Correlation function Siegert relation

The two normalized correlation functions are related by the Siegert equation ... 

The Siegert relation is valid except in the case of scattering volumes with a very small number of scatterers or when the motion of the scatterers is limited. We ignore the exceptions, which are rare in common uses of DLS, and consider only autocorrelations of the type shown in Equation (104). As mentioned above, modern DLS instruments use computer-controlled correlators to calculate the intensity autocorrelation function automatically and to obtain the results in terms of the function gi(s,/rf) therefore we only need to concern ourselves here with the interpretation of gi(s,td). 

In a dynamic light scattering experiment, the measured intensity-intensity time-correlation function g<2)(tc), where tc is the delay time, is related to the normalized electric field correlation function g(1)frc), representative of the motion of the particles, by the Siegert relation [18] ... 

In this section we shall see that the incorporation of polarization into the formulation for PCS enables the shape of the particles to be inferred. This is achieved by a modest augmentation of PCS equipment that facihtates the measurement of the cross-correlation of the scattered intensity that has been resolved into different polarization states. The temporal decay of the polarized intensity cross-correlation function is identical to that of the intensity autocorrelation function used in PCS, however it decays from value less than 2, and the difference from 2 is related to the particles departure from a sphere. Before demonstrating precisely how this occurs, it is first necessary to see how polarization generalizes the Siegert relation. 

As proved by Siegert [939] for optical fields with a Gaussian intensity distribution (7.60), the second-order correlation function G x) is related to G x) by the Siegert relation... 

The experimentally accessible quantity is the intensity line correlation function g2(t) which is connected to the theoretically simpler correlation function of the electric field, gi(t) via the Siegert relation... 

The autocorrelation function g(2)(t) is related to g(i)(t), the electric field correlation function (or first-order autocorrelation function) via the so-called Siegert relation (Equation 3.24) ... 

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