How is an autocorrelation function computed? (Dynamic Light Scattering)

AI Thread Summary
In Dynamic Light Scattering experiments, the autocorrelation function is computed using the formula G(τ) = ⟨I(t)I(t+τ)⟩, where scattered light intensity is collected by a detector and processed by a digital correlator. The correlator performs a Fast Fourier Transform (FFT) on the signal, multiplies the resulting spectra, and then applies an inverse FFT to obtain the autocorrelation. This process effectively filters the signal by itself, allowing for the calculation of the correlation over time. The average is implemented by recording the scattered intensity multiple times to ensure accuracy. Understanding this method is crucial for analyzing particle dynamics in various applications.
Salmone
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In an experiment of Dynamic Light Scattering, how is an autocorrelation like the one in the image computed?

dls-theory-figure-1-500.png

Mathematically a correlation function can be written as ##G(\tau)=\langle I(t)I(t+\tau) \rangle##, in an experiment like the one I mentioned the scattered intensity light is collected by a single detector, then the signal is sent to a digital correlator which computes the correlation function. How this process works? Once I have a signal from the detector, what does the correlator do? Does it multiply the intensity at time ##t## with the same intensity at time ##t+\tau## simply? How is the average implemented? By recording with the detector the same scattered intensity multiple times? Can you explain very generally how a digital correlator works?
 
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Salmone said:
Can you explain very generally how a digital correlator works?
A correlator would take the FFT of the two signals, multiply those two spectra, then inverse FFT. In effect, filtering a signal by another signal.

I expect autocorrelation could be performed by taking the FFT of the signal, squaring the vectors of the resulting spectrum, then computing the inverse FFT. In effect, filtering a signal by itself.
 
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