Diffusing-wave spectroscopy: Difference between revisions

Revision as of 20:30, 3 August 2012

Revision as of 08:08, 14 August 2012

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

For the case of non-interacting particles suspended in a (complex) fluid a direct relation between g₂-1 and the [[mean squaresquared displacement]] of the particles <Δr²> can be established. Let's note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as follows:<ref>

{{cite journal

|author=F. Scheffold ''et al.''

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with <math>k_0=\frac{2\pi n}{\lambda}</math> and <math>l*</math> is the transport mean free path of scattered light.

For simple cell geometries, it is thus possible to calculate the mean squaresquared displacement of the particles <Δr²> from the measured g₂-1 values analytically. 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:

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