Diffusing-wave spectroscopy: Difference between revisions

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{{Nolead|date=October 2009}}

==One speckle Diffusing-wave_spectroscopy==

==One-speckle diffusing-wave spectroscopy==

Diffusing-wave spectroscopy is an optical technique derivatedderived from [[Dynamicdynamic light scattering]] (DLS) that studystudies the dynamics of light scatterers in the case of strong multiple scattering.

<ref>G. Maret and P. E. Wolf, Z. Phys. B: Condens. Matter 65, 409 1987</ref>

<ref>D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 1988</ref>

. It has been widely used to study colloidal suspensions, emulsions, foams, gels, biological media, etc... If carefully calibrated, DWS allows the measurement of particle motion in a complex medium and then its rheology ([[Microrheology]])<br />.

A laser light is sent inside the product and the outcoming transmitted or backscattered light is detected by an optoelectric sensor. The light intensity detected is the result of the interference of all the optical waves coming from the different light paths. <br />

<gallery>

Image:figureDWS.png|Typical setup of Diffusingdiffusing-wave spectroscopy

</gallery>

The signal is analysed by calculating the intensity autocorrelation function called g₂.

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In general the relation between g₂-1 and the mean square displacement of the particles <Δr²> depends on the photons trajectories. Let's note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as following:<ref>F. Scheffold, S. Romer, F. Cardinaux, H. Bissig, A. Stradner, L. F. Rojas-Ochoa1, V. Trappe, C. Urban, S. E. Skipetrov, L. Cipelletti and P. Schurtenberger, New trends in optical microrheology of complex fluids and gels, Progress in Colloid and Polymer Science, vol 123/2004, pp 141-146 </ref> <br />

<math>g_2(\tau)-1=[\int {ds P(s) exp(-(s/l*)k_0^2 <\Delta r^2(\tau)>) }]^2</math><br />

with <math>k_0=\frac{2\pi n}{\lambda}</math> and <math>l*</math>: the transport length.<br />

For simple cell geometries, it is possible to calculate the mean square displacement of the particles <Δr²> with respect to g₂-1. For example, for the backscattering geometry, an infinitely thick cell, large laser spot illumination and detection of photons coming from the center of the spot, the relation ship between g₂-1 and <Δr² is :<br />

<math>g_2(\tau)-1=exp[-2 \gamma \sqrt{<\Delta r^2(\tau)>k_0^2}]</math>, γ value is around 2.<br />

For less thick cells and transmission, the relationship depends on l* (the transport length)<ref> D. A. Weitz and D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light scattering, W. Brown, ed., Clarendon Press, Oxford (1993) 652–720</ref>.

The multiple scattering implies a high dependancedependence on the cell geometry and . An advantage is that the control of the geometry allows to control the studied length scale.<br /><br />

==Multispeckle Diffusing-Wave Spectroscopy (MSDWS)==

This technique useuses a camera to detectsdetect many speckle grains (see [[Specklespeckle pattern]]) at the same time. In this case the averaging is done among the camera pixels, allowing a much faster acquisition time.

<gallery>

Image:figureMSDWS.png|Typical setup of Multispeckle Diffusing-wave spectroscopy

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<math>g_2(\tau)=\frac{<I(t)I(t+\tau)>_p}{<I(t)>_p^2}</math>

<br />

This MSDWS is particularly adapted for slow dynamics and non ergodic media.

An adaptive image processing