The (temporal) autocorrelation function is the correlation of a time series with itself shifted by time , as a function of :
where  is the deviation from the mean intensity. The normalization (denominator) here is the most commonly used for FCS, because then the correlation at , G(0), is related to the average number of particles in the measurement volume.
As an example, raw FCS data and its autocorrelation for freely diffusing Rhodamine 6G are shown in the figure to the right. The plot on top shows the fluorescent intensity versus time. The intensity fluctuates as Rhodamine 6G moves in and out of the focal volume. In the bottom plot is the autocorrelation on the same data. Information about the diffusion rate and concentration can be obtained using one of the models described below.
For a Gaussian illumination profile , the autocorrelation function is given by the general master formula
where the vector  denotes the stochastic displacement in space of a fluorophore after time .
The expression is valid if the average number  of fluorophores in the focal volume is low and if dark states, etc., of the fluorophore can be ignored. In particular, no assumption was made on the type of diffusive motion under investigation. The formula allows for an interpretation of  as (i) a return probability for small beam parameters  and (ii) the moment-generating function of  if  are varied.