Abstract

A frequency-domain photon migration (FDPM) technique is developed for quantitative measurement of the absorption and reduced scattering coefficients of highly turbid samples in a small-volume (0.45-ml) reflective cuvette. We present both an analytical model for the FDPM cuvette and its experimental verification, using calibrated phantoms and suspensions of living cells. FDPM model fits to experimental data demonstrate that the reduced scattering (μs′) and absorption (μa) coefficients can be derived with accuracies of 5–10% and 10–15%, respectively. Changing the cuvette wall reflectivity alters the frequency-dependent behavior of photon density waves (PDWs). For highly reflective wall boundaries (R eff ≥ 90–95%), PDW confinement leads to substantial enhancement in both amplitude and phase compared with identical samples in infinite media. Results from experiments on microsphere suspensions are compared with predictions from Mie theory to assess the potential of this method to interpret scattering properties in terms of scatterer size and density. Optical property measurements of biological cell suspensions are reported, and the possibility of optically monitoring cell physiology in a carefully controlled environment is demonstrated.

© 2001 Optical Society of America

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2000

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

1998

1997

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).
[CrossRef] [PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

1996

B. Gelebart, E. Tinet, J.-M. Tualle, S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

A. Dunn, R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2, 898–905 (1996).
[CrossRef]

1995

B. Beauvoit, S. M. Evans, Y. W. Jenkins, E. Miller, B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef] [PubMed]

B. J. Tromberg, R. C. Haskell, S. J. Madsen, L. O. Svaasand, “Characterization of tissue optical properties using photon density waves,” Comments Mol. Cell Biophys. 8, 359–386 (1995).

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. I. Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

F. Bevilacqua, P. Marquet, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. Part II: Measurements on biological tissues,” Opt. Eng. 34, 2064–2069 (1995).
[CrossRef]

1994

1993

1992

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]

1991

1990

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]

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]

J. R. Lakowicz, K. W. Berndt, “Frequency-domain measurements of photon migration in tissues,” Chem. Phys. Lett. 166, 246–252 (1990).
[CrossRef]

1989

1973

Anderson, E.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

Anderson, E. R.

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).
[CrossRef] [PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

Andreola, S.

Avrillier, S.

B. Gelebart, E. Tinet, J.-M. Tualle, S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Beauvoit, B.

B. Beauvoit, S. M. Evans, Y. W. Jenkins, E. Miller, B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef] [PubMed]

B. Beauvoit, K. Kitai, B. Chance, “Contribution of the mitochondrial compartment to the optical properties of rat liver: a theoretical and practical approach,” Biophys. J. 67, 2501–2510 (1994).
[CrossRef] [PubMed]

B. Beauvoit, H. Liu, K. Kang, P. D. Kaplan, M. Miwa, B. Chance, “Characterization of absorption and scattering properties of various yeast strains by time-resolved spectroscopy,” Cell Biophys. 23, 91–109 (1993).
[PubMed]

H. Liu, M. Miwa, B. Beauvoit, N. G. Wang, B. Chance, “Characterization of absorption and scattering properties of small-volume biological samples using time-resolved spectroscopy,” Anal. Biochem. 213, 378–385 (1993).
[CrossRef] [PubMed]

Beek, J. F.

Berndt, K. W.

Bertoni, A.

Bevilacqua, F.

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. I. Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

F. Bevilacqua, P. Marquet, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. Part II: Measurements on biological tissues,” Opt. Eng. 34, 2064–2069 (1995).
[CrossRef]

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Brenner, M.

Butler, J.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

Cahn, M.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

Chance, B.

B. Beauvoit, S. M. Evans, Y. W. Jenkins, E. Miller, B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef] [PubMed]

B. Beauvoit, K. Kitai, B. Chance, “Contribution of the mitochondrial compartment to the optical properties of rat liver: a theoretical and practical approach,” Biophys. J. 67, 2501–2510 (1994).
[CrossRef] [PubMed]

B. Beauvoit, H. Liu, K. Kang, P. D. Kaplan, M. Miwa, B. Chance, “Characterization of absorption and scattering properties of various yeast strains by time-resolved spectroscopy,” Cell Biophys. 23, 91–109 (1993).
[PubMed]

H. Liu, M. Miwa, B. Beauvoit, N. G. Wang, B. Chance, “Characterization of absorption and scattering properties of small-volume biological samples using time-resolved spectroscopy,” Anal. Biochem. 213, 378–385 (1993).
[CrossRef] [PubMed]

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

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]

Coquoz, O.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

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).
[CrossRef] [PubMed]

de Haller, E. B.

F. Bevilacqua, P. Marquet, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. Part II: Measurements on biological tissues,” Opt. Eng. 34, 2064–2069 (1995).
[CrossRef]

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. I. Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

Delpy, D. T.

P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

Depeursinge, C.

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. I. Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

F. Bevilacqua, P. Marquet, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. Part II: Measurements on biological tissues,” Opt. Eng. 34, 2064–2069 (1995).
[CrossRef]

Dunn, A.

A. Dunn, R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2, 898–905 (1996).
[CrossRef]

Eick, A. A.

Essenpreis, M.

P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

Evans, S. M.

B. Beauvoit, S. M. Evans, Y. W. Jenkins, E. Miller, B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef] [PubMed]

Farrell, T. J.

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]

Feng, T.-C.

Fishkin, J. B.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

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).
[CrossRef] [PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

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]

Flannery, B. D.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. D. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

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]

Freyer, J. P.

Gelebart, B.

B. Gelebart, E. Tinet, J.-M. Tualle, S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Gratton, E.

Gross, J.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

Hale, G. M.

Haskell, R. C.

Hielscher, A. H.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Jenkins, Y. W.

B. Beauvoit, S. M. Evans, Y. W. Jenkins, E. Miller, B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef] [PubMed]

Johnson, T. M.

Kang, K.

B. Beauvoit, H. Liu, K. Kang, P. D. Kaplan, M. Miwa, B. Chance, “Characterization of absorption and scattering properties of various yeast strains by time-resolved spectroscopy,” Cell Biophys. 23, 91–109 (1993).
[PubMed]

Kaplan, P. D.

B. Beauvoit, H. Liu, K. Kang, P. D. Kaplan, M. Miwa, B. Chance, “Characterization of absorption and scattering properties of various yeast strains by time-resolved spectroscopy,” Cell Biophys. 23, 91–109 (1993).
[PubMed]

Kitai, K.

B. Beauvoit, K. Kitai, B. Chance, “Contribution of the mitochondrial compartment to the optical properties of rat liver: a theoretical and practical approach,” Biophys. J. 67, 2501–2510 (1994).
[CrossRef] [PubMed]

Kumar, G.

Lakowicz, J. R.

Liu, H.

H. Liu, M. Miwa, B. Beauvoit, N. G. Wang, B. Chance, “Characterization of absorption and scattering properties of small-volume biological samples using time-resolved spectroscopy,” Anal. Biochem. 213, 378–385 (1993).
[CrossRef] [PubMed]

B. Beauvoit, H. Liu, K. Kang, P. D. Kaplan, M. Miwa, B. Chance, “Characterization of absorption and scattering properties of various yeast strains by time-resolved spectroscopy,” Cell Biophys. 23, 91–109 (1993).
[PubMed]

Madsen, S. J.

B. J. Tromberg, R. C. Haskell, S. J. Madsen, L. O. Svaasand, “Characterization of tissue optical properties using photon density waves,” Comments Mol. Cell Biophys. 8, 359–386 (1995).

S. J. Madsen, R. C. Haskell, B. J. Tromberg, “A portable, high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. 19, 1934–1936 (1994).
[CrossRef] [PubMed]

Marchesini, R.

Marquet, P.

P. Marquet, F. Bevilacqua, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. I. Comparison between experiments and simulations,” Opt. Eng. 34, 2055–2063 (1995).
[CrossRef]

F. Bevilacqua, P. Marquet, C. Depeursinge, E. B. de Haller, “Determination of reduced scattering and absorption coefficients by a single charge-coupled device array measurement. Part II: Measurements on biological tissues,” Opt. Eng. 34, 2064–2069 (1995).
[CrossRef]

McAdams, M. S.

Melloni, E.

Miller, E.

B. Beauvoit, S. M. Evans, Y. W. Jenkins, E. Miller, B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
[CrossRef] [PubMed]

Miwa, M.

B. Beauvoit, H. Liu, K. Kang, P. D. Kaplan, M. Miwa, B. Chance, “Characterization of absorption and scattering properties of various yeast strains by time-resolved spectroscopy,” Cell Biophys. 23, 91–109 (1993).
[PubMed]

H. Liu, M. Miwa, B. Beauvoit, N. G. Wang, B. Chance, “Characterization of absorption and scattering properties of small-volume biological samples using time-resolved spectroscopy,” Anal. Biochem. 213, 378–385 (1993).
[CrossRef] [PubMed]

Moes, C. J. M.

Moulton, J. D.

Mourant, J. R.

Patterson, M. S.

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. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
[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]

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

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]

Pham, D.

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

Pham, T.

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[CrossRef]

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T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
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W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. D. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

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B. Gelebart, E. Tinet, J.-M. Tualle, S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
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Tromberg, B. J.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

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).
[CrossRef] [PubMed]

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
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B. J. Tromberg, R. C. Haskell, S. J. Madsen, L. O. Svaasand, “Characterization of tissue optical properties using photon density waves,” Comments Mol. Cell Biophys. 8, 359–386 (1995).

R. C. Haskell, L. O. Svaasand, T.-T. Tsay, T.-C. 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).
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S. J. Madsen, R. C. Haskell, B. J. Tromberg, “A portable, high-bandwidth frequency-domain photon migration instrument for tissue spectroscopy,” Opt. Lett. 19, 1934–1936 (1994).
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[CrossRef] [PubMed]

Tsay, T.-T.

Tualle, J.-M.

B. Gelebart, E. Tinet, J.-M. Tualle, S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

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P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

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van Marle, J.

van Staveren, H. J.

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B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

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W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. D. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Wang, N. G.

H. Liu, M. Miwa, B. Beauvoit, N. G. Wang, B. Chance, “Characterization of absorption and scattering properties of small-volume biological samples using time-resolved spectroscopy,” Anal. Biochem. 213, 378–385 (1993).
[CrossRef] [PubMed]

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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]

Wilson, B. C.

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]

Anal. Biochem.

H. Liu, M. Miwa, B. Beauvoit, N. G. Wang, B. Chance, “Characterization of absorption and scattering properties of small-volume biological samples using time-resolved spectroscopy,” Anal. Biochem. 213, 378–385 (1993).
[CrossRef] [PubMed]

B. Beauvoit, S. M. Evans, Y. W. Jenkins, E. Miller, B. Chance, “Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors,” Anal. Biochem. 226, 167–174 (1995).
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[CrossRef] [PubMed]

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).
[CrossRef] [PubMed]

B. J. Tromberg, L. O. Svaasand, T.-T. Tsay, R. C. Haskell, “Properties of photon density waves in multiple-scattering media,” Appl. Opt. 32, 607–616 (1993).
[CrossRef] [PubMed]

M. S. Patterson, J. D. Moulton, B. C. Wilson, K. W. Berndt, J. R. Lakowicz, “Frequency-domain reflectance for the determination of the scattering and absorption properties of tissue,” Appl. Opt. 30, 4474–4476 (1991).
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B. J. Tromberg, R. C. Haskell, S. J. Madsen, L. O. Svaasand, “Characterization of tissue optical properties using photon density waves,” Comments Mol. Cell Biophys. 8, 359–386 (1995).

IEEE J. Quantum Electron.

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]

IEEE J. Sel. Top. Quantum Electron.

A. Dunn, R. Richards-Kortum, “Three-dimensional computation of light scattering from cells,” IEEE J. Sel. Top. Quantum Electron. 2, 898–905 (1996).
[CrossRef]

J. Opt. Soc. Am. A

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Philos. Trans. R. Soc. London Ser. B

B. J. Tromberg, O. Coquoz, J. B. Fishkin, T. Pham, E. R. Anderson, J. Butler, M. Cahn, J. Gross, V. Venugopalan, D. Pham, “Non-invasive measurements of breast tissue optical properties using frequency-domain photon migration,” Philos. Trans. R. Soc. London Ser. B 352, 661–668 (1997).
[CrossRef]

Phys. Med. Biol.

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]

Pure Appl. Opt.

B. Gelebart, E. Tinet, J.-M. Tualle, S. Avrillier, “Phase function simulation in tissue phantoms: a fractal approach,” Pure Appl. Opt. 5, 377–388 (1996).
[CrossRef]

Rev. Sci. Instrum.

T. H. Pham, O. Coquoz, J. B. Fishkin, E. Anderson, B. J. Tromberg, “Broad bandwidth frequency domain instrument for quantitative tissue optical spectroscopy,” Rev. Sci. Instrum. 71, 2500–2513 (2000).
[CrossRef]

Other

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. D. Flannery, Numerical Recipes in C: The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

P. van der Zee, M. Essenpreis, D. T. Delpy, “Optical properties of brain tissue,” in Photon Migration and Imaging in Random Media and Tissues, R. R. Alfano, B. Chance, eds., Proc. SPIE1888, 454–465 (1993).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the spherical chamber experimental setup with the FDPM portable device. The network analyzer produces a rf modulation sweep, which is superimposed to the dc bias through a bias tee, to modulate the current driving the laser diodes. The rf and optical switches enable one to select laser diodes of different wavelengths. The light is coupled into an optical fiber, which illuminates isotropically the sample at its center. The radius of the metallic spherical cavity containing the sample is 4.76 mm. The detection is performed by an avalanche photodiode (APD). The signal measured is fed into the network analyzer, where it is compared with a reference signal from a dedicated channel of the optical switch to extract the two desired quantities, phase shift Φ and modulation amplitude A. This experimental setup is remote driven by a computer (Macintosh equipped with LabVIEW, National Instruments Inc.).

Fig. 2
Fig. 2

Model functions for (a) phase shift versus frequency and (b) amplitude versus frequency in a comparison of PDWs in infinite-medium geometry (dashed curves) and in the small spherical cuvette featuring three different values for the effective reflection coefficient R eff = 0.95, 0.9, and 0.75 (solid curves with triangles, squares, and circles, respectively). The sample considered is IL 2% at 670 nm (μ s ′ = 2.42 mm-1 and μ a = 0.42 × 10-3 mm-1).

Fig. 3
Fig. 3

(a) Experimental phase shift and (b) amplitude data recorded on IL solutions in different concentrations (1%, 2%, and 4%), with no absorber added, in the small-volume cuvette at 849 nm. Model functions resulting from the simultaneous phase and amplitude fit are displayed as solid curves.

Fig. 4
Fig. 4

(a) Reduced scattering coefficients of IL solutions in different concentrations (1%, 2%, and 4%) at 674 nm (triangles), 811 nm (circles), and 849 nm (diamonds) measured in the 0.45-ml cuvette as a function of coefficient values measured in infinite-medium geometry; the corresponding measured absorption coefficients are reported in (b). Values obtained in the small-volume cuvette setup include IL 1%, IL 2% (two samples), and IL 4%. In both (a) and (b), a line is drawn as a guideline to illustrate what would be a perfect 1:1 correspondence between small-volume and infinite-medium values.

Fig. 5
Fig. 5

Reduced scattering (triangles) and absorption (filled diamonds) coefficients of IL 2% solutions with NiSPC in different concentrations (0, 1, 2, and 4 µg/ml), measured in the small-volume cuvette setup at 674 nm. The dashed line shows the IL 2% calibrated value for μ s ′ and the 1:1 correspondence between measured μ a and μ a calibrated with the spectrophotometer.

Fig. 6
Fig. 6

Comparison between μ s ′ values measured experimentally in the cuvette setup with values obtained from Mie theory. The samples are suspensions of microspheres of different sizes at three different wavelengths (674, 811, and 849 nm).

Fig. 7
Fig. 7

(a) Phase shift and (b) amplitude measurements on MCF7 cell suspensions (0.75 × 108/ml) in the small-volume cuvette setup at 674 nm; the curves with circles indicate the beads-only suspension, triangles and squares refer to the beads plus cells suspension in isotonic and hypertonic environments, respectively.

Tables (4)

Tables Icon

Table 1 Optical Properties of IL Solutions at 674, 811, and 849 nm

Tables Icon

Table 2 Optical Properties of IL Solutions with NiSPC in Different Concentrations at 674 nm

Tables Icon

Table 3 Optical Properties of Microsphere Solutions at 674, 811, and 849 nm

Tables Icon

Table 4 Optical Properties of MCF7 Cells in Isotonic and Hypertonic (saline 2%) Environments

Equations (20)

Equations on this page are rendered with MathJax. Learn more.

L=φ4π+34πj · l+,
j=-Dφ,
D=13μa+μs.
1cϕr, tt-D2φr, t+μaφr, t=Sr, t,
φ  exp-krexpiωt,
kreal=32 μaμs1/21+ωcμa21/2+11/2,
kimag=32 μaμs1/21+ωcμa21/2-11/2.
Φ=kimag r,
A=14πDexp-krealrr.
φ=B1rexp-kr+B2rexpkr,  r<a.
P=limr0 4πr2j.
φ|r=a=Ωj|r=a,
Ω=2 1+Reff1-Reff.
φ=Pa-ΩDsinhka-r+ΩDka coshka-r4πDra-ΩDsinhka+ΩDka coshka,
Φ=arctanImφReφ,
A=|φ|.
μs=Nσs=ϕ4/3 πa3 σs1-g=3ϕs4ρa Qscat1-g,
μs mix=μs mix1-gmix,
μs mix=i μsi,  gmix=i μsigii μsi.
μsmix=μs1+μs21-μs1g1+μs2g2μs1+μs2=μs1+μs2-μs1g1-μs2g2=μs1+μs2.

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