Abstract

We presented theoretical and experimental demonstrations of the possibilities of performing time-resolved diffusing wave spectroscopy: We successfully registered field fluctuations for selected photon path lengths that can surpass 300 transport mean free paths. Such performance opens new possibilities for biomedical optics applications.

© 2006 Optical Society of America

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  1. F. F. Jobsis, "Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters," Science 198, 1264-1267 (1977).
    [CrossRef] [PubMed]
  2. D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and imaging with diffusing temporal field correlations," Phys. Rev. Lett. 75, 1855-1858 (1985).
    [CrossRef]
  3. D. A. Boas and A. G. Yodh, "Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation," J. Opt. Soc. Am. A 14, 192-215 (1997).
    [CrossRef]
  4. M. Heckmeier, S. E. Skipetrov, G. Maret, and R. Maynard, "Imaging of dynamic heterogeneities in multiple-scattering media," J. Opt. Soc. Am. A 14, 185-191 (1997).
    [CrossRef]
  5. C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
    [CrossRef] [PubMed]
  6. A. Kienle, "Non-invasive determination of muscle blood flow in the extremities from laser Doppler spectra," Phys. Med. Biol. 46, 1231-1244 (2001).
    [CrossRef] [PubMed]
  7. G. Maret and P. E. Wolf, "Multiple light scattering from disordered media. The effect of Brownian motion of scatterers," Z. Phys. B 65, 409-413 (1987).
    [CrossRef]
  8. M. J. Stephen, "Temporal fluctuations in wave propagation in random media," Phys. Rev. B 37, 1-5 (1988).
    [CrossRef]
  9. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, "Diffusing-wave spectroscopy," Phys. Rev. Lett. 60, 1134-1137 (1988).
    [CrossRef] [PubMed]
  10. X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, "Diffusing-wave spectroscopy in a shear flow," J. Opt. Soc. Am. B 7, 15-20 (1990).
    [CrossRef]
  11. A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
    [CrossRef] [PubMed]
  12. R. J. Hunter, M. S. Patterson, Th. J. Farrell, and J. E. Haward, "Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness," Phys. Med. Biol. 47, 193-208 (2002).
    [CrossRef] [PubMed]
  13. A. Kienle and Th. Glanzmann, "In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model," Phys. Med. Biol. 44, 2689-2702 (1999).
    [CrossRef] [PubMed]
  14. J.-M. Tualle, H. L. Nghiem, D. Ettori, R. Sablong, E. Tinet, and S. Avrillier, "Asymptotic behavior and inverse problem in layered scattering media," J. Opt. Soc. Am. A 21, 24-34 (2004).
    [CrossRef]
  15. A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Moller, R. Macdonald, A. Villringer, and H. Rinneberg, "Time-resolved multidistance near-infrared spectroscopy of the adult head: intracerebral and extracerebral absorption changes from moments of distribution of times of flight of photons," Appl. Opt. 43, 3037-3047 (2004).
    [CrossRef] [PubMed]
  16. V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and L. Delfino, "Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination," J. Biomed. Opt. 6, 441-445 (2001).
    [CrossRef] [PubMed]
  17. J.-M. Tualle, E. Tinet, and S. Avrillier, "A new and easy way to perform time-resolved measurements of the light scattered by a turbid medium," Opt. Commun. 189, 211-220 (2001).
    [CrossRef]
  18. J. M. Tualle, H. L. Nghiêm, C. Schäfauer, P. Berthaud, E. Tinet, D. Ettori, and S. Avrillier, "Time-resolved measurements from speckle interferometry," Opt. Lett. 30, 50-52 (2005).
    [CrossRef] [PubMed]
  19. J.-M. Tualle, "Method for analysing a diffusing sample by time resolution measurement," international patent WO0188507 (November 22, 2001).
  20. M. X. Cowan, I. P. Jones, J. H. Page, and D. A. Weitz, "Diffusing acoustic wave spectroscopy," Phys. Rev. E 65, 1-11 (2002).
    [CrossRef]
  21. K. K. Bizheva, A. M. Siegel, and D. A. Boas, "Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy," Phys. Rev. E 58, 7664-7667 (1998).
    [CrossRef]
  22. E. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749-759 (1932).
    [CrossRef]
  23. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).
  24. M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
    [CrossRef] [PubMed]
  25. Rochester, webpage, http://www.me.rochester. edu/courses/ME241/SE3.html; we used a logarithmic extrapolation to get the values corresponding to our phantoms.
  26. F. G. Santamaria, "Photonic crystals based on silica microspheres," Ph.D. thesis (Instituto de Ciencia de Materiales de Madrid, 2003).
  27. E. Tinet, J.-M. Tualle, D. Ettori, and S. Avrillier, "Real time transformation of pre-computed Monte Carlo results for fitting optical measurements in biomedical applications," Monte Carlo Meth. Appl. 7, 397-409 (2001).
  28. H. L. Nghiêm Thi, "Mise en ouvre et calibration d'une méthode interférométrique à balayage spectral pour la mesure résolue dans le temps de la lumière diffuse,"Ph.D. thesis (Université Paris 13, 2005).

2005

2004

2002

R. J. Hunter, M. S. Patterson, Th. J. Farrell, and J. E. Haward, "Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness," Phys. Med. Biol. 47, 193-208 (2002).
[CrossRef] [PubMed]

M. X. Cowan, I. P. Jones, J. H. Page, and D. A. Weitz, "Diffusing acoustic wave spectroscopy," Phys. Rev. E 65, 1-11 (2002).
[CrossRef]

2001

V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and L. Delfino, "Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination," J. Biomed. Opt. 6, 441-445 (2001).
[CrossRef] [PubMed]

J.-M. Tualle, E. Tinet, and S. Avrillier, "A new and easy way to perform time-resolved measurements of the light scattered by a turbid medium," Opt. Commun. 189, 211-220 (2001).
[CrossRef]

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

A. Kienle, "Non-invasive determination of muscle blood flow in the extremities from laser Doppler spectra," Phys. Med. Biol. 46, 1231-1244 (2001).
[CrossRef] [PubMed]

E. Tinet, J.-M. Tualle, D. Ettori, and S. Avrillier, "Real time transformation of pre-computed Monte Carlo results for fitting optical measurements in biomedical applications," Monte Carlo Meth. Appl. 7, 397-409 (2001).

1999

A. Kienle and Th. Glanzmann, "In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model," Phys. Med. Biol. 44, 2689-2702 (1999).
[CrossRef] [PubMed]

1998

K. K. Bizheva, A. M. Siegel, and D. A. Boas, "Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy," Phys. Rev. E 58, 7664-7667 (1998).
[CrossRef]

1997

1996

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

1990

1988

M. J. Stephen, "Temporal fluctuations in wave propagation in random media," Phys. Rev. B 37, 1-5 (1988).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, "Diffusing-wave spectroscopy," Phys. Rev. Lett. 60, 1134-1137 (1988).
[CrossRef] [PubMed]

1987

G. Maret and P. E. Wolf, "Multiple light scattering from disordered media. The effect of Brownian motion of scatterers," Z. Phys. B 65, 409-413 (1987).
[CrossRef]

1985

D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and imaging with diffusing temporal field correlations," Phys. Rev. Lett. 75, 1855-1858 (1985).
[CrossRef]

1977

F. F. Jobsis, "Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters," Science 198, 1264-1267 (1977).
[CrossRef] [PubMed]

1932

E. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749-759 (1932).
[CrossRef]

Arridge, S. R.

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

Avrillier, S.

J. M. Tualle, H. L. Nghiêm, C. Schäfauer, P. Berthaud, E. Tinet, D. Ettori, and S. Avrillier, "Time-resolved measurements from speckle interferometry," Opt. Lett. 30, 50-52 (2005).
[CrossRef] [PubMed]

J.-M. Tualle, H. L. Nghiem, D. Ettori, R. Sablong, E. Tinet, and S. Avrillier, "Asymptotic behavior and inverse problem in layered scattering media," J. Opt. Soc. Am. A 21, 24-34 (2004).
[CrossRef]

J.-M. Tualle, E. Tinet, and S. Avrillier, "A new and easy way to perform time-resolved measurements of the light scattered by a turbid medium," Opt. Commun. 189, 211-220 (2001).
[CrossRef]

E. Tinet, J.-M. Tualle, D. Ettori, and S. Avrillier, "Real time transformation of pre-computed Monte Carlo results for fitting optical measurements in biomedical applications," Monte Carlo Meth. Appl. 7, 397-409 (2001).

Berthaud, P.

Biscotti, G.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Bizheva, K. K.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, "Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy," Phys. Rev. E 58, 7664-7667 (1998).
[CrossRef]

Boas, D. A.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, "Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy," Phys. Rev. E 58, 7664-7667 (1998).
[CrossRef]

D. A. Boas and A. G. Yodh, "Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation," J. Opt. Soc. Am. A 14, 192-215 (1997).
[CrossRef]

D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and imaging with diffusing temporal field correlations," Phys. Rev. Lett. 75, 1855-1858 (1985).
[CrossRef]

Campbell, L. E.

D. A. Boas, L. E. Campbell, and A. G. Yodh, "Scattering and imaging with diffusing temporal field correlations," Phys. Rev. Lett. 75, 1855-1858 (1985).
[CrossRef]

Chaikin, P. M.

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, "Diffusing-wave spectroscopy in a shear flow," J. Opt. Soc. Am. B 7, 15-20 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, "Diffusing-wave spectroscopy," Phys. Rev. Lett. 60, 1134-1137 (1988).
[CrossRef] [PubMed]

Chernomordik, V.

V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and L. Delfino, "Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination," J. Biomed. Opt. 6, 441-445 (2001).
[CrossRef] [PubMed]

Cheung, C.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Cowan, M. X.

M. X. Cowan, I. P. Jones, J. H. Page, and D. A. Weitz, "Diffusing acoustic wave spectroscopy," Phys. Rev. E 65, 1-11 (2002).
[CrossRef]

Cubeddu, R.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Culver, J. P.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Delfino, L.

V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and L. Delfino, "Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination," J. Biomed. Opt. 6, 441-445 (2001).
[CrossRef] [PubMed]

Delpy, D. T.

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

Esposito, R.

V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and L. Delfino, "Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination," J. Biomed. Opt. 6, 441-445 (2001).
[CrossRef] [PubMed]

Ettori, D.

Farrell, Th. J.

R. J. Hunter, M. S. Patterson, Th. J. Farrell, and J. E. Haward, "Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness," Phys. Med. Biol. 47, 193-208 (2002).
[CrossRef] [PubMed]

Ferrari, M.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Firbank, M.

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

Gandjbakhche, A.

V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and L. Delfino, "Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination," J. Biomed. Opt. 6, 441-445 (2001).
[CrossRef] [PubMed]

Glanzmann, Th.

A. Kienle and Th. Glanzmann, "In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model," Phys. Med. Biol. 44, 2689-2702 (1999).
[CrossRef] [PubMed]

Greenberg, J. H.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Haward, J. E.

R. J. Hunter, M. S. Patterson, Th. J. Farrell, and J. E. Haward, "Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness," Phys. Med. Biol. 47, 193-208 (2002).
[CrossRef] [PubMed]

Heckmeier, M.

Herbolzheimer, E.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, "Diffusing-wave spectroscopy," Phys. Rev. Lett. 60, 1134-1137 (1988).
[CrossRef] [PubMed]

Huang, J. S.

Hunter, R. J.

R. J. Hunter, M. S. Patterson, Th. J. Farrell, and J. E. Haward, "Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness," Phys. Med. Biol. 47, 193-208 (2002).
[CrossRef] [PubMed]

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978).

Jobsis, F. F.

F. F. Jobsis, "Noninvasive infrared monitoring of cerebral and myocardial oxygen sufficiency and circulatory parameters," Science 198, 1264-1267 (1977).
[CrossRef] [PubMed]

Jones, I. P.

M. X. Cowan, I. P. Jones, J. H. Page, and D. A. Weitz, "Diffusing acoustic wave spectroscopy," Phys. Rev. E 65, 1-11 (2002).
[CrossRef]

Kienle, A.

A. Kienle, "Non-invasive determination of muscle blood flow in the extremities from laser Doppler spectra," Phys. Med. Biol. 46, 1231-1244 (2001).
[CrossRef] [PubMed]

A. Kienle and Th. Glanzmann, "In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model," Phys. Med. Biol. 44, 2689-2702 (1999).
[CrossRef] [PubMed]

Lepore, M.

V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and L. Delfino, "Depth dependence of the analytical expression for the width of the point spread function (spatial resolution) in time-resolved transillumination," J. Biomed. Opt. 6, 441-445 (2001).
[CrossRef] [PubMed]

Liebert, A.

Macdonald, R.

Maret, G.

M. Heckmeier, S. E. Skipetrov, G. Maret, and R. Maynard, "Imaging of dynamic heterogeneities in multiple-scattering media," J. Opt. Soc. Am. A 14, 185-191 (1997).
[CrossRef]

G. Maret and P. E. Wolf, "Multiple light scattering from disordered media. The effect of Brownian motion of scatterers," Z. Phys. B 65, 409-413 (1987).
[CrossRef]

Maynard, R.

Moller, M.

Nghiem, H. L.

Nghiêm, H. L.

Nghiêm Thi, H. L.

H. L. Nghiêm Thi, "Mise en ouvre et calibration d'une méthode interférométrique à balayage spectral pour la mesure résolue dans le temps de la lumière diffuse,"Ph.D. thesis (Université Paris 13, 2005).

Obrig, H.

Page, J. H.

M. X. Cowan, I. P. Jones, J. H. Page, and D. A. Weitz, "Diffusing acoustic wave spectroscopy," Phys. Rev. E 65, 1-11 (2002).
[CrossRef]

Patterson, M. S.

R. J. Hunter, M. S. Patterson, Th. J. Farrell, and J. E. Haward, "Haemoglobin oxygenation of a two-layer tissue-simulating phantom from time-resolved reflectance: effect of top layer thickness," Phys. Med. Biol. 47, 193-208 (2002).
[CrossRef] [PubMed]

Pifferi, A.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Pine, D. J.

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, "Diffusing-wave spectroscopy in a shear flow," J. Opt. Soc. Am. B 7, 15-20 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, "Diffusing-wave spectroscopy," Phys. Rev. Lett. 60, 1134-1137 (1988).
[CrossRef] [PubMed]

Quaresima, V.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Rinneberg, H.

Rochester,

Rochester, webpage, http://www.me.rochester. edu/courses/ME241/SE3.html; we used a logarithmic extrapolation to get the values corresponding to our phantoms.

Sablong, R.

Santamaria, F. G.

F. G. Santamaria, "Photonic crystals based on silica microspheres," Ph.D. thesis (Instituto de Ciencia de Materiales de Madrid, 2003).

Schäfauer, C.

Schweiger, M.

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-783 (1996).
[CrossRef] [PubMed]

Siegel, A. M.

K. K. Bizheva, A. M. Siegel, and D. A. Boas, "Path-length-resolved dynamic light scattering in highly scattering random media: the transition to diffusing wave spectroscopy," Phys. Rev. E 58, 7664-7667 (1998).
[CrossRef]

Skipetrov, S. E.

Spinelli, L.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Steinbrink, J.

Stephen, M. J.

M. J. Stephen, "Temporal fluctuations in wave propagation in random media," Phys. Rev. B 37, 1-5 (1988).
[CrossRef]

Takahashi, K.

C. Cheung, J. P. Culver, K. Takahashi, J. H. Greenberg, and A. G. Yodh, "In vivo cerebrovascular measurement combining diffuse near-infrared absorption and correlation spectroscopies," Phys. Med. Biol. 46, 2053-2065 (2001).
[CrossRef] [PubMed]

Taroni, P.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Tinet, E.

J. M. Tualle, H. L. Nghiêm, C. Schäfauer, P. Berthaud, E. Tinet, D. Ettori, and S. Avrillier, "Time-resolved measurements from speckle interferometry," Opt. Lett. 30, 50-52 (2005).
[CrossRef] [PubMed]

J.-M. Tualle, H. L. Nghiem, D. Ettori, R. Sablong, E. Tinet, and S. Avrillier, "Asymptotic behavior and inverse problem in layered scattering media," J. Opt. Soc. Am. A 21, 24-34 (2004).
[CrossRef]

J.-M. Tualle, E. Tinet, and S. Avrillier, "A new and easy way to perform time-resolved measurements of the light scattered by a turbid medium," Opt. Commun. 189, 211-220 (2001).
[CrossRef]

E. Tinet, J.-M. Tualle, D. Ettori, and S. Avrillier, "Real time transformation of pre-computed Monte Carlo results for fitting optical measurements in biomedical applications," Monte Carlo Meth. Appl. 7, 397-409 (2001).

Torricelli, A.

A. Torricelli, V. Quaresima, A. Pifferi, G. Biscotti, L. Spinelli, P. Taroni, M. Ferrari, and R. Cubeddu, "Mapping of calf muscle oxygenation and haemoglobin content during dynamic plantar flexion exercise by multi-channel time-resolved near-infrared spectroscopy," Phys. Med. Biol. 49, 685-699 (2004).
[CrossRef] [PubMed]

Tualle, J. M.

Tualle, J.-M.

J.-M. Tualle, H. L. Nghiem, D. Ettori, R. Sablong, E. Tinet, and S. Avrillier, "Asymptotic behavior and inverse problem in layered scattering media," J. Opt. Soc. Am. A 21, 24-34 (2004).
[CrossRef]

J.-M. Tualle, E. Tinet, and S. Avrillier, "A new and easy way to perform time-resolved measurements of the light scattered by a turbid medium," Opt. Commun. 189, 211-220 (2001).
[CrossRef]

E. Tinet, J.-M. Tualle, D. Ettori, and S. Avrillier, "Real time transformation of pre-computed Monte Carlo results for fitting optical measurements in biomedical applications," Monte Carlo Meth. Appl. 7, 397-409 (2001).

J.-M. Tualle, "Method for analysing a diffusing sample by time resolution measurement," international patent WO0188507 (November 22, 2001).

Villringer, A.

Wabnitz, H.

Weitz, D. A.

M. X. Cowan, I. P. Jones, J. H. Page, and D. A. Weitz, "Diffusing acoustic wave spectroscopy," Phys. Rev. E 65, 1-11 (2002).
[CrossRef]

X. L. Wu, D. J. Pine, P. M. Chaikin, J. S. Huang, and D. A. Weitz, "Diffusing-wave spectroscopy in a shear flow," J. Opt. Soc. Am. B 7, 15-20 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, "Diffusing-wave spectroscopy," Phys. Rev. Lett. 60, 1134-1137 (1988).
[CrossRef] [PubMed]

Wigner, E.

E. Wigner, "On the quantum correction for thermodynamic equilibrium," Phys. Rev. 40, 749-759 (1932).
[CrossRef]

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[CrossRef]

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Yodh, A. G.

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J. Opt. Soc. Am. B

Monte Carlo Meth. Appl.

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Opt. Commun.

J.-M. Tualle, E. Tinet, and S. Avrillier, "A new and easy way to perform time-resolved measurements of the light scattered by a turbid medium," Opt. Commun. 189, 211-220 (2001).
[CrossRef]

Opt. Lett.

Phys. Med. Biol.

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[CrossRef]

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[CrossRef]

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Rochester, webpage, http://www.me.rochester. edu/courses/ME241/SE3.html; we used a logarithmic extrapolation to get the values corresponding to our phantoms.

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Figures (3)

Fig. 1
Fig. 1

Experimental setup. The wavelength-modulated source is a Littman extended-cavity laser diode. An optical isolator is used to cancel parasitic signals from the reference beam. An acousto-optic modulator (AOM), placed in the signal arm, plays the role of an optical shutter to perform a real-time background subtraction. The signal is acquired with a balanced detection. Graded-index multimode fibers are used for both the signal and the reference arms.

Fig. 2
Fig. 2

Correlation signal normalized by the time-resolved intensity versus photon time of flight τ at t p = 2 p Δ T varying from 6.7 to 33.3 ms ( Δ T = 1 300 Hz ) . For t = 6.7 ms ( p = 1 ) a good signal has been obtained up to τ = 1000 ps , which corresponds to more than 350 transport mean free paths and to about 2000 scattering events. As predicted, I 4 p ( τ ) I 0 ( τ ) exp μ f ( t ) c τ ; the linear fits of ln ( I 4 p I 0 ) are shown as thin lines.

Fig. 3
Fig. 3

Values of the effective absorption coefficient μ f obtained from the curve slope μ f c in Fig. 2 as a function of t p = 2 p Δ T . These results can be fitted by μ f ( t ) = α t . The fit, limited to the first three values of p , gives α = 15.2 ± 0.2 cm 1 s 1 .

Equations (27)

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s ( t ) R e { s 0 s ̃ * [ ω ( t ) , t ] } ,
s ( t ) + d τ R e { s 0 s * ( τ , t ) exp [ i ω ( t ) τ ] } .
Ref ( t , τ ) = sin 4 ( 2 π f t ) exp [ i Δ Ω τ cos ( 2 π f t ) ] ,
S D C , m ( τ ) = 2 f m Δ T 2 ( m + 1 ) Δ T 2 s ( t ) Ref ( t , τ ) d t ,
I p ( τ ) R e { Φ ( τ , ω , t 2 t 1 + p Δ T 2 ) G * ( τ , ω , t 1 , t 2 ) } × Ref ( t 1 , τ ) Ref * ( t 2 , τ ) d t 1 d t 2 d τ d ω ,
WT { f ( τ 1 , τ 2 ) } ( τ , ω ) = f ( τ + T 2 , τ T 2 ) exp [ i ω T ] d T ,
Φ ( τ , ω , t 2 t 1 ) = WT { s ( τ 1 , t 1 ) s * ( τ 2 , t 2 ) } ,
G ( τ , ω , t 1 , t 2 ) = W T { exp [ i ω ( t 1 ) τ 1 i ω ( t 2 ) τ 2 ] } ,
Φ ̃ ( Ω , ω , t ) = s ̃ i ( ω + Ω 2 ) s ̃ i * ( ω Ω 2 ) κ T κ exp [ i Δ ϕ κ ( t ) ] exp [ i Ω κ ( 0 ) c ] ,
Δ ϕ κ ( t ) = ( ω Ω 2 ) κ ( t ) κ ( 0 ) c .
Φ ̃ ( Ω , ω , t ) = n g 1 ( t , n ) E i f ( ω ) κ , n ( κ ) = n T κ exp [ i Ω κ ( 0 ) c ] ,
Φ ̃ ( Ω , ω , t ) f ( ω ) n g 1 ( t , n ) I ̃ ( n ) ( Ω ) .
Φ ( τ , ω , t ) f ( ω ) g 1 ( t , n = μ , c τ ) I ( τ ) ,
g 1 ( t 2 t 1 + p Δ T 2 , τ ) g 1 ( p Δ T 2 , τ ) ,
I p ( τ ) I ( τ ) g 1 ( p Δ T 2 , τ ) [ Π ( τ τ ) + Π ( τ + τ ) ] d τ ,
I p ( τ ) I ( τ ) g 1 ( p Δ T 2 , τ ) .
g 1 ( t , τ ) = exp μ f ( t ) c τ .
μ f ( t ) = 2 μ s t t 0 ,
D B = 6 π η a k B T .
S D C , m + p ( τ ) = 2 f m Δ T 2 ( m + 1 ) Δ T 2 s ( t + p Δ T 2 ) Ref ( t , τ ) d t .
s ( t ) + d τ { s 0 s * [ τ , t ] exp [ i ω ( t ) τ ] + s 0 * s [ τ , t ] exp [ i ω ( t ) τ ] } ,
I p ( τ ) { s [ τ 1 , t 1 ] s * [ τ 2 , t 2 + p Δ T 2 ] exp [ i ω ( t 2 ) τ 2 i ω ( t 1 ) τ 1 ] + c c } × Ref ( t 1 , τ ) Ref * ( t 2 , τ ) d t 1 d t 2 d τ 1 d τ 2 ,
I p ( τ ) Φ ( τ , ω , t 2 t 1 + p Δ T 2 ) G * ( τ , ω , t 1 , t 2 ) Ref ( t 1 , τ ) Ref * ( t 2 , τ ) d t 1 d t 2 d τ d ω + Φ * ( τ , ω , t 2 t 1 + p Δ T 2 ) G ( τ , ω , t 1 , t 2 ) Ref ( t 1 , τ ) Ref * ( t 2 , τ ) d t 1 d t 2 d τ d ω .
( 2 π ) 1 G ( τ , ω , t 1 , t 2 ) d ω = exp [ i ( ω ( t 1 ) ω ( t 2 ) ) τ ] .
I p ( τ ) I ( τ ) [ Π p ( τ τ , τ ) + Π p ( τ + τ , τ ) ] d τ ,
Π p ( τ , τ ) = g 1 ( t 2 t 1 + p Δ T 2 , τ ) Ref ( t 1 , τ ) × Ref * ( t 2 , τ ) d t 1 d t 2 .
Ref ( t 1 , τ ) d t 1 = Ref * ( t 2 , τ ) d t 2 J 2 ( Δ Ω τ ) τ 2 .

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