Abstract

Light propagation in two-layered turbid media that have an infinitely thick second layer is investigated with time-resolved reflectance. We used a solution of the diffusion equation for this geometry to show that it is possible to derive the absorption and the reduced scattering coefficients of both layers if the relative reflectance is measured in the time domain at two distances and if the thickness of the first layer is known. Solutions of the diffusion equation for semi-infinite and homogeneous turbid media are also applied to fit the reflectance from the two-layered turbid media in the time and the frequency domains. It is found that the absorption coefficient of the second layer can be more precisely derived for matched than for mismatched boundary conditions. In the frequency domain, its determination is further improved if phase and modulation data are used instead of phase and steady-state reflectance data. Measurements of the time-resolved reflectance were performed on solid two-layered tissue phantoms that confirmed the theoretical results.

© 1998 Optical Society of America

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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  35. J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
    [Crossref]
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    [Crossref]

1998 (2)

1997 (12)

M. Bassani, F. Martelli, G. Zaccanti, D. Contini, “Independence of the diffusion coefficient from absorption: experimental and numerical evidence,” Opt. Lett. 22, 853–855 (1997).
[Crossref] [PubMed]

T. Durduran, A. G. Yodh, B. Chance, D. A. Boas, “Does the photon-diffusion coefficient depend on absorption?,” J. Opt. Soc. Am. A 14, 3358–3365 (1997).
[Crossref]

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[Crossref]

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (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]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[Crossref] [PubMed]

I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, H.-J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. 36, 6529–6538 (1997).
[Crossref]

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahl-Christiansen, H. Orskov, M. Essenpreis, G. Schmelzeisen-Redeker, D. Böcker, “Correlation between blood glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[Crossref] [PubMed]

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. London Ser. B 352, 727–735 (1997).
[Crossref]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[Crossref] [PubMed]

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. A 14, 246–254 (1997).
[Crossref]

B. Gélébart, E. Tinet, J.-M. Tualle, S. Avrillier, J. P. Olliver, “Réflectance résolue dans le temps et dans l’espace appliquée à l’analyse de milieux en couches,” J. Opt. 28, 234–344 (1997).

1996 (3)

A. H. Hielscher, H. Liu, B. Chance, F. K. Tittel, S. L. Jacques, “Time-resolved photon emission from layered turbid media,” Appl. Opt. 35, 719–728 (1996).
[Crossref] [PubMed]

J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
[Crossref]

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[Crossref] [PubMed]

1995 (2)

A. Kienle, R. Hibst, “New optical wavelength for treatment of portwine stains?,” Phys. Med. Biol. 40, 1559–1576 (1995).
[Crossref] [PubMed]

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[Crossref] [PubMed]

1994 (1)

1993 (1)

1992 (1)

I. Dayan, S. Havlin, G. H. Weiss, “Photon migration in a two-layer turbid medium. A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).
[Crossref]

1990 (1)

1989 (2)

1988 (3)

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988).
[Crossref] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

1983 (1)

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distribution of light in tissue,” Med. Phys. 10, 824–830 (1983).
[Crossref] [PubMed]

1979 (1)

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[Crossref]

1941 (1)

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Aarnoudse, J. G.

Adam, G.

B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distribution of light in tissue,” Med. Phys. 10, 824–830 (1983).
[Crossref] [PubMed]

Akgün, N.

G. C. Beck, N. Akgün, A. Rück, R. Steiner, “Design and characterization of a tissue phantom system for optical diagnostics,” Las. Med. Sci. (in press).

Alexandrakis, G.

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 11–14.

Anderson, E. R.

Arridge, S. R.

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Avrillier, S.

B. Gélébart, E. Tinet, J.-M. Tualle, S. Avrillier, J. P. Olliver, “Réflectance résolue dans le temps et dans l’espace appliquée à l’analyse de milieux en couches,” J. Opt. 28, 234–344 (1997).

J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
[Crossref]

Ballini, J.-P.

T. Glanzmann, J.-P. Ballini, P. Jichlinski, P. Grosjean, H. van den Bergh, G. Wagnières, “Tissue characterization by time-resolved fluorescence spectroscopy of endogenous and exogenous fluorochromes: apparatus design and preliminary in vivo and ex vivo results,” in Optical Biopsies and Microscopic Techniques, I. Bigio, ed., Proc. SPIE2926, 41–50 (1996).
[Crossref]

Bassani, M.

Bays, R.

A. Kienle, M. S. Patterson, N. Utke, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[Crossref]

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

Beck, G. C.

G. C. Beck, N. Akgün, A. Rück, R. Steiner, “Design and characterization of a tissue phantom system for optical diagnostics,” Las. Med. Sci. (in press).

Berger, M.

Bevington, P. R.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1983), Chap. 11.

Boas, D. A.

Böcker, D.

Bonner, R.

Brenner, M.

Bruulsema, J. T.

Chance, B.

Change, B.

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Contini, D.

Cope, M.

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Coquoz, O.

Dassel, A. C. M.

Dayan, I.

I. Dayan, S. Havlin, G. H. Weiss, “Photon migration in a two-layer turbid medium. A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).
[Crossref]

de Mul, F. F. M.

Delpy, D. T.

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[Crossref] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Diamond, K. R.

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[Crossref] [PubMed]

Durduran, T.

Essenpreis, M.

Fabiani, M.

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. London Ser. B 352, 727–735 (1997).
[Crossref]

Fantini, S.

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. London Ser. B 352, 727–735 (1997).
[Crossref]

Farrell, T. J.

Feng, T. C.

Firbank, M.

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[Crossref] [PubMed]

Fishkin, J. B.

Fountain, M.

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Franceschini, M. A.

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. London Ser. B 352, 727–735 (1997).
[Crossref]

Gélébart, B.

B. Gélébart, E. Tinet, J.-M. Tualle, S. Avrillier, J. P. Olliver, “Réflectance résolue dans le temps et dans l’espace appliquée à l’analyse de milieux en couches,” J. Opt. 28, 234–344 (1997).

J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
[Crossref]

Glanzmann, T.

T. Glanzmann, J.-P. Ballini, P. Jichlinski, P. Grosjean, H. van den Bergh, G. Wagnières, “Tissue characterization by time-resolved fluorescence spectroscopy of endogenous and exogenous fluorochromes: apparatus design and preliminary in vivo and ex vivo results,” in Optical Biopsies and Microscopic Techniques, I. Bigio, ed., Proc. SPIE2926, 41–50 (1996).
[Crossref]

Graaff, R.

Graham, M. D.

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[Crossref]

Gratton, E.

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. London Ser. B 352, 727–735 (1997).
[Crossref]

Gratton, G.

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. London Ser. B 352, 727–735 (1997).
[Crossref]

Greenfeld, R.

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Greenstein, J. L.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Grosjean, P.

T. Glanzmann, J.-P. Ballini, P. Jichlinski, P. Grosjean, H. van den Bergh, G. Wagnières, “Tissue characterization by time-resolved fluorescence spectroscopy of endogenous and exogenous fluorochromes: apparatus design and preliminary in vivo and ex vivo results,” in Optical Biopsies and Microscopic Techniques, I. Bigio, ed., Proc. SPIE2926, 41–50 (1996).
[Crossref]

Haskell, R. C.

Havlin, S.

Hayward, J. E.

Heinemann, L.

Henyey, L. G.

L. G. Henyey, J. L. Greenstein, “Diffuse radiation in galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

Hibst, R.

A. Kienle, R. Hibst, “New optical wavelength for treatment of portwine stains?,” Phys. Med. Biol. 40, 1559–1576 (1995).
[Crossref] [PubMed]

Hielscher, A. H.

Holtom, G.

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chaps. 7 and 9.

Jacques, S. L.

Jichlinski, P.

T. Glanzmann, J.-P. Ballini, P. Jichlinski, P. Grosjean, H. van den Bergh, G. Wagnières, “Tissue characterization by time-resolved fluorescence spectroscopy of endogenous and exogenous fluorochromes: apparatus design and preliminary in vivo and ex vivo results,” in Optical Biopsies and Microscopic Techniques, I. Bigio, ed., Proc. SPIE2926, 41–50 (1996).
[Crossref]

Kent, J.

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Kiefer, J.

Kienle, A.

A. Kienle, M. S. Patterson, N. Utke, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[Crossref]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[Crossref] [PubMed]

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. A 14, 246–254 (1997).
[Crossref]

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[Crossref] [PubMed]

A. Kienle, R. Hibst, “New optical wavelength for treatment of portwine stains?,” Phys. Med. Biol. 40, 1559–1576 (1995).
[Crossref] [PubMed]

Koelink, M. H.

Koschinsky, T.

Liu, H.

Martelli, F.

McAdams, M.

McCully, K.

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Monnier, P.

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

Nakai, T.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[Crossref]

Nioka, S.

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Nishimura, G.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[Crossref]

Nossal, R.

Okada, E.

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[Crossref] [PubMed]

Olliver, J. P.

B. Gélébart, E. Tinet, J.-M. Tualle, S. Avrillier, J. P. Olliver, “Réflectance résolue dans le temps et dans l’espace appliquée à l’analyse de milieux en couches,” J. Opt. 28, 234–344 (1997).

Ollivier, J. P.

J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
[Crossref]

Orskov, H.

Patterson, M. S.

T. J. Farrell, M. S. Patterson, M. Essenpreis, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998).
[Crossref]

A. Kienle, M. S. Patterson, N. Utke, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[Crossref]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[Crossref] [PubMed]

J. T. Bruulsema, J. E. Hayward, T. J. Farrell, M. S. Patterson, L. Heinemann, M. Berger, T. Koschinsky, J. Sandahl-Christiansen, H. Orskov, M. Essenpreis, G. Schmelzeisen-Redeker, D. Böcker, “Correlation between blood glucose concentration in diabetics and noninvasively measured tissue optical scattering coefficient,” Opt. Lett. 22, 190–192 (1997).
[Crossref] [PubMed]

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[Crossref] [PubMed]

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. A 14, 246–254 (1997).
[Crossref]

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[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]

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 11–14.

Robert, D.

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

Rück, A.

G. C. Beck, N. Akgün, A. Rück, R. Steiner, “Design and characterization of a tissue phantom system for optical diagnostics,” Las. Med. Sci. (in press).

Sandahl-Christiansen, J.

Savary, J.-F.

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

Schmelzeisen-Redeker, G.

Schmitt, J. M.

Schwarzmaier, H.-J.

Steiner, R.

G. C. Beck, N. Akgün, A. Rück, R. Steiner, “Design and characterization of a tissue phantom system for optical diagnostics,” Las. Med. Sci. (in press).

Svaasand, L. O.

Taitelbaum, H.

Takatani, S.

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[Crossref]

Tamura, M.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[Crossref]

Theumann, J.-F.

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

Tinet, E.

B. Gélébart, E. Tinet, J.-M. Tualle, S. Avrillier, J. P. Olliver, “Réflectance résolue dans le temps et dans l’espace appliquée à l’analyse de milieux en couches,” J. Opt. 28, 234–344 (1997).

J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
[Crossref]

Tittel, F. K.

Tromberg, B. J.

Tsay, T. T.

Tualle, J. M.

J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
[Crossref]

Tualle, J.-M.

B. Gélébart, E. Tinet, J.-M. Tualle, S. Avrillier, J. P. Olliver, “Réflectance résolue dans le temps et dans l’espace appliquée à l’analyse de milieux en couches,” J. Opt. 28, 234–344 (1997).

Tuchin, V. V.

Utke, N.

van den Bergh, H.

A. Kienle, M. S. Patterson, N. Utke, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[Crossref]

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

T. Glanzmann, J.-P. Ballini, P. Jichlinski, P. Grosjean, H. van den Bergh, G. Wagnières, “Tissue characterization by time-resolved fluorescence spectroscopy of endogenous and exogenous fluorochromes: apparatus design and preliminary in vivo and ex vivo results,” in Optical Biopsies and Microscopic Techniques, I. Bigio, ed., Proc. SPIE2926, 41–50 (1996).
[Crossref]

van der Zee, P.

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Vitkin, A.

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

Wagnières, G.

A. Kienle, M. S. Patterson, N. Utke, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[Crossref]

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
[Crossref]

T. Glanzmann, J.-P. Ballini, P. Jichlinski, P. Grosjean, H. van den Bergh, G. Wagnières, “Tissue characterization by time-resolved fluorescence spectroscopy of endogenous and exogenous fluorochromes: apparatus design and preliminary in vivo and ex vivo results,” in Optical Biopsies and Microscopic Techniques, I. Bigio, ed., Proc. SPIE2926, 41–50 (1996).
[Crossref]

Walker, E. C.

Wall, R. T.

Weersink, R. A.

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[Crossref] [PubMed]

Weiss, G. H.

Wilson, B. C.

Wray, S.

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Wyatt, J. S.

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Yamamoto, K.

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[Crossref]

Yaroslavsky, A. N.

Yaroslavsky, I. V.

Yodh, A. G.

Zaccanti, G.

Zhou, G. X.

Zijlstr, W. G.

Anal. Biochem. (1)

B. Change, S. Nioka, J. Kent, K. McCully, M. Fountain, R. Greenfeld, G. Holtom, “Time-resolved spectroscopy of hemoglobin and myoglobin in resting and ischemic muscle,” Anal. Biochem. 174, 698–707 (1988).
[Crossref]

Appl. Opt. (9)

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H. Taitelbaum, S. Havlin, G. H. Weiss, “Approximate theory of photon migration in a two-layer medium,” Appl. Opt. 28, 2245–2249 (1989).
[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]

R. Graaff, M. H. Koelink, F. F. M. de Mul, W. G. Zijlstr, A. C. M. Dassel, J. G. Aarnoudse, “Condensed Monte Carlo simulations for the description of light transport,” Appl. Opt. 32, 426–434 (1993).
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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).
[Crossref] [PubMed]

T. J. Farrell, M. S. Patterson, M. Essenpreis, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998).
[Crossref]

A. H. Hielscher, H. Liu, B. Chance, F. K. Tittel, S. L. Jacques, “Time-resolved photon emission from layered turbid media,” Appl. Opt. 35, 719–728 (1996).
[Crossref] [PubMed]

I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, H.-J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. 36, 6529–6538 (1997).
[Crossref]

A. Kienle, M. S. Patterson, N. Utke, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[Crossref]

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L. G. Henyey, J. L. Greenstein, “Diffuse radiation in galaxy,” Astrophys. J. 93, 70–83 (1941).
[Crossref]

IEEE Trans. Biomed. Eng. (1)

S. Takatani, M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. BME-26, 656–664 (1979).
[Crossref]

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I. Dayan, S. Havlin, G. H. Weiss, “Photon migration in a two-layer turbid medium. A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).
[Crossref]

J. Opt. (1)

B. Gélébart, E. Tinet, J.-M. Tualle, S. Avrillier, J. P. Olliver, “Réflectance résolue dans le temps et dans l’espace appliquée à l’analyse de milieux en couches,” J. Opt. 28, 234–344 (1997).

J. Opt. Soc. A (1)

A. Kienle, M. S. Patterson, “Improved solutions of the steady-state and time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. A 14, 246–254 (1997).
[Crossref]

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

Laser Surg. Med. (1)

R. Bays, G. Wagnières, D. Robert, J.-F. Theumann, A. Vitkin, J.-F. Savary, P. Monnier, H. van den Bergh, “Three-dimensional optical phantom and its application in photodynamic therapy,” Laser Surg. Med. 21, 227–234 (1997).
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B. C. Wilson, G. Adam, “A Monte Carlo model for the absorption and flux distribution of light in tissue,” Med. Phys. 10, 824–830 (1983).
[Crossref] [PubMed]

Opt. Commun. (1)

J. M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements,” Opt. Commun. 124, 216–221 (1996).
[Crossref]

Opt. Lett. (2)

Philos. Trans. R. Soc. London Ser. B (1)

E. Gratton, S. Fantini, M. A. Franceschini, G. Gratton, M. Fabiani, “Measurements of scattering and absorption changes in muscle and brain,” Philos. Trans. R. Soc. London Ser. B 352, 727–735 (1997).
[Crossref]

Photochem. Photobiol. (1)

R. A. Weersink, J. E. Hayward, K. R. Diamond, M. S. Patterson, “Accuracy of noninvasive in vivo measurements of photosensitizer uptake based on a diffusion model of reflectance spectroscopy,” Photochem. Photobiol. 66, 326–335 (1997).
[Crossref] [PubMed]

Phys. Med. Biol. (6)

A. Kienle, M. S. Patterson, “Determination of the optical properties of turbid media from a single Monte Carlo simulation,” Phys. Med. Biol. 41, 2221–2227 (1996).
[Crossref] [PubMed]

E. Okada, M. Firbank, D. T. Delpy, “The effect of overlying tissue on the spatial sensitivity profile of near-infrared spectroscopy,” Phys. Med. Biol. 40, 2093–2108 (1995).
[Crossref] [PubMed]

A. Kienle, R. Hibst, “New optical wavelength for treatment of portwine stains?,” Phys. Med. Biol. 40, 1559–1576 (1995).
[Crossref] [PubMed]

T. Nakai, G. Nishimura, K. Yamamoto, M. Tamura, “Expression of optical diffusion coefficient in high-absorption turbid media,” Phys. Med. Biol. 42, 2541–2549 (1997).
[Crossref]

A. Kienle, M. S. Patterson, “Determination of the optical properties of semi-infinite turbid media from frequency-domain reflectance close to source,” Phys. Med. Biol. 42, 1801–1819 (1997).
[Crossref] [PubMed]

D. T. Delpy, M. Cope, P. van der Zee, S. R. Arridge, S. Wray, J. S. Wyatt, “Estimation of optical pathlength through tissue from direct time of flight measurement,” Phys. Med. Biol. 33, 1433–1442 (1988).
[Crossref] [PubMed]

Other (5)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Chaps. 7 and 9.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, New York, 1983), Chap. 11.

T. Glanzmann, J.-P. Ballini, P. Jichlinski, P. Grosjean, H. van den Bergh, G. Wagnières, “Tissue characterization by time-resolved fluorescence spectroscopy of endogenous and exogenous fluorochromes: apparatus design and preliminary in vivo and ex vivo results,” in Optical Biopsies and Microscopic Techniques, I. Bigio, ed., Proc. SPIE2926, 41–50 (1996).
[Crossref]

G. C. Beck, N. Akgün, A. Rück, R. Steiner, “Design and characterization of a tissue phantom system for optical diagnostics,” Las. Med. Sci. (in press).

G. Alexandrakis, T. J. Farrell, M. S. Patterson, “Accuracy of the diffusion approximation in determining the optical properties of a two-layer turbid medium,” in Advances in Optical Imaging and Photon Migration, J. G. Fujimoto, M. S. Patterson, eds., Vol. 21 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1998), pp. 11–14.

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Figures (9)

Fig. 1
Fig. 1

Time-resolved reflectance from a two-layered turbid medium calculated with the diffusion equation (solid curve) and with Monte Carlo simulations (open circles) are shown. The thickness of the first layer is l = 6 mm. The optical parameters are μ s 1 = 1.28 mm-1, μ a1 = 0.0074 mm-1, μ s 2 = 0.67 mm-1, and μ a2 = 0.019 mm-1. Also shown are R(ρ, t) for semi-infinite and homogeneous media calculated with μ s = 1.28 mm-1, μ a = 0.0074 mm-1 (short-dashed curve) and μ s = 0.67 mm-1, μ a = 0.019 mm-1 (long-dashed curve). The matched boundary condition is assumed (n i = n o = 1.4), and the distance ρ equals 14.5 mm.

Fig. 2
Fig. 2

Estimated absorption coefficients ( μ a 2 * ) (open circles) of the second layer determined by nonlinear regressions of time-resolved reflectance by use of the two-layered solution of the diffusion equation to Monte Carlo data are shown versus the true absorption coefficient of the second layer used in the Monte Carlo simulations (μ a2). The optical parameters of the Monte Carlo simulations are μ s 1 = 1.28 mm-1, μ a1 = 0.0074 mm-1, and μ s 2 = 0.67 mm-1, and μ a2 is varied between μ a2 = 0.01 mm-1 and μ a2 = 0.04 mm-1. The thickness of the first layer is l = 6 mm. The line indicates μ a2. Relative time-resolved reflectance data at distances ρ = 14.5 and 19.5 mm were used in the nonlinear regression.

Fig. 3
Fig. 3

Estimated absorption coefficients ( μ a * ) determined by nonlinear regressions of time-resolved reflectance with the homogeneous solution of the diffusion equation to two-layered data are shown versus the true absorption coefficient of the second layer (μ a2). The optical parameters of the two-layered medium are μ s 1 = 1.28 mm-1, μ a1 = 0.0074 mm-1, and μ s 2 = 0.67 mm-1, and μ a2 is varied between μ a2 = 0.01 mm-1 and μ a2 = 0.04 mm-1. The thickness of the first layer is l = 6 mm. The line indicates μ a2. Results for time-resolved reflectance data at distances ρ = 14.5 (open circles), ρ = 19.5 (filled circles), and ρ = 24.5 mm (crosses) are shown.

Fig. 4
Fig. 4

Estimated absorption coefficients ( μ a * ) determined by nonlinear regressions of the homogeneous solution of the diffusion equation in the frequency domain to two-layered data are shown versus the true absorption coefficient of the second layer (μ a2). The optical parameters of the two-layered medium are μ s 1 = 1.28 mm-1, μ a1 = 0.0074 mm-1, and μ s 2 = 0.67 mm-1, and μ a2 is varied between μ a2 = 0.01 mm-1 and μ a2 = 0.04 mm-1. The thickness of the first layer is l = 6 mm. The line indicates μ a2. Results from nonlinear regression by phase and steady-state reflectance (filled circles) and phase and modulation data (open circles) are depicted. The matched boundary condition is used (n o = n i = 1.4). Also shown are μ a * determined from the same two-layered media by use of modulation and phase data, but the mismatched boundary condition (n o = 1.0, n i = 1.4) is applied (crosses). Relative data between ρ = 14.5 and 24.5 mm are used in the nonlinear regression.

Fig. 5
Fig. 5

Mean optical path lengths in the first and the second layers of a two-layered medium versus distance ρ by use of matched (dashed curves) and mismatched (solid curves) boundary conditions. The optical parameters of the two-layered medium are μ s 1 = 1.28 mm-1, μ a1 = 0.0074 mm-1, μ s 2 = 0.67 mm-1, and μ a2 = 0.019 mm-1. The thickness of the first layer is l = 6 mm.

Fig. 6
Fig. 6

Estimated reduced scattering coefficients ( μ s * ) determined by nonlinear regressions of the homogeneous solution of the diffusion equation in the frequency domain to two-layered data are shown versus the true absorption coefficient of the second layer (μ a2). The optical parameters of the two-layered medium are μ s 1 = 1.28 mm-1, μa1 = 0.0074 mm-1, and μ s 2 = 0.67 mm-1, and μ a2 is varied between μ a2= 0.01 mm-1 and μ a2 = 0.04 mm-1. The thickness of the first layer is l = 6 mm. The line indicates μ s 2 . Results from nonlinear regression by phase and steady-state reflectance (solid circles) and phase and modulation data (open circles) are shown. Relative data between ρ = 14.5 and 24.5 mm are used. Also shown is μ s * obtained from nonlinear regressions in the time domain at ρ = 19.5 mm. The matched boundary condition is used.

Fig. 7
Fig. 7

Estimated absorption coefficients ( μ a * ) determined by nonlinear regressions of the homogeneous solution of the diffusion equation in the frequency domain to two-layered data are shown versus the true absorption coefficient of the second layer (μ a2). The optical parameters of the two-layered medium are μ s 1 = 1.28 mm-1, μa1 = 0.0074 mm-1, and μ s 2 = 0.67 mm-1, and μ a2 is varied between μ a2 = 0.01 mm-1 and μ a2 = 0.04 mm-1. The thickness of the first layer is l = 10 mm. The line indicates μ a2. Results from nonlinear regression by use of phase and steady-state reflectance (solid circles) and phase and modulation data (open circles) are depicted. The matched boundary condition is used (n o = n i = 1.4). Also shown are μ a * determined from the same two-layered media by use of modulation and phase data, but the mismatched boundary condition (n o = 1.0, n i = 1.4) is applied (crosses). Relative data between ρ = 14.5 and 24.5 mm are used in the nonlinear regression.

Fig. 8
Fig. 8

Time-resolved reflectance measurements on the side of phantom 1 (semi-infinite and homogeneous geometry) at three distances ρ = 14, 18, and 20 mm (solid curves) are shown. The theoretical time-resolved reflectance is also depicted (dashed curves). The optical parameters used in the calculations are μ s = 1.28 mm-1 and μ a = 0.0074 mm-1. The theoretical curves are convolved with a Gaussian curve with σ = 60 ps.

Fig. 9
Fig. 9

Time-resolved reflectance measurements on the top of phantom 2 (two-layered geometry) at three distances ρ = 15, 20, and 25 mm (solid curves) are shown. The theoretical time-resolved reflectance (dashed curves) is also depicted. The optical parameters used are μ s 1 = 1.28 mm-1, μa1 = 0.0074 mm-1, μ s 2 = 0.67 mm-1, and μ a2 = 0.019 mm-1. The thickness of the first layer is l = 6 mm. The theoretical curves are convolved with a Gaussian curve (σ = 60 ps).

Tables (1)

Tables Icon

Table 1 Optical Coefficients Derived from Measurements on the Top of Phantom 2 (Two-Layered Geometry, l = 6 mm) by Use of the Semi-Infinite Model in the Time Domain in the Nonlinear Regression and the Results from Nonlinear Regressions to Data Obtained from the Two-Layered Diffusion Equations

Equations (14)

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Φ i ρ ,   z ,   ω = exp j ω t 2 π 0   ϕ i z ,   ω ,   s sJ 0 s ρ d s ,
ϕ 1 z ,   ω ,   s = sinh α 1 z b   +   z 0 D 1 α 1 D 1 α 1 cosh α 1 l   -   z   +   D 2 α 2 sinh α 1 l   -   z D 1 α 1 cosh α 1 l   +   z b   +   D 2 α 2 sinh α 1 l   +   z b   -   sinh α 1 z 0   -   z D 1 α 1 ,     0   z < z 0 ;
ϕ 1 z ,   ω ,   s = sinh α 1 z b + z 0 D 1 α 1 D 1 α 1 cosh α 1 l - z + D 2 α 2 sinh α 1 l - z D 1 α 1 cosh α 1 l + z b + D 2 α 2 sinh α 1 l + z b ,   z 0 < z < l ,
ϕ 2 z = sinh α 1 z b + z 0 exp α 2 l - z D 1 α 1 cosh α 1 l + z b + D 2 α 2 sinh α 1 l + z b .
z b = 1 + R eff 1 - R eff   2 D 1 .
R ρ ,   ω = 2 π d Ω 1 - R fres θ 1 4 π Φ 1 ρ ,   z = 0 ,   ω + 3 D 1 z   Φ 1 ρ ,   z ,   ω | z = 0 cos   θ cos   θ ,
R ρ ,   ω = 0.118 Φ 1 ρ ,   z = 0 ,   ω + 0.306 D 1 z   Φ 1 ρ ,   z , ω | z = 0 ,
R ρ , ω = 1 4   Φ 1 ρ ,   z = 0 ,   ω + 1 2   D 1 z   Φ 1 ρ ,   z ,   ω | z = 0 .
θ = tan - 1 Im R ρ ,   ω Re R ρ ,   ω ,
M = Im   R ρ ,   ω 2 + Re   R ρ ,   ω 2 R ρ ,   ω = 0 2 1 / 2 .
R ρ = R ρ ,   ω = 0 .
Φ ρ ,   z ,   ω = exp j ω t 4 π D exp - k z - z 0 2 + ρ 2 1 / 2 z - z 0 2 + ρ 2 1 / 2 - exp - k z + z 0 + 2 z b 2 + ρ 2 1 / 2 z + z 0 + 2 z b 2 + ρ 2 1 / 2 ,
Φ ρ ,   z ,   t = c 4 π Dct 3 / 2 exp - μ a ct × exp - z - z 0 2 + ρ 2 4 Dct - exp - z + z 0 + 2 z b 2 + ρ 2 4 Dct .
L i ρ = - Δ ln   R ρ / Δ μ ai ,

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