The diffusion of correlation is used to detect, localize, and characterize dynamical and optical spatial inhomogeneities in turbid media and is accurately modeled by a correlation diffusion equation. We demonstrate experimentally and with Monte Carlo simulations that the transport of correlation can be viewed as a correlation wave {analogous to a diffuse photon-density wave [Phys. Today48, 34 (1995)]} that propagates spherically outward from sources and scatters from macroscopic spatial variations in dynamical and/or optical properties. We demonstrate the utility of inverse scattering algorithms for reconstructing images of the spatially varying dynamical properties of turbid media. The biomedical applicability of this diffuse correlation probe is illustrated in studies of the depth of burned tissues.

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Spatially varying dynamical properties of turbid media probed with diffusing temporal light correlation

Hydrodynamic and hydromagnetic stability

Since its invention about a decade ago, dynamic multiple light scattering has found many applications in various areas of soft condensed matter science. It has become a particularly important quantitative tool in colloid physics because of its applicability to systems containing very high concentrations of scatterers, and its extreme sensitivity to small motions. Recent advances of this technique, currently called diffusing-wave spectroscopy because of the diffusive transport of the light waves, include remote optical measurements of frequency-dependent viscoelasticity, studies of the microscopic dynamical processes in flowing sand and aging foam, a theoretical description of dynamic scattering from orientational fluctuations in liquid crystals and imaging of dynamic heterogeneities buried inside a turbid background medium.

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Diffusing-wave spectroscopy

We use near-infrared dynamic multiple scattering of light diffusing-wave spectroscopy DWS to detect the activation of the somato-motor cortex in 11 right-handed volunteers performing a fin- ger opposition task separately with their right and left hands. Temporal autocorrelation functions g 1 r, of the scattered light field are mea- sured during 100-s periods of motor task alternating with 100-s rest- ing baseline periods. From an analysis of the experimental data with an analytical theory for g 1 r, from a three-layer geometry with optical and dynamical heterogeneity representing scalp, skull, and cortex, we obtain quantitative estimates of the diffusion coefficient in cortical regions. Consistent with earlier results, the measured cortical diffusion coefficient is found to be increased during the motor task, with a strong contralateral and a weaker ipsilateral increase consistent with the known brain hemispheric asymmetry for right-handed sub- jects. Our results support the interpretation of the increase of the cor- tical diffusion coefficient during finger opposition being due to the functional increase in cortical blood flow rate related to vasodilation. © 2005 Society of Photo-Optical Instrumentation Engineers. DOI: 10.1117/1.2007987

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Noninvasive detection of functional brain activity with near-infrared diffusing-wave spectroscopy

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.

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Fiber-based multispeckle detection for time-resolved diffusing-wave spectroscopy: characterization and application to blood flow detection in deep tissue

We report dynamic light scattering experiments on turbid colloidal suspension under stationary and laminar flow, as well as in the regime of flow instabilities. It is shown that the time autocorrelation function C 1 ( t ) = E (0) E ∗ ( t )>/ E (0)¦ 2 > of the scattered light field E ( t ) is not sensitive to the mean velocity flow but rather to the root mean square of velocity gradient. C 1 ( t ) is characterised on the level of each scattering event by the correlation time required by a pair of scatterers initially separated by a transport mean free path to move a relative distance of optical wavelength due to the velocity gradient. We verified this theoretical analysis using planar Couette flow as an example for homogenous velocity gradients, and planar Poiseuille flow for inhomogeneous velocity gradients. Agreement between expirement and theory is excellent. Finally, this technique is applied to spatially varying velocity gradient fields for measuring the threshold and wave number of the Taylor-Coutte instability. This illustrates the possibility of studying hydrodynamic instabilities and quasi-local velocity gradients even under conditions of strong multiple scattering.

Multiple light scattering in Taylor-Couette flow

A theoretical study of the time-dependent correlation function of the multiply scattered light in laminar and stationary flow is presented. We study an inhomogeneous system of flow, i.e. when the strain tensor σ ij ( r ) depends on the space variables. Since in such flows the dephasing of light is space dependent, we introduce the useful function of the local density distribution of diffusion paths. We show that the time-dependent correlation function C1(t) of the scattered field is sensitive to the root mean square of velocity gradients weighted by the cloud of diffusive light paths. We establish a general formulation of C1(t) for laminar and stationary flow in the weak scattering limit kl ⪢ 1. The effects of the dimension of the inhomogeneous system and of the boundary conditions are also discussed. These results are applied to the cases of an infinitely thin and continuous sheet of vorticity, of a Rankine vortex, and of a Gaussian shaped velocity gradient.

D. Bicout

Papers

Multiple light scattering in Taylor-Couette flow

Diffusing wave spectroscopy in inhomogeneous flows