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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 12 — Sep. 30, 2010
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Time-resolved diffusing wave spectroscopy with a CCD camera

Katarzyna Zarychta, Eric Tinet, Leila Azizi, Sigrid Avrillier, Dominique Ettori, and Jean-Michel Tualle  »View Author Affiliations


Optics Express, Vol. 18, Issue 16, pp. 16289-16301 (2010)
http://dx.doi.org/10.1364/OE.18.016289


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Abstract

We show how time-resolved measurements of the diffuse light transmitted through a thick scattering slab can be performed with a standard CCD camera, thanks to an interferometric protocol. Time-resolved correlations measured at a fixed photon transit time are also presented. The high number of pixels of the camera allows us to attain a quite good sensitivity for a reasonably low acquisition time.

© 2010 OSA

1. Introduction

We already proposed [25

25. J.-M. Tualle, “Method for analyzing a diffusing sample by time resolution measurement”, US Patent 6903825 (2001).

27

27. J.-M. Tualle, H. L. Nghiêm, C. Schäfauer, P. Berthaud, É. Tinet, D. Ettori, and S. Avrillier, “Time-resolved measurements from speckle interferometry,” Opt. Lett. 30(1), 50–52 (2005). [CrossRef] [PubMed]

] a simple interferometric setup able to perform such time-resolved measurements, based on the use of a wavelength modulated continuous-wave source: if the optical pulsation ω was linearly varied, the time delay τ between the two waves in the interferometer would correspond to a proportional frequency shift, and to a beating at the same frequency shift like in heterodyne measurements. The discrimination of a beating frequency is therefore equivalent to the discrimination of a time delay. We proved that such a protocol can be extended to diffuse light: in our setup, interferences between the speckle pattern from the turbid medium and a reference beam are recorded by a lock-in detection. More precisely, the recorded photocurrent i(t) ≈i0 + iint(t), where i0 is the photocurrent from the reference beam and where iint(t) corresponds to interferences, is multiplied by a demodulation function Ref(t,τ); it is then integrated over half a period T/2 = 1/(2f) of the wavelength modulation, in order to obtain a demodulated signal SDC(τ). A possible choice for the function Ref(t,τ) with a sine modulation of ω is:
Ref(t,τ)=sin4(2πft)cos[ΔΩτcos(2πft)]
(1)
where ΔΩ is the depth of the wavelength modulation. This function mainly contains a demodulation term cos[ΔΩτ cos(2π f t)], which follows the frequency shift due to the sine modulation of ω at a fixed transit time τ ; the sin4(2π f t) term is an anti-windowing filter. Such a demodulation procedure discriminates light traveling through the turbid medium with a transit time τ, and we proved [26

26. 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(4–6), 211–220 (2001). [CrossRef]

] that the ensemble averaging <SDC(τ)2> is proportional to the average time-resolved flux ϕ(τ). Furthermore, we also proved [28

28. J.-M. Tualle, H. L. Nghiêm, M. Cheikh, D. Ettori, E. Tinet, and S. Avrillier, “Time-resolved diffusing wave spectroscopy beyond 300 transport mean free paths,” J. Opt. Soc. Am. A 23(6), 1452 (2006). [CrossRef]

,29

29. M. Cheikh, H. L. Nghiêm, D. Ettori, E. Tinet, S. Avrillier, and J. M. Tualle, “Time-resolved diffusing wave spectroscopy applied to dynamic heterogeneity imaging,” Opt. Lett. 31(15), 2311–2313 (2006). [CrossRef] [PubMed]

] that correlations like <SDC,i(τ)SDC,i + p(τ)>, where integers i and i + p denote two different integration periods separated by a time pT, constitute a unique way to measure the time-resolved normalized correlation function of the field, g 1(t,τ), for a correlation time t and a photon transit time τ. We have (see Appendix):
SDC,i(τ)SDC,i+p(τ)g2(0)ηei04fΠ(ττ')φ(τ')g1(pT/2,τ')dτ'
(2)
where φ(τ) is the time-resolved diffuse light flux that we would measure in a real time-resolved experiment with the same incident energy, expressed as a photon flux; η is the detector quantum efficiency, e the electron charge and Π(τ)=g2(τ)/g2(0) is the normalized temporal response of the system, with:

g(τ)=2f0T/2Ref(t,τ)dt
(3)

The measurement of the correlation function of diffuse light, also called Diffuse Correlation Spectroscopy (DCS) or Diffusing Wave Spectroscopy (DWS) [30

30. G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B Condens. Matter 65(4), 409–413 (1987). [CrossRef]

33

33. 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(1), 15–20 (1990). [CrossRef]

], is a great challenge in biomedical optics, due to the difficulty to reach a reasonable signal to noise ratio (SNR). Such measurements however seem to have a real potential, with very promising results already obtained for tumors detection [34

34. T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, “Diffuse optical measurement of blood flow in breast tumors,” Opt. Lett. 30(21), 2915–2917 (2005). [CrossRef] [PubMed]

] or blood flow monitoring [35

35. J. Li, F. Jaillon, G. Dietsche, G. Maret, and T. Gisler, “Pulsation-resolved deep tissue dynamics measured with diffusing-wave spectroscopy,” Opt. Express 14(17), 7841–7851 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7841. [CrossRef] [PubMed]

37

37. G. Dietsche, M. Ninck, C. Ortolf, J. Li, F. Jaillon, and T. Gisler, “Fiber-based multispeckle detection for time-resolved diffusing-wave spectroscopy: characterization and application to blood flow detection in deep tissue,” Appl. Opt. 46(35), 8506–8514 (2007). [CrossRef] [PubMed]

]. The present interferometric method enables to take advantages of both DCS and time-resolved measurements.

ξ(t)=Ref(t,τ)+Ref(t,0)
(4)

Let us insist on the fact that this modulation of the intensity of the source is completely disconnected from the wavelength modulation, and that the frequencies implies in ξ(t) or in Ref(t,τ) can be up to one hundred times higher than the modulation frequency f (see equ. 1). The half-period integration is performed on each pixel. In such a setup, the DC component due to the reference beam is no more cancelled, and a difference between two frames is needed for this cancellation. Each pixel then corresponds to a value SDC,i, and correlations between two different frames should then be computed pixel by pixel in order to get the average value <SDC,i SDC,i + p >.

We need quite a high modulation frequency f in order to ‘freeze’ speckle pattern fluctuations, and to subsequently measure the correlations in such fluctuations. A high speed camera is therefore expected in order to obtain a measurement for each modulation period, and to compute frames correlations with short correlation times. High speed cameras however usually have low quantum efficiency, and a high spatially correlated electronic noise that prevents to reach the SNR expected from a multi-pixel detection [41

41. D. Ettori, K. Zarychta, E. Tinet, S. Avrillier, and J.-M. Tualle, “Time-resolved measurement of the scattered light with an interferometric method based on the use of a camera”, in Diffuse Optical Imaging of Tissue, R. Cubeddu ed., Vol. 6629 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6629_20.

]. In this paper we show the possibility to compute correlations using a standard CCD camera, with great SNR improvement despite the low duty cycle of such an acquisition process.

2. Time-resolved measurements

2.1 The experimental setup

Our experimental setup is depicted on Fig. 1
Fig. 1 Experimental setup: two weak reflectivity (15%) beamsplitters (BS) constitute a two-arms interferometer; a lens (L1, f1 = −12mm) allows uniform illumination of the CCD camera; a lens (L2, f2 = + 50mm) project the transmitted scattered light on the camera, which registers the interferometric signal with a typical grain size of 3μm, that is of about half the pixel size; the value of the BS reflectivity was chosen in order to have both a correct detection of the reference beam and a maximal illumination of the scattering sample; a (3:1) anamorphic prisms pair allows to correct the ellipticity of the laser beam; an acousto-optic modulator (AOM) allows lock-in detection through the multiplication by the positive function ξ(t).
. The source is a continuous wave Distributed feedback (DFB) laser diode cheetah from Sacher Lasertechnik, emitting at about 780 nm. One can obtain a modehop free wavelength modulation up to relatively high frequency through a weak modulation of the power current (the resulting modulation of the laser intensity, lower than 5%, will have a negligible impact in the following): the experiments reported in the present paper are performed with a frequency modulation f = 500Hz, but we can obtain frequencies higher than 10kHz with such a system. The frequency modulation depth is ΔΩ=2π2.3GHz. This corresponds to a time-resolution of 270ps. Of course we could obtain a better time-resolution with a greater modulation depth, but the counterpart is a decrease of the SNR. We chose a compromise corresponding to the expected nanosecond scale of the time-resolved signal.

We use the diffraction order + 1 of an acousto-optic modulator (AOM) which allows a high-frequency modulation of the laser beam intensity, in order to perform the multiplication by the positive function ξ(t) defined in Eq. (4). If i(t) ≈i0 + iint(t) is the photocurrent that a pixel should record without this modulation, then the charge stored in this pixel is:

Q=ξ(t)i(t)dt
(5)

At first we will consider that for each acquisition frame the integral runs over only one modulation half-period. Let us note here that the integration interval is not controlled by the frame acquisition shutter (which has a 20ms duration in the present experiment), but by the function ξ(t) which is set to zero outside this half-period integration interval.

The photocurrent i0 from the reference beam leads in (5) to a contribution Q0 (with Q0 = [g(0) + g(τ)]i0T/2 ) while, from the expression (4) of ξ(t), the photocurrent iint leads to the terms SDC(τ) and SDC(0). A time delay δτ = 2060 ps is introduced between the two arms of the interferometer (Fig. 1): transit times are therefore always higher than this value, and the term SDC(0) can be neglected (like the term g(τ) in the expression of Q0).

As the reference beam illuminates the CCD sensor quite evenly, we should be able to cancel the term Q0 through a simple high-pass spatial digital filter. The signal is however really low, and even small heterogeneities on the acquired frame could lead to non-negligible components with high spatial frequencies. So, in addition to digital filtering (with a cutoff of ~0.17 pixel−1; see ref [42

42. A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing” (Prentice-Hall signal processing series, ISBN 0–13–754920–2, 1999).

]. for details), we perform the difference between two images (a) and (b) in order to complete this cancellation and to leave only the SDC terms, which appear as a uniform white noise:

ΔQ=Q(a)Q(b)SDC(a)(τ)SDC(b)(τ)
(6)

Note that digital filtering also has an incidence on the signal ΔQ: the averaged squared value of this quantity over all pixels is mathematically identical to the averaged squared modulus of the Fourier components; a spatial filter reduces the effective number of Fourier components, which is statistically equivalent to a reduction of the effective pixels number. We estimate that our digital filtering implies a 58% reduction of this effective pixels number. The CCD camera is a Hamamatsu C8484-05G, with 1.37 million pixels (i.e. an effective pixel number equals to N≈0.8million) for a frame rate ~9 images/s, and with quantum efficiency η ~25% @800nm. The time correlations we are going to consider in this paper are in the millisecond range, so that there is no correlation between two successive frames and the variance of ΔQ can be written:

Δ2Q2SDC2(τ)=g2(0)ηei02fΠ(ττ')φ(τ')dτ'=g2(0)ηei02fΠφ(τ)
(7)

The phantom used for the experiments presented in this paper is a scattering slab with a 4 cm thickness, made with a suspension of calibrated microspheres (Estapor K050, 520 ± 37nm diameter) in glycerol. The microspheres concentration was calculated in order to have a reduced scattering coefficient μ’s = 10cm−1. The absorption coefficient of glycerol at 800nm is μa = 0.03cm−1 [43

43. 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(4), 767–783 (1996). [CrossRef] [PubMed]

]. Such optical coefficients are representative of bulk optical properties of breast tissue [44

44. T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47(16), 2847–2861 (2002). [CrossRef] [PubMed]

,45

45. D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50(11), 2451–2468 (2005). [CrossRef] [PubMed]

], so this phantom is a reasonable model for a compressed breast. We observe the diffuse light transmitted through this phantom. A lens (L2) images a small region facing the illumination beam.

The temporal response of the setup can be measured using a sheet of tracing paper instead of the breast mimicking phantom. The recorded response is plotted on Fig. 2
Fig. 2 Temporal response of the setup, which has the expected position (δτ = 2060 ps) and width (270 ps).
: we observe a peak centered on the time delay δτ with the expected full width at half maximum (FWHM) equal to 270 ps. A time origin t0 can be defined in the following way: in a real time-resolved experiment, the pulse would arrive on the input face of the sample at time t = t0, and would then reach the detector 4cm farther; if there is no scattering medium but only air between these positions, light will only experience a 4cm/c0 ≈130ps free-space travel, so that one has to set:

t0=dτ 130ps= 1930ps.

2.2 Influence of the quantum noise

Quantum noise is the main source of noise in this experiment: a Gaussian white noise δi has to be added to the photocurrent, with <δi(t)δi(t’)> = ei0(t)δ(t-t’), resulting in an additional random term δS =δi(t)dt in the definition of the stored charge Q. This term is of course not correlated with the signal SDC, and its variance is [41

41. D. Ettori, K. Zarychta, E. Tinet, S. Avrillier, and J.-M. Tualle, “Time-resolved measurement of the scattered light with an interferometric method based on the use of a camera”, in Diffuse Optical Imaging of Tissue, R. Cubeddu ed., Vol. 6629 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6629_20.

]:

δ2S=δi(t)δi(t')dtdt'=ei00T/2ξ(t)dtei0g(0)T/2
(8)

This therefore leads to an additional constant SNL=2δ2S in the variance (7) of ΔQ:
Δ2Q2SDC2(τ)+2δ2S=2eQ0{1+ηg(0)2   Πφ(τ)}
(9)
with g(0)=3/8.

This shot noise level (SNL) enables a calibration of the received photon number Π *ϕ(τ). Figure 3
Fig. 3 Raw data recorded with the breast phantom illuminated by a 5 mW laser beam. The shot noise level (SNL) is indicated by a dotted line. The transmittance at its maximum is 15 times lower than the SNL. A spurious peak is surrounded by a dotted line.
shows raw data recorded with the breast phantom illuminated by a 5mW laser beam. The evolution of the transmittance with the transit time appears as a small variation above the SNL, indicated by the dotted line: the transmittance at its maximum is 15 times lower than the SNL, which corresponds to 1.5 photons per pixel and per acquisition. The relevant signal is in fact quite lower than noise, and only an average over a high number of measurements – here a high pixel number – enables us to extract it from noise.

Due to the low level of the signal, quantum noise gives the main contribution to the overall noise. From the Gaussian nature of this noise, it can be easily shown [41

41. D. Ettori, K. Zarychta, E. Tinet, S. Avrillier, and J.-M. Tualle, “Time-resolved measurement of the scattered light with an interferometric method based on the use of a camera”, in Diffuse Optical Imaging of Tissue, R. Cubeddu ed., Vol. 6629 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6629_20.

] that the variance of δ2S is 2<δ2S>2, and the standard deviation σ of the noise on the value of Δ2Q averaged over N pixels is simply:

σ=2δ2S2N=2eQ02N
(10)

The standard deviation σ is therefore the SNL times 2, and divided by a factor N called “improvement factor” in the following, which should be 890 in the present experiment. This highlights the challenge of this project: to perform a measurement of the SNL with an accuracy of about 10−3. This implies the cancellation of pixel-correlated classical noises that do not decrease as 1/N with pixel averaging. This cancellation is the role of the image difference and of the high-pass real-time digital filter. But small fluctuations of the variance of the quantum noise could significantly reduce the performance of this setup. For instance, fluctuations of the average power of the reference beam, ie of Q0, could preclude the improvement factor N. This problem can be circumvented as Q0 is measured by the camera: <Δ2Q> in Eq. (9) is proportional to Q0, and the multiplicative factor is the only relevant quantity. For each pixel i we have a value xi ≈αQ0/e for each acquired image (where α is the gray level/ charge conversion factor), and a value Δ2xi=α2Δ2Qi/e2 for each squared image difference. The signal plotted in Fig. 3 is actually the optimal slope of Δ2xi as a function of xi from the least squares method:

ixiΔ2xiixi22α{1+ηg(0)2   Πφ(τ)}
(11)

The quantity defined in Eq. (11) is not very different than the average of Δ2Q, but it is free of any fluctuations of Q0 . Of course, fluctuations of the conversion factor α can be a problem too. Some peaks appear for instance on the raw data in Fig. 3 (one of them is surrounded by a dotted line): the origin of these peaks is not clear, but they can be easily removed as outliers (cancellation of values farther than from the local mean). With all these precautions, we reached the expected performance, with an improvement factor of about 910 ± 30.

2.3 Analysis of the experimental results

3. Time-resolved correlations

We mentioned in the introduction the possibility to perform correlation measurements through the measurement of <SDC,i(τ)SDC,i + p(τ)>, where SDC,i(τ) and SDC,i + p(τ) correspond to two different acquisitions. We also mentioned the fact that, with a standard CCD camera, the images on two successive frames are completely decorrelated.

The possibility to record correlations of the scattered light with a CCD camera using different exposure times was already reported [51

51. A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic imaging of cerebral blood flow using laser speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001). [CrossRef] [PubMed]

]. In the present paper we will not propose to vary the exposure time but, for each acquired image, to integrate over two modulation half-periods separated by a time interval pT, as depicted on Fig. 5
Fig. 5 Acquisition protocol for correlation measurements: the red curve symbolizes the wavelength modulation, and the blue curve represents the modulation function ξ(t), which is zero excepted on two modulation half-periods separated by a time interval pT.
.

Two successive images are acquired using the same protocol, and their pixel to pixel difference ΔQ is now:
ΔQSDC,i(a)(τ)+δSi(a)+SDC,i+p(a)(τ)+δSi+p(a)SDC,j(b)(τ)δSj(a)SDC,j+p(b)(τ)δSj+p(a)
(12)
where we recall that δS accounts for quantum noise. This leads for the variance of ΔQ to:
Δ2Q=4(δ2S+SDC2(τ)+SDC,i(τ)SDC,p(τ))
(13)
or, in term of the measured quantity defined in Eq. (11):

ixiΔ2xiixi24α{1+ηg(0)2Πφ(τ)[1+g1(pT,τ)]}
(14)

Experiments were performed at a fixed transit time τ = 1.5ns, and experimental results for each value of the correlation time pT was averaged over 25 measurements, with cancellation of the outliers. The shot noise level was estimated from measurements performed without modulation (ie without the term Ref(t,τ) in Eq. (3). With the term 4αη   g(0)φ(τ)/T obtained from measurements at large correlation times (t = 7T = 14ms), we can derive values of the correlation function g 1 for p running from 1 to 5. The logarithm of these values are plotted on Fig. 6
Fig. 6 Experimental values of ln[g1(t,τ)] for a transit time τ = 1,5ns and a correlation time t = pT (T = 2ms) with p running from 1 to 5. The red line is a fit, weighted according to the statistical error, by the function α t with α = −0.35 ± −0.015 ms −1.
, exhibiting the linear dependence on the correlation time t expected from the Brownian motion of the scatterers:
lng1(t,τ)=2μ'scτtt0, with t0=1k2DB=λ2(2πn)2DB and DB=kBTa6πηga
(15)
where n = 1.45 is the glycerol refractive index [52

52. F. G. Santamaria, Photonic crystals based on silica microsphères”, Ph. D. thesis:Institude de Ciencia de Materials de Madride, (2003).

], kB the Boltzmann constant, Ta the temperature and a the microspheres radius.

The fit in Fig. 6 leads to t0=1.8±0.1s, which is consistent with the viscosity of glycerol with 12% water at 19°C g≈200 mPa.s [53] leads to t0≈1.8s). Each point in Fig. 6, which corresponds to correlation measurements performed at only one fixed photon transit time through a thick turbid medium, is taken within a reasonably low acquisition time of a few seconds.

4. Conclusion

Appendix

Let us briefly recall the theoretical basis of the experiment [26

26. 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(4–6), 211–220 (2001). [CrossRef]

,28

28. J.-M. Tualle, H. L. Nghiêm, M. Cheikh, D. Ettori, E. Tinet, and S. Avrillier, “Time-resolved diffusing wave spectroscopy beyond 300 transport mean free paths,” J. Opt. Soc. Am. A 23(6), 1452 (2006). [CrossRef]

]. Using a scalar model, the monochromatic (CW) optical fields can be written s0ω(t) and sω(t) for the reference beam and the scattered light, respectively. These quantities are proportional to the Fourier components s˜0 and s˜ of a time-resolved experiment [26

26. 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(4–6), 211–220 (2001). [CrossRef]

], with a proportionality factor K(ω) that can be determined from energy considerations in the following way: let us write the spectral power of the pulsed source |s˜0(ω)|2=Ff(ω), where F is the pulse fluence and f(ω) the normalized spectral profile (f(ω)dω=2π); we will set an equivalence between pulsed and CW experiments by assuming that the fluence |s0ω|2T/2 in the CW case during the acquisition time T/2 is equal to the pulse fluence F, leading to:

s0ω(t)=K(ω)s˜0[ω(t)] and sω(t)=K(ω)s˜[ω(t),t] with K2(ω)2f(ω)T
(A.1)

We consider that the spectral profile is large compared to the wavelength modulation, so that f(ω)f(ω0). The Fourier component s˜ slowly depends on time t because of the movements of the scatterers: this leads to time-resolved decorrelation. One can introduce the correlation function:

s˜[ω1,0]s˜*[ω2,t]ϕ˜(ω,Ω,t)
(A.2)

where ω(ω1+ω2)/2 refers to light pulsation, and where Ωω1ω2 is conjugate to the time of flight τ(τ1+τ2)/2. The inverse Fourier transform ϕ(ω,τ,t) of ϕ˜ can be interpreted as a time-resolved averaged spectral intensity, the decorrelation being accounted through an effective absorption coefficient μ(t). This function essentially follows the source spectrum [28

28. J.-M. Tualle, H. L. Nghiêm, M. Cheikh, D. Ettori, E. Tinet, and S. Avrillier, “Time-resolved diffusing wave spectroscopy beyond 300 transport mean free paths,” J. Opt. Soc. Am. A 23(6), 1452 (2006). [CrossRef]

], and ϕ(ω,τ,t)f(ω)ϕ(τ)g1(τ,t), where ϕ(τ) is the time-resolved averaged intensity and where g1(τ,t) is the time-resolved normalized correlation function of the field. With a phase definition so that s0ωs0 is a constant, and for a quasi point-like detector with an area A (see ref [41

41. D. Ettori, K. Zarychta, E. Tinet, S. Avrillier, and J.-M. Tualle, “Time-resolved measurement of the scattered light with an interferometric method based on the use of a camera”, in Diffuse Optical Imaging of Tissue, R. Cubeddu ed., Vol. 6629 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6629_20.

]. for a complete computation taking into account the spatial extension of the detector), the interferometric signal iint(t) is:

iint(t)=SAK(ω){   s0s˜*[ω(t),t]+s0*s˜[ω(t),t]   }
(A.3)

where S=ηe/(hν) is the sensitivity of the detector. At this stage, we did not take the intensity modulation ξ(t) into account: as explained just before Eq. (5), one only has for that purpose to multiply the photocurrent that should be recorded without modulation by this function ξ(t), leading to the stored charge Q=ξ(t)i(t)dt and subsequent terms like SDC. From SDC=Ref(t,τ)iint(t)dt and assuming [28

28. J.-M. Tualle, H. L. Nghiêm, M. Cheikh, D. Ettori, E. Tinet, and S. Avrillier, “Time-resolved diffusing wave spectroscopy beyond 300 transport mean free paths,” J. Opt. Soc. Am. A 23(6), 1452 (2006). [CrossRef]

] s˜s˜=s˜*s˜*=0 one has quite directly (with φ(τ)Aϕ(τ)):

SDC,iSDC,i+p=Si0Tdt1dt2dτ'φ(τ')g1(t2t1+pT/2,τ')×                                                               [Ref(t2,ττ')+Ref(t2,τ+τ')][Ref(t2,ττ')+Ref(t2,τ+τ')]
(A.4)

When one assumes [28

28. J.-M. Tualle, H. L. Nghiêm, M. Cheikh, D. Ettori, E. Tinet, and S. Avrillier, “Time-resolved diffusing wave spectroscopy beyond 300 transport mean free paths,” J. Opt. Soc. Am. A 23(6), 1452 (2006). [CrossRef]

] that the wavelength modulation is fast enough to freeze the speckle fluctuations linked to the movement of the scatterers, i.e. g1(t2t1+pT/2,τ')g1(pT/2,τ') and with Eq. (3), one has:

SDC,iSDC,i+p=Si04fφ(τ')g1(pT/2,τ')[g(ττ')+g(τ+τ')]2dτ'
(A.5)

As φ(τ)=0 when τ<0, the time gate g(τ+τ') can be neglected, leading to Eq. (2).

Acknowledgements

The authors acknowledge Thierry Billeton for technical support. This work has been supported by the Agence Nationale de la Recherche through the project ANR-08-PCVI-0038-01.

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A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008). [CrossRef] [PubMed]

3.

R. Esposito, S. De Nicola, M. Brambilla, A. Pifferi, L. Spinelli, and M. Lepore, “Depth dependence of estimated optical properties of a scattering inclusion by time-resolved contrast functions,” Opt. Express 16(22), 17667–17681 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-17667. [CrossRef] [PubMed]

4.

A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, 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(15), 3037–3047 (2004). [CrossRef] [PubMed]

5.

A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express 16(17), 13188–13202 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13188. [CrossRef] [PubMed]

6.

J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10(1), 011013 (2005). [CrossRef]

7.

A. Kienle, M. S. Patterson, N. Dögnitz, R. Bays, G. Wagniνres, and H. van den Bergh, “Noninvasive Determination of the Optical Properties of Two-Layered Turbid Media,” Appl. Opt. 37(4), 779–791 (1998). [CrossRef]

8.

L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008). [CrossRef] [PubMed]

9.

B. Montcel, R. Chabrier, and P. Poulet, “Detection of cortical activation with time-resolved diffuse optical methods,” Appl. Opt. 44(10), 1942–1947 (2005). [CrossRef] [PubMed]

10.

J.-M. Tualle, H. L. Nghiem, D. Ettori, R. Sablong, É. Tinet, and S. Avrillier, “Asymptotic behavior and inverse problem in layered scattering media,” J. Opt. Soc. Am. A 21(1), 24–34 (2004). [CrossRef]

11.

S. Andersson-Engels, R. Berg, S. Svanberg, and O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett. 15(21), 1179–1181 (1990). [CrossRef] [PubMed]

12.

G. Le Tolguenec, F. Devaux, and E. Lantz, “Imaging through thick biological tissues by parametric image amplification and phase conjugation,” J. Opt. 28(5), 214–217 (1997). [CrossRef]

13.

V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and I. 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(4), 441–445 (2001). [CrossRef] [PubMed]

14.

L. Azizi, K. Zarychta, D. Ettori, E. Tinet, and J.-M. Tualle, “Ultimate spatial resolution with Diffuse Optical Tomography,” Opt. Express 17(14), 12132–12144 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-12132. [CrossRef] [PubMed]

15.

A. Kienle and T. Glanzmann, “In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model,” Phys. Med. Biol. 44(11), 2689–2702 (1999). [CrossRef] [PubMed]

16.

J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47(23), 4155–4166 (2002). [CrossRef] [PubMed]

17.

E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46(4), 1117–1130 (2001). [CrossRef] [PubMed]

18.

T. D. Yates, J. C. Hebden, A. P. Gibson, N. L. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50(11), 2503–2517 (2005). [CrossRef] [PubMed]

19.

C. V. Zint, W. Uhring, M. Torregrossa, B. Cunin, and P. Poulet, “Streak camera: a multidetector for diffuse optical tomography,” Appl. Opt. 42(16), 3313–3320 (2003). [CrossRef] [PubMed]

20.

J.-M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, and J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements in biological tissues,” Opt. Commun. 124(3–4), 216–221 (1996). [CrossRef]

21.

A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt. 9(6), 1143–1151 (2004). [CrossRef] [PubMed]

22.

D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50(11), 2429–2449 (2005). [CrossRef] [PubMed]

23.

P. Taroni, A. Torricelli, L. Spinelli, A. Pifferi, F. Arpaia, G. Danesini, and R. Cubeddu, “Time-resolved optical mammography between 637 and 985 nm: clinical study on the detection and identification of breast lesions,” Phys. Med. Biol. 50(11), 2469–2488 (2005). [CrossRef] [PubMed]

24.

R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Compact tissue oximeter based on dual-wavelength multichannel time-resolved reflectance,” Appl. Opt. 38(16), 3670–3680 (1999). [CrossRef]

25.

J.-M. Tualle, “Method for analyzing a diffusing sample by time resolution measurement”, US Patent 6903825 (2001).

26.

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(4–6), 211–220 (2001). [CrossRef]

27.

J.-M. Tualle, H. L. Nghiêm, C. Schäfauer, P. Berthaud, É. Tinet, D. Ettori, and S. Avrillier, “Time-resolved measurements from speckle interferometry,” Opt. Lett. 30(1), 50–52 (2005). [CrossRef] [PubMed]

28.

J.-M. Tualle, H. L. Nghiêm, M. Cheikh, D. Ettori, E. Tinet, and S. Avrillier, “Time-resolved diffusing wave spectroscopy beyond 300 transport mean free paths,” J. Opt. Soc. Am. A 23(6), 1452 (2006). [CrossRef]

29.

M. Cheikh, H. L. Nghiêm, D. Ettori, E. Tinet, S. Avrillier, and J. M. Tualle, “Time-resolved diffusing wave spectroscopy applied to dynamic heterogeneity imaging,” Opt. Lett. 31(15), 2311–2313 (2006). [CrossRef] [PubMed]

30.

G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B Condens. Matter 65(4), 409–413 (1987). [CrossRef]

31.

M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B Condens. Matter 37(1), 1–5 (1988). [CrossRef] [PubMed]

32.

D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988). [CrossRef] [PubMed]

33.

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(1), 15–20 (1990). [CrossRef]

34.

T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, “Diffuse optical measurement of blood flow in breast tumors,” Opt. Lett. 30(21), 2915–2917 (2005). [CrossRef] [PubMed]

35.

J. Li, F. Jaillon, G. Dietsche, G. Maret, and T. Gisler, “Pulsation-resolved deep tissue dynamics measured with diffusing-wave spectroscopy,” Opt. Express 14(17), 7841–7851 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7841. [CrossRef] [PubMed]

36.

L. Gagnon, M. Desjardins, J. Jehanne-Lacasse, L. Bherer, and F. Lesage, “Investigation of diffuse correlation spectroscopy in multi-layered media including the human head,” Opt. Express 16(20), 15514–15530 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15514. [CrossRef] [PubMed]

37.

G. Dietsche, M. Ninck, C. Ortolf, J. Li, F. Jaillon, and T. Gisler, “Fiber-based multispeckle detection for time-resolved diffusing-wave spectroscopy: characterization and application to blood flow detection in deep tissue,” Appl. Opt. 46(35), 8506–8514 (2007). [CrossRef] [PubMed]

38.

T. Spirig, P. Seitz, O. Vietze, and F. Heitger, “The lock-in CCD- two-dimensional synchronous detection of light,” IEEE J. Quantum Electron. 31(9), 1705–1708 (1995). [CrossRef]

39.

P. Gleyzes, A. C. Boccara, and H. Saint-Jalmes, “Multichannel Nomarski microscope with polarization modulation: performance and applications,” Opt. Lett. 22(20), 1529–1531 (1997). [CrossRef]

40.

M. Gross, P. Goy, B. C. Forget, M. Atlan, F. Ramaz, A. C. Boccara, and A. K. Dunn, “Heterodyne detection of multiply scattered monochromatic light with a multipixel detector,” Opt. Lett. 30(11), 1357–1359 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ol-30-11-1357. [CrossRef] [PubMed]

41.

D. Ettori, K. Zarychta, E. Tinet, S. Avrillier, and J.-M. Tualle, “Time-resolved measurement of the scattered light with an interferometric method based on the use of a camera”, in Diffuse Optical Imaging of Tissue, R. Cubeddu ed., Vol. 6629 of Proceedings of SPIE-OSA Biomedical Optics (Optical Society of America, 2007), paper 6629_20.

42.

A. V. Oppenheim, R. W. Schafer, and J. R. Buck, Discrete-time signal processing” (Prentice-Hall signal processing series, ISBN 0–13–754920–2, 1999).

43.

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(4), 767–783 (1996). [CrossRef] [PubMed]

44.

T. Durduran, R. Choe, J. P. Culver, L. Zubkov, M. J. Holboke, J. Giammarco, B. Chance, and A. G. Yodh, “Bulk optical properties of healthy female breast tissue,” Phys. Med. Biol. 47(16), 2847–2861 (2002). [CrossRef] [PubMed]

45.

D. Grosenick, H. Wabnitz, K. T. Moesta, J. Mucke, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: II. Optical properties and tissue parameters of 87 carcinomas,” Phys. Med. Biol. 50(11), 2451–2468 (2005). [CrossRef] [PubMed]

46.

M. S. Patterson, B. Chance, and B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties,” Appl. Opt. 28(12), 2331–2336 (1989). [CrossRef] [PubMed]

47.

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12(11), 2532–2539 (1995). [CrossRef]

48.

A. Pifferi, A. Torricelli, A. Bassi, P. Taroni, R. Cubeddu, H. Wabnitz, D. Grosenick, M. Möller, R. Macdonald, J. Swartling, T. Svensson, S. Andersson-Engels, R. L. P. van Veen, H. J. C. M. Sterenborg, J.-M. Tualle, H. L. Nghiem, S. Avrillier, M. Whelan, and H. Stamm, “Performance assessment of photon migration instruments: the MEDPHOT protocol,” Appl. Opt. 44(11), 2104–2114 (2005), http://www.opticsinfobase.org/abstract.cfm?URI=ao-44-11-2104. [CrossRef] [PubMed]

49.

M. A. Webster, T. D. Gerke, A. M. Weiner, and K. J. Webb, “Spectral and temporal speckle field measurements of a random medium,” Opt. Lett. 29(13), 1491–1493 (2004), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-29-13-1491. [CrossRef] [PubMed]

50.

B. Varghese, V. Rajan, T. G. Van Leeuwen, and W. Steenbergen, “Path-length-resolved measurements of multiple scattered photons in static and dynamic turbid media using phase-modulated low-coherence interferometry,” J. Biomed. Opt. 12(2), 024020 (2007). [CrossRef] [PubMed]

51.

A. K. Dunn, H. Bolay, M. A. Moskowitz, and D. A. Boas, “Dynamic imaging of cerebral blood flow using laser speckle,” J. Cereb. Blood Flow Metab. 21(3), 195–201 (2001). [CrossRef] [PubMed]

52.

F. G. Santamaria, Photonic crystals based on silica microsphères”, Ph. D. thesis:Institude de Ciencia de Materials de Madride, (2003).

53.

http://www.me.rochester.edu/courses/ME241/SE3.html

OCIS Codes
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.6920) Medical optics and biotechnology : Time-resolved imaging
(110.0113) Imaging systems : Imaging through turbid media

ToC Category:
Imaging Systems

History
Original Manuscript: April 2, 2010
Revised Manuscript: May 31, 2010
Manuscript Accepted: June 16, 2010
Published: July 19, 2010

Virtual Issues
Vol. 5, Iss. 12 Virtual Journal for Biomedical Optics

Citation
Katarzyna Zarychta, Eric Tinet, Leila Azizi, Sigrid Avrillier, Dominique Ettori, and Jean-Michel Tualle, "Time-resolved diffusing wave spectroscopy with a CCD camera," Opt. Express 18, 16289-16301 (2010)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-18-16-16289


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References

  1. A. Torricelli, A. Pifferi, L. Spinelli, R. Cubeddu, F. Martelli, S. Del Bianco, and G. Zaccanti, “Time-resolved reflectance at null source-detector separation: improving contrast and resolution in diffuse optical imaging,” Phys. Rev. Lett. 95(7), 078101 (2005). [CrossRef] [PubMed]
  2. A. Pifferi, A. Torricelli, L. Spinelli, D. Contini, R. Cubeddu, F. Martelli, G. Zaccanti, A. Tosi, A. Dalla Mora, F. Zappa, and S. Cova, “Time-resolved diffuse reflectance using small source-detector separation and fast single-photon gating,” Phys. Rev. Lett. 100(13), 138101 (2008). [CrossRef] [PubMed]
  3. R. Esposito, S. De Nicola, M. Brambilla, A. Pifferi, L. Spinelli, and M. Lepore, “Depth dependence of estimated optical properties of a scattering inclusion by time-resolved contrast functions,” Opt. Express 16(22), 17667–17681 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-22-17667 . [CrossRef] [PubMed]
  4. A. Liebert, H. Wabnitz, J. Steinbrink, H. Obrig, M. Möller, 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(15), 3037–3047 (2004). [CrossRef] [PubMed]
  5. A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express 16(17), 13188–13202 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-17-13188 . [CrossRef] [PubMed]
  6. J. Selb, J. J. Stott, M. A. Franceschini, A. G. Sorensen, and D. A. Boas, “Improved sensitivity to cerebral hemodynamics during brain activation with a time-gated optical system: analytical model and experimental validation,” J. Biomed. Opt. 10(1), 011013 (2005). [CrossRef]
  7. A. Kienle, M. S. Patterson, N. Dögnitz, R. Bays, G. Wagniνres, and H. van den Bergh, “Noninvasive Determination of the Optical Properties of Two-Layered Turbid Media,” Appl. Opt. 37(4), 779–791 (1998). [CrossRef]
  8. L. Gagnon, C. Gauthier, R. D. Hoge, F. Lesage, J. Selb, and D. A. Boas, “Double-layer estimation of intra- and extracerebral hemoglobin concentration with a time-resolved system,” J. Biomed. Opt. 13(5), 054019 (2008). [CrossRef] [PubMed]
  9. B. Montcel, R. Chabrier, and P. Poulet, “Detection of cortical activation with time-resolved diffuse optical methods,” Appl. Opt. 44(10), 1942–1947 (2005). [CrossRef] [PubMed]
  10. J.-M. Tualle, H. L. Nghiem, D. Ettori, R. Sablong, É. Tinet, and S. Avrillier, “Asymptotic behavior and inverse problem in layered scattering media,” J. Opt. Soc. Am. A 21(1), 24–34 (2004). [CrossRef]
  11. S. Andersson-Engels, R. Berg, S. Svanberg, and O. Jarlman, “Time-resolved transillumination for medical diagnostics,” Opt. Lett. 15(21), 1179–1181 (1990). [CrossRef] [PubMed]
  12. G. Le Tolguenec, F. Devaux, and E. Lantz, “Imaging through thick biological tissues by parametric image amplification and phase conjugation,” J. Opt. 28(5), 214–217 (1997). [CrossRef]
  13. V. Chernomordik, A. Gandjbakhche, M. Lepore, R. Esposito, and I. 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(4), 441–445 (2001). [CrossRef] [PubMed]
  14. L. Azizi, K. Zarychta, D. Ettori, E. Tinet, and J.-M. Tualle, “Ultimate spatial resolution with Diffuse Optical Tomography,” Opt. Express 17(14), 12132–12144 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-14-12132 . [CrossRef] [PubMed]
  15. A. Kienle and T. Glanzmann, “In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model,” Phys. Med. Biol. 44(11), 2689–2702 (1999). [CrossRef] [PubMed]
  16. J. C. Hebden, A. Gibson, R. M. Yusof, N. Everdell, E. M. C. Hillman, D. T. Delpy, S. R. Arridge, T. Austin, J. H. Meek, and J. S. Wyatt, “Three-dimensional optical tomography of the premature infant brain,” Phys. Med. Biol. 47(23), 4155–4166 (2002). [CrossRef] [PubMed]
  17. E. M. C. Hillman, J. C. Hebden, M. Schweiger, H. Dehghani, F. E. W. Schmidt, D. T. Delpy, and S. R. Arridge, “Time resolved optical tomography of the human forearm,” Phys. Med. Biol. 46(4), 1117–1130 (2001). [CrossRef] [PubMed]
  18. T. D. Yates, J. C. Hebden, A. P. Gibson, N. L. Everdell, S. R. Arridge, and M. Douek, “Optical tomography of the breast using a multi-channel time-resolved imager,” Phys. Med. Biol. 50(11), 2503–2517 (2005). [CrossRef] [PubMed]
  19. C. V. Zint, W. Uhring, M. Torregrossa, B. Cunin, and P. Poulet, “Streak camera: a multidetector for diffuse optical tomography,” Appl. Opt. 42(16), 3313–3320 (2003). [CrossRef] [PubMed]
  20. J.-M. Tualle, B. Gélébart, E. Tinet, S. Avrillier, and J. P. Ollivier, “Real time optical coefficients evaluation from time and space resolved reflectance measurements in biological tissues,” Opt. Commun. 124(3–4), 216–221 (1996). [CrossRef]
  21. A. Pifferi, J. Swartling, E. Chikoidze, A. Torricelli, P. Taroni, A. Bassi, S. Andersson-Engels, and R. Cubeddu, “Spectroscopic time-resolved diffuse reflectance and transmittance measurements of the female breast at different interfiber distances,” J. Biomed. Opt. 9(6), 1143–1151 (2004). [CrossRef] [PubMed]
  22. D. Grosenick, K. T. Moesta, M. Möller, J. Mucke, H. Wabnitz, B. Gebauer, C. Stroszczynski, B. Wassermann, P. M. Schlag, and H. Rinneberg, “Time-domain scanning optical mammography: I. Recording and assessment of mammograms of 154 patients,” Phys. Med. Biol. 50(11), 2429–2449 (2005). [CrossRef] [PubMed]
  23. P. Taroni, A. Torricelli, L. Spinelli, A. Pifferi, F. Arpaia, G. Danesini, and R. Cubeddu, “Time-resolved optical mammography between 637 and 985 nm: clinical study on the detection and identification of breast lesions,” Phys. Med. Biol. 50(11), 2469–2488 (2005). [CrossRef] [PubMed]
  24. R. Cubeddu, A. Pifferi, P. Taroni, A. Torricelli, and G. Valentini, “Compact tissue oximeter based on dual-wavelength multichannel time-resolved reflectance,” Appl. Opt. 38(16), 3670–3680 (1999). [CrossRef]
  25. J.-M. Tualle, “Method for analyzing a diffusing sample by time resolution measurement”, US Patent 6903825 (2001).
  26. 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(4–6), 211–220 (2001). [CrossRef]
  27. J.-M. Tualle, H. L. Nghiêm, C. Schäfauer, P. Berthaud, É. Tinet, D. Ettori, and S. Avrillier, “Time-resolved measurements from speckle interferometry,” Opt. Lett. 30(1), 50–52 (2005). [CrossRef] [PubMed]
  28. J.-M. Tualle, H. L. Nghiêm, M. Cheikh, D. Ettori, E. Tinet, and S. Avrillier, “Time-resolved diffusing wave spectroscopy beyond 300 transport mean free paths,” J. Opt. Soc. Am. A 23(6), 1452 (2006). [CrossRef]
  29. M. Cheikh, H. L. Nghiêm, D. Ettori, E. Tinet, S. Avrillier, and J. M. Tualle, “Time-resolved diffusing wave spectroscopy applied to dynamic heterogeneity imaging,” Opt. Lett. 31(15), 2311–2313 (2006). [CrossRef] [PubMed]
  30. G. Maret and P. E. Wolf, “Multiple light scattering from disordered media. The effect of Brownian motion of scatterers,” Z. Phys. B Condens. Matter 65(4), 409–413 (1987). [CrossRef]
  31. M. J. Stephen, “Temporal fluctuations in wave propagation in random media,” Phys. Rev. B Condens. Matter 37(1), 1–5 (1988). [CrossRef] [PubMed]
  32. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, “Diffusing wave spectroscopy,” Phys. Rev. Lett. 60(12), 1134–1137 (1988). [CrossRef] [PubMed]
  33. 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(1), 15–20 (1990). [CrossRef]
  34. T. Durduran, R. Choe, G. Yu, C. Zhou, J. C. Tchou, B. J. Czerniecki, and A. G. Yodh, “Diffuse optical measurement of blood flow in breast tumors,” Opt. Lett. 30(21), 2915–2917 (2005). [CrossRef] [PubMed]
  35. J. Li, F. Jaillon, G. Dietsche, G. Maret, and T. Gisler, “Pulsation-resolved deep tissue dynamics measured with diffusing-wave spectroscopy,” Opt. Express 14(17), 7841–7851 (2006), http://www.opticsinfobase.org/abstract.cfm?URI=oe-14-17-7841 . [CrossRef] [PubMed]
  36. L. Gagnon, M. Desjardins, J. Jehanne-Lacasse, L. Bherer, and F. Lesage, “Investigation of diffuse correlation spectroscopy in multi-layered media including the human head,” Opt. Express 16(20), 15514–15530 (2008), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-20-15514 . [CrossRef] [PubMed]
  37. G. Dietsche, M. Ninck, C. Ortolf, J. Li, F. Jaillon, and T. Gisler, “Fiber-based multispeckle detection for time-resolved diffusing-wave spectroscopy: characterization and application to blood flow detection in deep tissue,” Appl. Opt. 46(35), 8506–8514 (2007). [CrossRef] [PubMed]
  38. T. Spirig, P. Seitz, O. Vietze, and F. Heitger, “The lock-in CCD- two-dimensional synchronous detection of light,” IEEE J. Quantum Electron. 31(9), 1705–1708 (1995). [CrossRef]
  39. P. Gleyzes, A. C. Boccara, and H. Saint-Jalmes, “Multichannel Nomarski microscope with polarization modulation: performance and applications,” Opt. Lett. 22(20), 1529–1531 (1997). [CrossRef]
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