In the Malvern Zetasizer software we measure the intensity auto-correlation function. This is obtained from correlating the scattering intensity with itself. The resulting intensity auto-correlation function is often denoted by the symbol G2(τ) in its normalized form. For Gaussian scattering, there is a relationship between the intensity and the field correlation function, known as the Siegert relation.
If we denote the normalized field correlation function as G1(τ) then under ideal conditions:
G2(τ) = 1 + G1(τ)^2 (In real measurements there would also be a baseline and a signal-to-noise ratio)
Within the Malvern software, the Correlogram (M) report in the size workspace shows the “raw correlation function” versus delay time data in the form of
G2(τ) – 1. This would be the same as the square of the field correlation function. The Cumulants Fit (M) report of the size workspace displays the G1 correlation function. This is the field correlation function.
Below, you can see an an example where the value of the data point at time 9.5 μsec is 0.843. In the Cumulants Fit report, the value at the same time point is 0.918.
Let’s check if this makes sense: the intensity correlation function value at this point should be the square of the field correlation function, 0.843 = 0.918 * 0.918 – that’s correct!
Further details of interest are described in this technical note “Dynamic Light Scattering : an Introduction in 30 minutes”.
How about the intercept?
An additional parameter related to this is the intercept, the value where the correlation function intersects with the z-axis. Therefore, there are two intercept values available from the software. The intercept of the intensity correlation function and the intercept of the field correlation function. You can locate the intensity intercept at Record View Parameters – Size – Measured Intercept. The popup tooltip for this parameter indicates “Autocorrelation function G2 intercept”. You can find the field intercept under Record View Parameters – Size – Intercept. Subsequently, for this parameter the popup tooltip says “Autocorrelation function G1 intercept”.
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