Pattern recognition in DWS graphs

Dynamic Light Scattering (DLS) is a technique used to determine size distributions of small particles in suspension or polymers in solution. $^{[1]}$ Fluctuations in time are analyzed using the intensity or photon autocorrelation function (ACF) $^{[2]}$ which usually decays from zero delay time, and faster dynamics due to smaller particles leading to faster decorrelation of scattered intensity trace. Diffusing-Wave Spectroscopy (DWS) is a technique deriving from DLS which studies the dynamics of scattered light limited to multiple scattering. In this variation, both transmission (FW) and backscatter (BS) are measured and the seperate correlation functions analyzed to characterize emulsions in motion.

Signal analysis using the ACF

(1) (2)

In our case, the auto-correlation function is of the following form

$$g _2(t _{\mathtt{age}};t)=\frac{\langle I(t _{\mathtt{age}};\mathtt{pixel}) \cdot I(t _{\mathtt{age}}+t;\mathtt{pixel}) \rangle _{\mathtt{pixel}}}{\langle I(t _{\mathtt{age}};\mathtt{pixel}) \rangle \langle I(t _{\mathtt{age}}+t;\mathtt{pixel}) \rangle _{\mathtt{pixel}}}$$

where $I$ represents the intensity function, $t$ the delayed time, $t _{\mathtt{age}}$ the $k$-th element from $t _{\mathtt{age}}$ and $\mathtt{pixel}$ the particular pixel intensity. The pixel intensity comes from the fact that the ACF is calculated starting from pictures generated by a "line camera".

The picture (1) above (click to zoom) is a snip of a full resolution (200x10000) picture coming directly from the line camera. Each row of the image corresponds, in terms of the ACF described, to the intensity of the pixel in regards to $t_0$ (row) and to the correlation function at certain $t _{\mathtt{age}}$ (column). (2) Shows the intensities of the backscattered light, quite like the other picture but horizontally, a function of time in the same terms. $^{[3]}$

Plotting the ACF

The data we work with comes directly from a DWS experiment involving foams. Inside a MATLAB data file (here not provided) we have a variable called g2_map (51x508450) that contains all the correlation functions as columns. We check the behaviour of the sample by plotting its function of time (x-axis) and g(2) (y-axis) using the following command

semilogx(dt*lagtimes, g2_norm(:,100000),'r-')

The objective

Can we determine or at least highlight, when do transient events happen? Is there a way to automate the detection of the transient peaks shown in the first two pictures?

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$[1]$ Dynamic Ligh Scattering, with applications to Chemistry, Biology, and Physics (Bruce J. Berne, Robert Pecora)
$[2]$ Probability and random processes for electrical and computer engineers (P.392) (John A. Gubner)
$[3]$ Rev. Sci. Instrum. 92, 124503 (2021); https://doi.org/10.1063/5.0062946