Here g₁ denotes the field amplitude, and δ(τ) equals one at τ = 0 and zero otherwise. A more detailed derivation of Eq. (4.40) is given in [51].

4.6.2 Autocorrelation and its practical implementation

Figure 4.15. Schematic representation of signal conversion.

For a scattering volume Δvᵢ and the phase difference ΔΦᵢ between the scattered beams, the following proportionality holds:

Here E_detector represents the sum of the electric fields at the detector. As noted in the previous section, the experimentally accessible quantity is the intensity I(t), for which:

If a fixed observation volume is considered, ΔΦᵢ,ⱼ does not change with time. The scattering amplitude, however, varies as particles diffuse into and out of the observed volume. This leads to the time dependence examined on the following page.

Original mathematical notation and illustrations are preserved as extracted image assets.