Abstract

We describe a method to characterize spatial or temporal changes in the optical properties of turbid media using diffuse reflectance images acquired under broad-beam illumination conditions. We performed experiments on liquid phantoms whose absorption (μa) and reduced scattering (μs′) coefficients were representative of those of biological tissues in the near infrared. We found that the relative diffuse reflectance R depends on μa and μs′ only through the ratio μas′ and that dependence can be well described with an analytical expression previously reported in the literature [S. L. Jacques, Kluwer Academic Dordrecht (1996)]. We have found that this expression for R deviates from experimental values by no more than 8% for various illumination and detection angles within the range 0°–30°. Therefore, this analytical expression for R holds with good approximation even if the investigated medium presents curved or irregular surfaces. Using this expression, it is possible to translate spatial or temporal changes in the relative diffuse reflectance from a turbid medium into quantitative estimates of the corresponding changes of (μas′)1/2. In the case of media with optical properties similar to those of tissue in the near infrared, we found that the changes of μas′ should occur over a volume approximately 2 mm deep and 4 mm × 4 mm wide to apply this expression.

© 2003 Optical Society of America

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2001 (2)

D. M. Rector, R. F. Rogers, J. S. Schwaber, R. M. Harper, J. S. George, “Scattered-light imaging in vivo tracks fast and slow processes of neurophysiological activation,” Neouroimage 14, 977–994 (2001).
[CrossRef]

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[CrossRef] [PubMed]

2000 (3)

M. Gurfinkel, A. B. Thompson, W. Ralston, T. L. Troy, A. L. Moore, T. A. Moore, J. D. Gust, D. Tatman, J. S. Reynolds, B. Muggenberg, K. Nikula, R. Pandey, R. Mayer, D. J. Hawrysz, E. M. Sevick-Muraca, “Pharmacokinetics of ICG and HPPH-car for the detection of normal and tumor tissue using fluorescence, near-infrared reflectance imaging: a case study,” Photochem. Photobiol. 72, 94–102 (2000).
[CrossRef] [PubMed]

B. Farina, C. Bartoli, A. Bono, A. Colombo, M. Lualdi, G. Tragni, R. Marchesini, “spectral imaging approach in the diagnosis of cutaneous melanoma: potentiality and limits,” Phys. Med. Biol. 45, 1243–1254 (2000).
[CrossRef] [PubMed]

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef] [PubMed]

1999 (4)

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

D. Grosenick, H. Wabnitz, H. H. Rinneberg, K. T. Moesta, P. M. Schlag, “Development of a time-domain optical mammograph and first in vivo applications,” Appl. Opt. 38, 2927–2943 (1999).
[CrossRef]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, M. W. Berns, “ctance measurements of layered media with photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

J. S. Reynolds, T. L. Troy, R. H. Mayer, A. B. Thompson, D. J. Waters, K. K. Cornell, P. W. Snyder, E. M. Sevick-Muraca, “Imaging of spontaneous canine mammary tumors using fluorescent contrast agents,” Photochem. Photobiol. 70, 87–94 (1999).
[CrossRef] [PubMed]

1998 (1)

1997 (3)

1995 (1)

R. Marchesini, S. Tomatis, C. Bartoli, A. Bono, C. Clemente, C. Cupeta, I. Del Prato, E. Pignoli, A. E. Sichirollo, N. Cascinelli, “In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. III. CCD camera-based reflectance imaging,” Photochem. Photobiol. 62, 151–154 (1995).
[CrossRef] [PubMed]

1994 (2)

L. O. Svaasand, L. T. Norvang, E. J. Fiskertrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine strains,” Lasers Med. Sci. 65, 55–65 (1994).

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

1993 (1)

1992 (4)

S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
[CrossRef] [PubMed]

S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
[CrossRef] [PubMed]

T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[CrossRef] [PubMed]

M. M. Haglund, G. A. Ojeman, D. W. Hochman, “Optical imaging of epileptiform and functional activity in human cerebral cortex,” Nature 358, 668–671 (1992).
[CrossRef] [PubMed]

1991 (1)

1990 (2)

D. Y. Ts’o, R. D. Frostig, E. Lieke, A. Grinvald, “Functional organization of primate visual cortex revealed by high resolution optical imaging,” Science 249, 417–420 (1990).
[CrossRef] [PubMed]

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

1989 (2)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—I: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
[CrossRef] [PubMed]

C. J. M. Moes, M. J. C. van Gemert, W. M. Star, J. P. A. Marijnissen, S. A. Prahl, “Measurements and calculations of the energy fluence rate in a scattering and absorbing phantom at 633 nm,” Appl. Opt. 28, 2292–2296 (1989).
[CrossRef] [PubMed]

1987 (2)

M. J. C. van Gemert, W. M. Star, “Relations between the Kubelka-Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287–298 (1987).

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

1986 (1)

A. Grinvald, E. Lieke, R. Frostig, C. D. Gilbert, T. N. Wiesel, “Functional architecture of cortex revealed by optical imaging of intrinsic signals,” Nature 324, 361–364 (1986).
[CrossRef]

1981 (1)

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Investig. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

1977 (1)

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

1974 (1)

1973 (1)

1972 (2)

1971 (2)

P. S. Mudgett, L. W. Richards, “Multiple scattering calculations for technology,” Appl. Opt. 10, 1485–1502 (1971).
[CrossRef] [PubMed]

B. J. Brinkworth, “On the theory of reflection by scattering and absorbing media,” J. Appl. Phys. Phys. D 4, 1105–1106 (1971).
[CrossRef]

1962 (1)

1961 (2)

1955 (1)

R. G. Giovanelli, “Reflection by semi-infinite diffusers,” Opt. Acta 2, 153–162 (1955).
[CrossRef]

1948 (1)

1905 (1)

A. Schuster, “Radiation through a foggy atmosphere,” Astrophys. J. 21, 1–22 (1905).
[CrossRef]

Achilefu, S.

J. E. Bugaj, S. Achilefu, R. B. Dorshow, R. Rajagopalan, “Novel fluorescent contrast agents for optical imaging of in vivo tumors based on a receptor-targeted dye-peptide conjugate platform,” J. Biomed. Opt. 6, 122–133 (2001).
[CrossRef] [PubMed]

Alter, C. A.

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

Anderson, E. R.

Anderson, R. R.

R. R. Anderson, J. A. Parrish, “The optics of human skin,” J. Investig. Dermatol. 77, 13–19 (1981).
[CrossRef] [PubMed]

Barbieri, B.

Bartoli, C.

B. Farina, C. Bartoli, A. Bono, A. Colombo, M. Lualdi, G. Tragni, R. Marchesini, “spectral imaging approach in the diagnosis of cutaneous melanoma: potentiality and limits,” Phys. Med. Biol. 45, 1243–1254 (2000).
[CrossRef] [PubMed]

R. Marchesini, S. Tomatis, C. Bartoli, A. Bono, C. Clemente, C. Cupeta, I. Del Prato, E. Pignoli, A. E. Sichirollo, N. Cascinelli, “In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. III. CCD camera-based reflectance imaging,” Photochem. Photobiol. 62, 151–154 (1995).
[CrossRef] [PubMed]

Berns, M. W.

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, M. W. Berns, “ctance measurements of layered media with photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
[CrossRef] [PubMed]

L. O. Svaasand, L. T. Norvang, E. J. Fiskertrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine strains,” Lasers Med. Sci. 65, 55–65 (1994).

Blevin, W. R.

Bogdanov, A.

R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
[CrossRef] [PubMed]

Bono, A.

B. Farina, C. Bartoli, A. Bono, A. Colombo, M. Lualdi, G. Tragni, R. Marchesini, “spectral imaging approach in the diagnosis of cutaneous melanoma: potentiality and limits,” Phys. Med. Biol. 45, 1243–1254 (2000).
[CrossRef] [PubMed]

R. Marchesini, S. Tomatis, C. Bartoli, A. Bono, C. Clemente, C. Cupeta, I. Del Prato, E. Pignoli, A. E. Sichirollo, N. Cascinelli, “In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. III. CCD camera-based reflectance imaging,” Photochem. Photobiol. 62, 151–154 (1995).
[CrossRef] [PubMed]

Brenner, M.

Brinkworth, B. J.

B. J. Brinkworth, “Interpretation of the Kubelka-Munk coefficients in reflection theory,” Appl. Opt. 11, 1434–1435 (1972).
[CrossRef] [PubMed]

B. J. Brinkworth, “On the theory of reflection by scattering and absorbing media,” J. Appl. Phys. Phys. D 4, 1105–1106 (1971).
[CrossRef]

Brown, W. J.

Bugaj, J. E.

J. E. Bugaj, S. Achilefu, R. B. Dorshow, R. Rajagopalan, “Novel fluorescent contrast agents for optical imaging of in vivo tumors based on a receptor-targeted dye-peptide conjugate platform,” J. Biomed. Opt. 6, 122–133 (2001).
[CrossRef] [PubMed]

Burger, T.

Butler, J.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef] [PubMed]

Caps, R.

Cascinelli, N.

R. Marchesini, S. Tomatis, C. Bartoli, A. Bono, C. Clemente, C. Cupeta, I. Del Prato, E. Pignoli, A. E. Sichirollo, N. Cascinelli, “In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. III. CCD camera-based reflectance imaging,” Photochem. Photobiol. 62, 151–154 (1995).
[CrossRef] [PubMed]

Cerussi, A.

B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
[CrossRef] [PubMed]

Chandrasekhar, S.

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

Cheong, W. F.

W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues,” IEEE J. Quantum Electron. 26, 2166–2185 (1990).
[CrossRef]

Clemente, C.

R. Marchesini, S. Tomatis, C. Bartoli, A. Bono, C. Clemente, C. Cupeta, I. Del Prato, E. Pignoli, A. E. Sichirollo, N. Cascinelli, “In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. III. CCD camera-based reflectance imaging,” Photochem. Photobiol. 62, 151–154 (1995).
[CrossRef] [PubMed]

Colombo, A.

B. Farina, C. Bartoli, A. Bono, A. Colombo, M. Lualdi, G. Tragni, R. Marchesini, “spectral imaging approach in the diagnosis of cutaneous melanoma: potentiality and limits,” Phys. Med. Biol. 45, 1243–1254 (2000).
[CrossRef] [PubMed]

Coquoz, O.

Cornell, K. K.

J. S. Reynolds, T. L. Troy, R. H. Mayer, A. B. Thompson, D. J. Waters, K. K. Cornell, P. W. Snyder, E. M. Sevick-Muraca, “Imaging of spontaneous canine mammary tumors using fluorescent contrast agents,” Photochem. Photobiol. 70, 87–94 (1999).
[CrossRef] [PubMed]

Cupeta, C.

R. Marchesini, S. Tomatis, C. Bartoli, A. Bono, C. Clemente, C. Cupeta, I. Del Prato, E. Pignoli, A. E. Sichirollo, N. Cascinelli, “In vivo spectrophotometric evaluation of neoplastic and non-neoplastic skin pigmented lesions. III. CCD camera-based reflectance imaging,” Photochem. Photobiol. 62, 151–154 (1995).
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L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, M. W. Berns, “ctance measurements of layered media with photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
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J. B. Fishkin, O. Coquoz, E. R. Anderson, M. Brenner, B. J. Tromberg, “Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject,” Appl. Opt. 36, 10–20 (1997).
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J. S. Reynolds, T. L. Troy, R. H. Mayer, A. B. Thompson, D. J. Waters, K. K. Cornell, P. W. Snyder, E. M. Sevick-Muraca, “Imaging of spontaneous canine mammary tumors using fluorescent contrast agents,” Photochem. Photobiol. 70, 87–94 (1999).
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D. Y. Ts’o, R. D. Frostig, E. Lieke, A. Grinvald, “Functional organization of primate visual cortex revealed by high resolution optical imaging,” Science 249, 417–420 (1990).
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van Staveren, H. J.

Wabnitz, H.

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J. S. Reynolds, T. L. Troy, R. H. Mayer, A. B. Thompson, D. J. Waters, K. K. Cornell, P. W. Snyder, E. M. Sevick-Muraca, “Imaging of spontaneous canine mammary tumors using fluorescent contrast agents,” Photochem. Photobiol. 70, 87–94 (1999).
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S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
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S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—I: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
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IEEE Trans. Biomed. Eng. (1)

S. T. Flock, M. S. Patterson, B. C. Wilson, D. R. Wyman, “Monte Carlo modeling of light propagation in highly scattering tissues—I: model predictions and comparison with diffusion theory,” IEEE Trans. Biomed. Eng. 36, 1162–1168 (1989).
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J. E. Bugaj, S. Achilefu, R. B. Dorshow, R. Rajagopalan, “Novel fluorescent contrast agents for optical imaging of in vivo tumors based on a receptor-targeted dye-peptide conjugate platform,” J. Biomed. Opt. 6, 122–133 (2001).
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M. J. C. van Gemert, W. M. Star, “Relations between the Kubelka-Munk and the transport equation models for anisotropic scattering,” Lasers Life Sci. 1, 287–298 (1987).

S. L. Jacques, C. A. Alter, S. A. Prahl, “Angular dependence of HeNe laser light scattering by human dermis,” Lasers Life Sci. 1, 309–333 (1987).

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L. O. Svaasand, L. T. Norvang, E. J. Fiskertrand, E. K. S. Stopps, M. W. Berns, J. S. Nelson, “Tissue parameters determining the visual appearance of normal skin and port-wine strains,” Lasers Med. Sci. 65, 55–65 (1994).

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S. T. Flock, S. L. Jacques, B. C. Wilson, W. M. Star, M. J. C. van Gemert, “Optical properties of Intralipid: a phantom medium for light propagation studies,” Lasers Surg. Med. 12, 510–519 (1992).
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T. J. Farrell, M. S. Patterson, B. C. Wilson, “A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
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R. Weissleder, C. H. Tung, U. Mahmood, A. Bogdanov, “In vivo imaging of tumors with protease-activated near infrared fluorescent probes,” Nat. Biotechnol. 17, 375–378 (1999).
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B. J. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, L. Svaasand, J. Butler, “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000).
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J. S. Reynolds, T. L. Troy, R. H. Mayer, A. B. Thompson, D. J. Waters, K. K. Cornell, P. W. Snyder, E. M. Sevick-Muraca, “Imaging of spontaneous canine mammary tumors using fluorescent contrast agents,” Photochem. Photobiol. 70, 87–94 (1999).
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L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, M. W. Berns, “ctance measurements of layered media with photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).
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S. J. Madsen, M. S. Patterson, B. C. Wilson, “The use of India ink as an optical absorber in tissue-simulating phantoms,” Phys. Med. Biol. 37, 985–993 (1992).
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Science (2)

D. Y. Ts’o, R. D. Frostig, E. Lieke, A. Grinvald, “Functional organization of primate visual cortex revealed by high resolution optical imaging,” Science 249, 417–420 (1990).
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F. F. Jöbsis, “Noninvasive, infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters,” Science 198, 1264–1267 (1977).
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S. A. Prahl, “Light transport in tissue,” Ph.D. dissertation (University of Texas at Austin, Austin, Tex., 1988).

R. D. Frostig, “What does in vivo optical imaging tell us about the primary visual cortex in primates?” in Cerebral Cortex, A. Peters, K. S. Rockland eds. (Plenum, New York, 1994), Vol. 10, pp. 331–358.

A. J. Welch, M. J. C. van Gemert, W. M. Star, B. C. Wilson, “Overview of tissue optics,” in Optical Thermal Response of Laser Irradiated Tissue, A. J. Welch, M. J. C. van Gemert, eds. (Plenum, New York, 1995), Chap. 2.

J. J. Duderstadt, L. J. Hamilton, Nuclear Reactor Analysis (Wiley, New York, 1976).

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

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W. F. Cheong, S. A. Prahl, A. J. Welch, “A review of the optical properties of biological tissues” (1996), http://omlc.ogi.edu/pubs/abs/cheong90a.html .

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