Abstract

We present a technique for the measurement of temporal field autocorrelation functions of multiply scattered light with subsecond acquisition time. The setup is based on the parallel detection and autocorrelation of intensity fluctuations from statistically equivalent but independent speckles using a fiber bundle, an array of avalanche photodiodes, and a multichannel autocorrelator with variable integration times between 6.5 and 104 ms. Averaging the autocorrelation functions from the different speckles reduces the integration time in diffusing-wave spectroscopy experiments drastically, thus allowing us to resolve nonstationary scatterer dynamics with single-trial measurements. We present applications of the technique to the measurement of arterial and venous blood flow in deep tissue. We find strong deviations both of the shape and characteristic decay time of autocorrelation functions recorded at different phases of the pulsation cycle from time-averaged autocorrelation functions.

© 2007 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  23. J. Li, F. Jaillon, G. Dietsche, G. Maret, and T. Gisler, "Pulsation-resolved deep tissue dynamics measured with diffusing-wave spectroscopy," Opt. Express 14, 7841-7851 (2006).
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    [CrossRef]
  26. L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214-3221 (1999).
    [CrossRef]
  27. R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: A tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110 (2005).
    [CrossRef]
  28. Deutsches Institut f. Normung e. V., Deutsche Industrie-Norm EN 60825-1: Sicherheit von Laser-Einrichtungen (Beuth, 2003).
  29. E.-G. Neumann, Single-Mode Fibers (Springer, 1988).
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    [CrossRef]
  31. I. Flammer and J. Ricka, "Dynamic light scattering with single-mode receivers: partial heterodyning regime," Appl. Opt. 36, 7508-7517 (1997).
    [CrossRef]
  32. D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, "Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit," J. Phys. (Paris) 18, 2101-2127 (1990).
  33. D. E. Koppel, "Statistical accuracy in fluorescence correlation spectroscopy," Phys. Rev. A 10, 1938-1945 (1974).
    [CrossRef]
  34. K. Schätzel, "Noise in photon correlation and photon structure functions," Opt. Acta 30, 155-166 (1983).
    [CrossRef]
  35. S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, and E. O. R. Reynolds, "Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation," Biochim. Biophys. Acta 933, 184-192 (1988).
    [CrossRef] [PubMed]
  36. E. Okada and D. T. Delpy, "Near-infrared light propagation in an adult head model. II. Effect of superficial tissue thickness on the sensitivity of the near-infrared spectroscopy signal," Appl. Opt. 42, 2915-2922 (2003).
    [CrossRef] [PubMed]
  37. S. Feng, F. Zeng, and B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," Appl. Opt. 34, 3826-3837 (1995).
    [CrossRef] [PubMed]
  38. R. D. Bauer and R. Busse, "Biophysik des Kreislaufs," in Kreislaufphysiologie, R. Busse, ed. (Thieme, 1982), pp. 3-40.

2007 (2)

2006 (5)

C. Zhou, G. Yu, D. Furuya, J. H. Greenberg, A. G. Yodh, and T. Durduran, "Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain," Opt. Express 14, 1125-1144 (2006).
[CrossRef] [PubMed]

J. Li, F. Jaillon, G. Dietsche, G. Maret, and T. Gisler, "Pulsation-resolved deep tissue dynamics measured with diffusing-wave spectroscopy," Opt. Express 14, 7841-7851 (2006).
[CrossRef] [PubMed]

F. Jaillon, S. E. Skipetrov, J. Li, G. Dietsche, G. Maret, and T. Gisler, "Diffusing-wave spectroscopy from head-like tissue phantoms: influence of a non-scattering layer," Opt. Express 14, 10181-10194 (2006).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Q. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, "Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study," J. Biomed. Opt. 11, 064021 (2006).
[CrossRef]

G. Yu, T. Durduran, C. Zhou, T. C. Zhu, J. C. Finlay, T. M. Busch, S. B. Malkowicz, S. M. Hahn, and A. G. Yodh, "Real-time in situ monitoring of human prostate photodynamic therapy with diffuse light," Photochem. Photobiol. 82, 1279-1284 (2006).
[CrossRef] [PubMed]

2005 (5)

G. Yu, T. Durduran, G. Lech, C. Zhou, B. Chance, E. R. Mohler, III, and A. G. Yodh, "Time-dependent blood flow and oxygenation in human skeletal muscles measured with noninvasive near-infrared diffuse optical spectroscopies," J. Biomed. Opt. 10, 024027 (2005).
[CrossRef] [PubMed]

J. Li, G. Dietsche, D. Iftime, S. E. Skipetrov, G. Maret, T. Elbert, B. Rockstroh, and T. Gisler, "Non-invasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy," J. Biomed. Opt. 10, 044002 (2005).
[CrossRef] [PubMed]

G. Yu, T. Durduran, C. Zhou, H.-W. Wang, M. E. Putt, H. M. Saunders, C. S. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
[CrossRef] [PubMed]

B. S. Chae and E. M. Furst, "Probe surface chemistry dependence and local polymer network structure in F-actin microrheology," Langmuir 21, 3084-3089 (2005).
[CrossRef] [PubMed]

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: A tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110 (2005).
[CrossRef]

2004 (1)

2003 (3)

Deutsches Institut f. Normung e. V., Deutsche Industrie-Norm EN 60825-1: Sicherheit von Laser-Einrichtungen (Beuth, 2003).

E. Okada and D. T. Delpy, "Near-infrared light propagation in an adult head model. II. Effect of superficial tissue thickness on the sensitivity of the near-infrared spectroscopy signal," Appl. Opt. 42, 2915-2922 (2003).
[CrossRef] [PubMed]

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

2001 (1)

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]

1999 (2)

T. Gisler and D. A. Weitz, "Scaling of the microrheology of semidilute F-actin solutions," Phys. Rev. Lett. 82, 1606-1609 (1999).
[CrossRef]

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

1997 (1)

1996 (2)

M. Heckmeier and G. Maret, "Visualization of flow in multiple-scattering liquids," Europhys. Lett. 34, 257-262 (1996).
[CrossRef]

D. A. Boas, "Diffuse photon probes of structural and dynamical properties of turbid media: Theory and biomedical applications," Ph.D. dissertation (University of Pennsylvania, 1996).

1995 (3)

1994 (1)

D. Bicout and G. Maret, "Multiple light scattering in Taylor-Couette flow," Physica A 210, 87-112 (1994).
[CrossRef]

1993 (1)

A. P. Y. Wong and P. Wiltzius, "Dynamic light scattering with a CCD camera," Rev. Sci. Instrum. 64, 2547-2549 (1993).
[CrossRef]

1990 (4)

B. J. Berne and R. Pecora, Dynamic Light Scattering (Krieger, 1990).

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

K. Schätzel, "Noise on photon correlation data: I. Autocorrelation functions," Quantum Opt. 2, 287-305 (1990).
[CrossRef]

D. J. Pine, D. A. Weitz, J. X. Zhu, and E. Herbolzheimer, "Diffusing-wave spectroscopy: dynamic light scattering in the multiple scattering limit," J. Phys. (Paris) 18, 2101-2127 (1990).

1988 (3)

E.-G. Neumann, Single-Mode Fibers (Springer, 1988).

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, and E. O. R. Reynolds, "Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation," Biochim. Biophys. Acta 933, 184-192 (1988).
[CrossRef] [PubMed]

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 (1)

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]

1983 (1)

K. Schätzel, "Noise in photon correlation and photon structure functions," Opt. Acta 30, 155-166 (1983).
[CrossRef]

1982 (1)

R. D. Bauer and R. Busse, "Biophysik des Kreislaufs," in Kreislaufphysiologie, R. Busse, ed. (Thieme, 1982), pp. 3-40.

1974 (1)

D. E. Koppel, "Statistical accuracy in fluorescence correlation spectroscopy," Phys. Rev. A 10, 1938-1945 (1974).
[CrossRef]

Bandyopadhyay, R.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: A tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110 (2005).
[CrossRef]

Bauer, R. D.

R. D. Bauer and R. Busse, "Biophysik des Kreislaufs," in Kreislaufphysiologie, R. Busse, ed. (Thieme, 1982), pp. 3-40.

Berne, B. J.

B. J. Berne and R. Pecora, Dynamic Light Scattering (Krieger, 1990).

Bicout, D.

D. Bicout and G. Maret, "Multiple light scattering in Taylor-Couette flow," Physica A 210, 87-112 (1994).
[CrossRef]

Boas, D. A.

D. A. Boas, "Diffuse photon probes of structural and dynamical properties of turbid media: Theory and biomedical applications," Ph.D. dissertation (University of Pennsylvania, 1996).

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

Buerk, D. G.

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

Burnett, M. G.

Busch, T. M.

G. Yu, T. Durduran, C. Zhou, T. C. Zhu, J. C. Finlay, T. M. Busch, S. B. Malkowicz, S. M. Hahn, and A. G. Yodh, "Real-time in situ monitoring of human prostate photodynamic therapy with diffuse light," Photochem. Photobiol. 82, 1279-1284 (2006).
[CrossRef] [PubMed]

G. Yu, T. Durduran, C. Zhou, H.-W. Wang, M. E. Putt, H. M. Saunders, C. S. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
[CrossRef] [PubMed]

Busse, R.

R. D. Bauer and R. Busse, "Biophysik des Kreislaufs," in Kreislaufphysiologie, R. Busse, ed. (Thieme, 1982), pp. 3-40.

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 (1995).
[CrossRef] [PubMed]

Chae, B. S.

B. S. Chae and E. M. Furst, "Probe surface chemistry dependence and local polymer network structure in F-actin microrheology," Langmuir 21, 3084-3089 (2005).
[CrossRef] [PubMed]

Chaikin, P. M.

X.-L. Wu, D. J. Pine, P. M. Chaikin, J. P. 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]

Chance, B.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Q. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, "Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study," J. Biomed. Opt. 11, 064021 (2006).
[CrossRef]

G. Yu, T. Durduran, G. Lech, C. Zhou, B. Chance, E. R. Mohler, III, and A. G. Yodh, "Time-dependent blood flow and oxygenation in human skeletal muscles measured with noninvasive near-infrared diffuse optical spectroscopies," J. Biomed. Opt. 10, 024027 (2005).
[CrossRef] [PubMed]

S. Feng, F. Zeng, and B. Chance, "Photon migration in the presence of a single defect: a perturbation analysis," Appl. Opt. 34, 3826-3837 (1995).
[CrossRef] [PubMed]

Cheung, C.

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

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]

Choe, R.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Q. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, "Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study," J. Biomed. Opt. 11, 064021 (2006).
[CrossRef]

Cipelletti, L.

L. Cipelletti and D. A. Weitz, "Ultralow-angle dynamic light scattering with a charge coupled device camera based multispeckle, multitau correlator," Rev. Sci. Instrum. 70, 3214-3221 (1999).
[CrossRef]

Cope, M.

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, and E. O. R. Reynolds, "Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation," Biochim. Biophys. Acta 933, 184-192 (1988).
[CrossRef] [PubMed]

Culver, J. P.

C. Menon, G. M. Polin, I. Prabakaran, A. Hsi, C. Cheung, J. P. Culver, J. F. Pingpank, C. S. Sehgal, A. G. Yodh, D. G. Buerk, and D. L. Fraker, "An integrated approach to measuring tumor oxygen status using human melanoma xenografts as a model," Cancer Res. 63, 7232-7240 (2003).
[PubMed]

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]

Delpy, D. T.

E. Okada and D. T. Delpy, "Near-infrared light propagation in an adult head model. II. Effect of superficial tissue thickness on the sensitivity of the near-infrared spectroscopy signal," Appl. Opt. 42, 2915-2922 (2003).
[CrossRef] [PubMed]

S. Wray, M. Cope, D. T. Delpy, J. S. Wyatt, and E. O. R. Reynolds, "Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation," Biochim. Biophys. Acta 933, 184-192 (1988).
[CrossRef] [PubMed]

Detre, J. A.

Dietsche, G.

Dixon, P. K.

R. Bandyopadhyay, A. S. Gittings, S. S. Suh, P. K. Dixon, and D. J. Durian, "Speckle-visibility spectroscopy: A tool to study time-varying dynamics," Rev. Sci. Instrum. 76, 093110 (2005).
[CrossRef]

Du, J.

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Q. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, "Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study," J. Biomed. Opt. 11, 064021 (2006).
[CrossRef]

Durduran, T.

G. Yu, T. F. Floyd, T. Durduran, C. Zhou, J. Wang, J. A. Detre, and A. G. Yodh, "Validation of diffuse correlation spectroscopy for muscle blood flow with concurrent arterial spin labeled perfusion MRI," Opt. Express 15, 1064-1075 (2007).
[CrossRef] [PubMed]

G. Yu, T. Durduran, C. Zhou, T. C. Zhu, J. C. Finlay, T. M. Busch, S. B. Malkowicz, S. M. Hahn, and A. G. Yodh, "Real-time in situ monitoring of human prostate photodynamic therapy with diffuse light," Photochem. Photobiol. 82, 1279-1284 (2006).
[CrossRef] [PubMed]

U. Sunar, H. Quon, T. Durduran, J. Zhang, J. Du, C. Zhou, G. Q. Yu, R. Choe, A. Kilger, R. Lustig, L. Loevner, S. Nioka, B. Chance, and A. G. Yodh, "Noninvasive diffuse optical measurement of blood flow and blood oxygenation for monitoring radiation therapy in patients with head and neck tumors: a pilot study," J. Biomed. Opt. 11, 064021 (2006).
[CrossRef]

C. Zhou, G. Yu, D. Furuya, J. H. Greenberg, A. G. Yodh, and T. Durduran, "Diffuse optical correlation tomography of cerebral blood flow during cortical spreading depression in rat brain," Opt. Express 14, 1125-1144 (2006).
[CrossRef] [PubMed]

G. Yu, T. Durduran, G. Lech, C. Zhou, B. Chance, E. R. Mohler, III, and A. G. Yodh, "Time-dependent blood flow and oxygenation in human skeletal muscles measured with noninvasive near-infrared diffuse optical spectroscopies," J. Biomed. Opt. 10, 024027 (2005).
[CrossRef] [PubMed]

G. Yu, T. Durduran, C. Zhou, H.-W. Wang, M. E. Putt, H. M. Saunders, C. S. Sehgal, E. Glatstein, A. G. Yodh, and T. M. Busch, "Noninvasive monitoring of murine tumor blood flow during and after photodynamic therapy provides early assessment of therapeutic efficacy," Clin. Cancer Res. 11, 3543-3552 (2005).
[CrossRef] [PubMed]

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[CrossRef]

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[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Side and top views of the multifiber receiver head, and (b) receiver head with attached collection optics. The receiver head consists of a stainless-steel sleeve holding a POM cylinder. Few-mode fibers, whose isolation jacket and coating were removed on a length of 1 cm, are bundled inside a hole in the POM cylinder and fixed with epoxy adhesive. The collection tip with an integrated convex lens (b), screwed onto the receiver head (a), is used to image the speckle pattern from a small (diameter < 3 mm ) area on the skin onto the fiber faces. The red lines indicate the extremal rays from an LP 01 fiber mode. The tip allows protecting the polished fiber faces from direct contact with the skin, which over time degrades the polish and the collection efficiency of the fibers. The conical brass funnel is used to move hair from the field of view.

Fig. 2
Fig. 2

Squared bundle-averaged field autocorrelation function | g j ( 1 ) ( τ ) N | 2 from a suspension of polystyrene latex spheres with N = 28 fibers and integration time T = 26 ms , measured in transmission through a slab with thickness 1.0 cm and lateral dimensions 5.0 × 5.0 cm 2 . Average count rate: R = 82 kHz . (a) Average over M = 20 runs; (b) single run. Dashed curves: least-squares fit of the prediction for the slab transmission geometry with expanded source and point-like receiver [32], with the reduced scattering coefficient μ s as a free parameter. The independently determined particle diffusion coefficient D = 9.2 × 10 9 cm 2 / s and the absorption coefficient μ a = 0.0223 cm 1 were used as fixed parameters. The values μ s = 8.2 cm 1 (a) and μ s = 7.9 cm 1 (b) agree within 5% with Mie calculations [10].

Fig. 3
Fig. 3

(a) Standard deviation σ ( τ ; N ) of the reduced squared bundle-averaged field autocorrelation function β N | g j ( 1 ) ( τ ) N | 2 for N = 28 fibers and N = 1 fiber, as a function of lag time τ, measured on a polystyrene latex suspension. Sample and geometry are as in Fig. 2. The dashed-dotted curve is the prediction Eq. (3) for a single receiver fiber. The steps arise from the doubling of the sampling time increment [33, 34]. (b) Normalized integrated standard deviation s ( N ) / s ( 1 ) [see Eq. (5)] as a function of the number of fibers N (symbols) and prediction s ( N ) / s ( 1 ) = N 1 / 2 for statistically independent fibers (solid line).

Fig. 4
Fig. 4

(a) Decay time τ d and (b) average photon count rate R measured on the tip of the index finger. Source-receiver distance: 1.4 cm; integration time: 26 ms. Number of receiver channels: N = 23 . Data in (a) and (b) were smoothed by a 130 ms sliding average, corresponding to 14% of the average pulsation period.

Fig. 5
Fig. 5

(a) Decay time τ d and (b) average photon count rate R measured over the medial cubital vein. Source-receiver distance: 1.6 cm; integration time: 26 ms. Number of receiver channels: N = 8 . Data in (a) and (b) were smoothed by a 78 ms sliding average, corresponding to 11% of the average pulsation period. Experimental noise level in (b): 0.03% per data point.

Fig. 6
Fig. 6

(a) Decay time τ d and (b) average photon-count rate R measured over the forehead. Source-receiver distance: 2.9 cm; integration time: 26 ms. Number of receiver channels: N = 14 . Data in (a) and (b) were smoothed by a 104 ms sliding average, corresponding to 14% of the average pulsation period of 758 ms. Note the consistent phase lag of 175 ms between the minima of τ d and the ones of R. Experimental noise level in (b): 0.1% per data point.

Fig. 7
Fig. 7

Field autocorrelation functions g j ( 1 ) ( τ ) N as a function of lag time τ at the diastolic maxima (blue solid curve) and systolic minima (red curve) of τ d measured at the fingertip. Number of receiver channels: N = 23 . Integration time per field autocorrelation function: 26 ms. Data are averages over 11 field autocorrelation functions measured at the maxima and minima of the τ d curve (blue and red arrows, respectively, in inset). Black curve: g j ( 1 ) ( τ ) N averaged over 10 s. For easier comparison with the diastolic data, the systolic field autocorrelation function was shifted in time (red dashed curve). Note the larger curvature at short lag times of the field autocorrelation function recorded at the systolic minimum.

Equations (5)

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g j ( 1 ) ( τ ) N = [ 1 N i = 1 N ( g i , j ( 2 ) ( τ ) 1 ) / β i ] 1 / 2 ,
τ d = τ 1 τ 2 d τ | g j ( 1 ) ( τ ) N | 2 ,
σ ( τ k ) = ( T k / T ) 1 / 2 × [ β 2 ( 1 + e 2 Γ T k ) ( 1 + e 2 Γ τ k ) + 2 k ( 1 e 2 Γ T k ) e 2 Γ τ k 1 e 2 Γ T k + 2 β n k ( 1 + e 2 Γ T k ) + 1 n k 2 ( 1 + β e Γ τ k ) ] 1 / 2 ,
σ ( τ ; N ) = β N [ 1 M 1 j = 1 M ( | g ( 1 ) ( τ ) N , M | 2 | g j ( 1 ) ( τ ) N | 2 ) 2 ] 1 / 2 .
s ( N ) = τ 1 τ 2 σ ( τ ; N ) d τ ,

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