Sevick, E.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Sevick, E. M.

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Svaasand, L. O.

Tromberg, B. J.

Tsay, T.

van der Zee, P.

van Gemert, M. J. C.

Wang, Y.

Y. Yao, Y. Wang, R. L. Barbour, H. L. Graber, J. Chang, “Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 291–303 (1995).

Weng, J.

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

Wilson, B. C.

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[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]

Wyman, D. R.

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

Yao, Y.

Y. Yao, Y. Wang, R. L. Barbour, H. L. Graber, J. Chang, “Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 291–303 (1995).

Yodh, A.

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Yodh, A. G.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, 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]

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

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

Zeng, F.

Zhang, Y.

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

Anal. Biochem. (2)

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

E. M. Sevick, B. Chance, J. Leigh, S. Nioka, M. Maris, “Quantitation of time- and frequency-resolved optical spectra for the determination of tissue oxygenation,” Anal. Biochem. 195, 330–351 (1991).
[CrossRef] [PubMed]

Appl. Opt. (6)

J. Opt. Soc. Am. A (3)

Med. Phys. (1)

A. H. Gandjbakhche, R. Nossal, R. F. Bonner, “Resolution limits for optical transillumination of abnormalities deeply embedded in tissues,” Med. Phys. 21, 185–191 (1994).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Med. Biol. (3)

H. Liu, D. A. Boas, Y. Zhang, A. G. Yodh, B. Chance, “Determination of optical properties and blood oxygenation using continuous NIR light,” Phys. Med. Biol. 40, 1983–1993 (1995).
[CrossRef] [PubMed]

V. G. Peters, D. R. Wyman, M. S. Patterson, G. L. Frank, “Optical properties of normal and diseased human breast tissues in the visible and near infrared,” Phys. Med. Biol. 35, 1317–1334 (1990).
[CrossRef] [PubMed]

B. W. Pogue, M. S. Patterson, “Frequency-domain optical-absorption spectroscopy of finite tissue volumes using diffusion-theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[CrossRef] [PubMed]

Phys. Rev. E (1)

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering and wavelength transduction of diffuse photon density waves,” Phys. Rev. E 47, R2999–R3002 (1993).
[CrossRef]

Phys. Rev. Lett. (2)

D. A. Boas, L. E. Campbell, A. G. Yodh, “Scattering and imaging with diffusing temporal field correlation,” Phys. Rev. Lett. 75, 1855–1858 (1995).
[CrossRef] [PubMed]

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

Phys. Today (1)

A. Yodh, B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48(3), 34–40 (1995).
[CrossRef]

Proc. IEEE (1)

B. C. Wilson, E. M. Sevick, M. S. Patterson, B. Chance, “Time-dependent optical spectroscopy and imaging for biomedical applications,” Proc. IEEE 80, 918–930 (1992).
[CrossRef]

Proc. Natl. Acad. Sci. USA (2)

B. Chance, K. Kang, L. He, J. Weng, E. Sevick, “Highly sensitive object location in tissue models with linear in-phase and anti-phase multi-element optical arrays in one and two dimensions,” Proc. Natl. Acad. Sci. USA 90, 3423–3427 (1993).
[CrossRef] [PubMed]

D. A. Boas, M. A. O’Leary, B. Chance, 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]

Science (1)

F. F. Jobsis, “Nonivasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
[CrossRef]

Other (6)

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

A table of published optical properties compiled by L. Wang, S. Jacques, is available from ftp://laser.mda.uth.tmc.edu/pub/tissue/Cheong1990.msw or ftp://laser.mda.uth.tmc.edu/pub/tissue/Cheong1990.ps.

J. Maier, E. Gratton, “Frequency domain methods in optical tomography: Detection of localized absorbers and a backscattering reconstruction scheme,” in Photon Migration and Imaging in Random Media and Tissues, B. Chance, R. R. Alfano, eds., Proc. SPIE1888, 440–451 (1993).
[CrossRef]

D. Pattanayuk, “Resolution of optical images formed by diffusive waves in highly scattering media,” (General Electric, Schenectady, N.Y., 1992).

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1969).

Y. Yao, Y. Wang, R. L. Barbour, H. L. Graber, J. Chang, “Scattering characteristics of photon density waves from an object embedded in a spherically two-layer turbid medium,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 291–303 (1995).

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Figures (16)

Fig. 1
Fig. 1

DPDW’s are generated by the injection of light from a sinusoidally modulated source into a turbid medium. The 3-mW, 780-nm source is modulated at 200 MHz. The turbid medium is 6.0 cm thick with a reduced scattering coefficient, μs, of 10.0 cm-1 and μa = 0.05 cm-1. A spherical object is embedded in the middle of the slab. Light is collected and delivered to a photomultiplier tube by means of an optical fiber with a diameter of 0.4 cm. For the simulations, the source and the detector are scanned together along the boundary or the source is held fixed close to the object and the detector is scanned. Two different objects are studied: an absorbing object with μs, in = 10.0 cm-1 and μa, in = 0.15 cm-1 and a scattering object with μs, in = 15.0 cm-1 and μa, in = 0.05 cm-1. Other parameters are considered as indicated in the text.

Fig. 2
Fig. 2

Errors from positional uncertainty can arise from an inaccurate positioning of the source and the detector relative to each other [as depicted in (a)] or relative to the sample under study [as shown in (b)]. These errors are random unless no vibrations are present and no realignment of the source and the detector are made for multiple measurements. In a clinical environment vibrations will be present that are due to breathing and the heart beat. In case (a) and (b) σr is reduced when repeated measurements are made. Positional uncertainties induced by sample vibrations of type (b) are reduced by longer integration times.

Fig. 3
Fig. 3

(a) Fractional change in the amplitude. (b) Change in degrees of the phase that are due to the presence of the absorbing object as functions of the lateral position of the source–detector. The system is described in the caption of Fig. 1. Results are given for 1.0-mm- (dashed curve), 2.0-mm- (dotted curve), and 3.0-mm- (solid curve) diameter absorbers. The noise threshold is given by the solid horizontal line. Note that the signal does not exceed the noise threshold unless the object’s diameter is greater than or equal to 3.0 mm, and then it is only the change in the amplitude and not the phase that is detectable.

Fig. 4
Fig. 4

Diameter of the smallest detectable absorber is plotted as a function of (a) μs, out and μa, in, (b) μa, out and μa, in, (c) source modulation frequency and μa, in. The contours indicate the diameter of the smallest detectable absorber in units of centimeters. The system and measurements are described in Fig. 1. In (a), f = 200 MHz, μa, out = 0.05 cm-1, and μs, in = μs, out. In (b), f = 200 MHz and μs, out = μs, in = 10.0 cm-1. In (c), μs, out = μs, in = 10.0 cm-1, and μa, out = 0.05 cm-1. The noise levels are based on a positional uncertainty of 10 µm and a 1-s integration time.

Fig. 5
Fig. 5

(a) Fractional change in the amplitude. (b) Change in degrees of the phase that are due to the scattering object as functions of the lateral position of the source–detector. The solid curves correspond to a 0.4-cm-diameter object, and the dotted and the dashed curves correspond to a 0.3-cm- and 0.2-cm-diameter object, respectively. System parameters are described in the caption of Fig. 1. The noise threshold is given by the solid horizontal line and is 0.3% for the amplitude change and 0.08° phase. The scattering object is detectable when the diameter is 0.40 cm because the phase change exceeds the noise threshold.

Fig. 6
Fig. 6

Diameter of the smallest detectable scatterer plotted as a function of (a) μs, out and μs, in, (b) μa, out and μs, in, (c) source modulation frequency and μs, in. The contours indicate the diameter of the smallest detectable scatterer in units of centimeters. The system and measurements are described in Fig. 1. In (a), f = 200 MHz and μa, out = μa, in = 0.05 cm-1. In (b), f = 200 MHz, μs, out = 10.0 cm-1, and μa, out = μa, in. In (c), μs, in = 10.0 cm-1 and μa, out = μa, in = 0.05 cm-1. The noise levels are based on a positional uncertainty of 10 µm and a 1-s integration time.

Fig. 7
Fig. 7

Fractional uncertainties in (a), (c), (e) the object diameter, (b), (d), (f) the object absorption coefficient plotted in contour plots for a large range of parameter space. The labels on the contours indicate the fractional uncertainty. In (a) and (b) uncertainties are plotted versus the diameter and absorption coefficient of the object. In (c) and (d) the background scattering coefficient and object absorption coefficient are varied. In (e) and (f) the background absorption coefficient and object absorption coefficient are varied. The dashed curves in (e) and (f) indicate where μa (outside) = μa (inside).

Fig. 8
Fig. 8

(a) Amplitude, (b) phase contributions of the monopole (solid curves), dipole (dotted curves), and quadrupole (dashed curves) moments of the scattered wave to the incident wave graphed versus the diameter of the absorbing object. The noise threshold is indicated by the horizontal line at 2.9 × 10-3 for the amplitude and 8 × 10-2 for the phase. When the monopole term exceeds the noise threshold at 0.3 cm, the absorber is detectable. However, the diameter and the absorption coefficient of the absorber cannot be simultaneously determined until the monopole and dipole terms are detectable. This is the case for diameters greater than 0.8 cm.

Fig. 9
Fig. 9

Fractional uncertainties in (a), (c), (e) the object diameter, (b), (d), (f) the object scattering coefficient plotted in contour plots. The labels on the contours indicate the fractional uncertainty. In (a) and (b) uncertainties are plotted versus the diameter and the scattering coefficient of the object. In (c) and (d) the background scattering coefficient and the object scattering coefficient are varied. In (e) and (f) the background absorption coefficient and the object scattering coefficient are varied. The dashed curves in (c) and (d) indicate where μs (outside) = μs (inside).

Fig. 10
Fig. 10

Fractional uncertainties for (a) the object diameter, (b) the object absorption coefficient are plotted versus the known object diameter for different sets of measurements. The solid curves correspond to the set of measurements presented in Fig. 7, that is, the detector is scanned from x = -2.0 to 2.0 cm whereas the source is fixed at x = 0. The dotted curves correspond to keeping the source fixed at x = 0 and scanning the detector from x = -3.0 to 3.0 cm, whereas for the dashed curves the source and the detector were scanned together from x = -3.0 to 3.0 cm. In all cases 21 independent measurements of the phase and the amplitude were obtained at even intervals over the range of the scan. The system parameters are described in Fig. 1.

Fig. 11
Fig. 11

(a) Amplitude, (b) phase contributions of the monopole, dipole, and quadrupole moments of the scattered wave to the incident wave are graphed versus the lateral position of the detector. The source was scanned with the detectors for the solid curves and fixed at x = 0 for the dashed curves. At x = 0 the top, middle, and bottom pairs of solid and dashed curves correspond respectively to the contributions of the monopole, dipole, and quadrupole moments. The noise threshold is indicated by the horizontal line at 2 × 10-3 for the amplitude and 3 × 10-2 for the phase. When the source is fixed at x = 0, i.e., near the object, the signal is larger, permitting an accurate characterization of smaller objects.

Fig. 12
Fig. 12

Contributions of the monopole (solid curves), dipole (dotted curves), and quadrupole (dashed curves) moments of the scattered wave to (a) the amplitude, (b) the phase of the total wave are plotted versus the modulation frequency of the source. The source and the detector are separated by 6.0 cm with a 1.0-cm-diameter absorbing object centered between them. The optical properties of the object are given in Fig. 1. The noise in the amplitude and phase is given in (c) and (d), respectively. The dotted (dashed) curve corresponds to the positional (shot) noise. The solid curve is the combination of positional and shot noise. The signal-to-noise ratio for amplitude and phase is given in (e) and (f), respectively, for the monopole (solid curves), dipole (dotted curves), and quadrupole (dashed curves) moments.

Fig. 13
Fig. 13

Contributions of the monopole (solid curves), dipole (dotted curves), and quadrupole (dashed curves) moments of the scattered wave to (a) the amplitude, (b) the phase of the total wave are plotted versus the modulation frequency of the source. The source and the detector are separated by 6.0 cm with a 1.0-cm-diameter scattering object centered between them. The optical properties of the object are given in Fig. 1. The noise in the amplitude and phase is given in (c) and (d), respectively. The dotted (dashed) curve corresponds to the positional (shot) noise. The solid curve is the combination of positional and shot noise. The signal-to-noise ratio for amplitude and phase is given in (e) and (f), respectively, for the monopole (solid curves), dipole (dotted curves), and quadrupole (dashed curves) moments.

Fig. 14
Fig. 14

Fractional uncertainties in (a) the diameter, (b) the absorption coefficient of an absorbing object are given versus the diameter of the object. In (c) and (d) the fractional uncertainties are given for a scattering object. Results are given for three different source detector configurations. In all configurations the source was held fixed closest to the object at x = 0 and the detector was scanned from x = -2.0 to 2.0 cm in steps of 0.2 cm. The solid curves correspond to a modulation frequency of 200 MHz, with 10 measurements made at each position. The dotted curves result from the modulation frequency scanned from 0 to 1000 MHz in steps of 200 MHz with two measurements at each position. Finally, the dashed curves correspond to one measurement at each position, with the frequency scanned from 0 to 1000 MHz in steps of 100 MHz. Note that the spectral measurements improve the characterization of the scattering coefficient of the scattering object but do not enhance the characterization of the absorbing object.

Fig. 15
Fig. 15

Possible chi-squared valleys for a two-parameter fit for the object radius and the absorption coefficient at two different optical wavelengths.

Fig. 16
Fig. 16

Fractional deviation in the optical parameter versus the fractional deviation in the diameter. The optical parameter represents either the absorption coefficient or the scattering coefficient.

Equations (8)

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Φrs, rd=Sexpikoutrs-rd4πDoutrs-rd+l=0 Alhl1koutrdxYl0Ωˆd.
Φscl=0=Sexpikrs4πDoutrsexpikrd4πrd4πa33-νδμaDout,
Φscl=1=Sexpikrs4πDoutrsexpikrd4πrdik-1rsik-1rd×3 cos θ4πa33-δμs3μs, out+2δμs,
Φscl=2=Sexpikrs4πDoutrsexpikrd4πrdk2+3ikrs-3rs2×k2+3ikrd-3rd23 cos2 θ-14πa545×δμs5μs, out+3δμs.
σACΦrs, rd=Imk+1rs-rd σr=3/21/2μaμs1/21+ωνμa21/2-11/2+1rs-rdσr,
σθ=Rekσr=3/21/2μaμs1/21+ωνμa21/2+11/2σr.
χ2μs, μa, a=i=1NΦexpirsi, rdi-Φanalirsi, rdi, μs, in, μa, in, a2σACi2+argΦexpirsi, rdi-argΦanalirsi, rdi, μs, in, μa, in, a2σθi2.
Φscl/Φinc.

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