Diffusing wave spectroscopy

One-speckle diffusing-wave spectroscopy

Laser light is sent to the sample 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.

The signal is analysed by calculating the intensity autocorrelation function called g₂. g 2 ( τ ) = ⟨ I ( t ) I ( t + τ ) ⟩ t ⟨ I ( t ) ⟩ t 2

For the case of non-interacting particles suspended in a (complex) fluid a direct relation between g₂-1 and the mean squared 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:

g 2 ( τ ) − 1 = [ ∫ d s P ( s ) exp ⁡ ( − ( s / l ∗ ) k 0 2 ⟨ Δ r 2 ( τ ) ⟩ ) ] 2

with k 0 = 2 π n λ and l ∗ is the transport mean free path of scattered light.

For simple cell geometries, it is thus possible to calculate the mean squared 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 relationship between g₂-1 and <Δr²> is:

g 2 ( τ ) − 1 = exp ⁡ ( − 2 γ ⟨ Δ r 2 ( τ ) ⟩ k 0 2 ) , γ value is around 2.

For less thick cells and in transmission, the relationship depends also on l* (the transport length).

Multispeckle Diffusing-Wave Spectroscopy (MSDWS)

This technique either uses a camera to detect many speckle grains (see speckle pattern) or a ground glass to create a large number of speckle realizations (Echo-DWS ). In both cases an average over a large number of statistically independent intensity values is obtained, allowing a much faster data acquisition time.

g 2 ( τ ) = ⟨ I ( t ) I ( t + τ ) ⟩ p ⟨ I ( t ) ⟩ p 2

MSDWS is particularly adapted for the study of slow dynamics and non ergodic media. Echo-DWS allows seamless integration of MSDWS in a traditional DWS-scheme with superior temporal resolution down to 12 ns. Camera based adaptive image processing allows online measurement of particle dynamics for example during drying.