Diffusing-wave spectroscopy

Diffusing-wave spectroscopy is an optical technique derived from dynamic light scattering (DLS) that studies the dynamics of light scatterers in the case of strong multiple scattering. ^{[1] [2]} 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).

One-speckle diffusing-wave spectroscopy

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.

•  
  Typical setup of diffusing-wave spectroscopy

The signal is analysed by calculating the intensity autocorrelation function called g₂. ${\displaystyle g_{2}(\tau )={\frac {<I(t)I(t+\tau )>_{t}}{<I(t)>_{t}^{2}}}}$ 

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:^[3]
${\displaystyle g_{2}(\tau )-1=[\int {dsP(s)exp(-(s/l*)k_{0}^{2}<\Delta r^{2}(\tau )>)}]^{2}}$ 
with ${\displaystyle k_{0}={\frac {2\pi n}{\lambda }}}$  and ${\displaystyle l*}$ : the transport length.

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 :
${\displaystyle g_{2}(\tau )-1=exp[-2\gamma {\sqrt {<\Delta r^{2}(\tau )>k_{0}^{2}}}]}$ , γ value is around 2.

For less thick cells and transmission, the relationship depends on l* (the transport length)^[4]. The multiple scattering implies a high dependence on the cell geometry and . An advantage is that the control of the geometry allows to control the studied length scale.

Multispeckle Diffusing-Wave Spectroscopy (MSDWS)

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

•  
  Typical setup of Multispeckle Diffusing-wave spectroscopy

${\displaystyle g_{2}(\tau )={\frac {<I(t)I(t+\tau )>_{p}}{<I(t)>_{p}^{2}}}}$ 

This MSDWS is particularly adapted for slow dynamics and non ergodic media. An adaptive image processing ^[5] [2] allows online measurement of particle dynamics for example drying.

References

1. G. Maret and P. E. Wolf, Z. Phys. B: Condens. Matter 65, 409 1987
2. D. J. Pine, D. A. Weitz, P. M. Chaikin, and E. Herbolzheimer, Phys. Rev. Lett. 60, 1134 1988
3. 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
4. D. A. Weitz and D. J. Pine, “Diffusing-wave spectroscopy,” in Dynamic Light scattering, W. Brown, ed., Clarendon Press, Oxford (1993) 652–720
5. L. Brunel, A. Brun, P. Snabre, and L. Cipelletti, Optics Express, Vol. 15, Issue 23, pp. 15250-15259 [1]

External links

• Illustrated description of DWS with movies