On the statistics of fluorescence correlation spectroscopy

I present a detailed statistical analysis of fluorescence correlation spectroscopy (FCS) which is a natural extension of an early work. This analysis more realistically takes account of the following issues. (1) A spatial Gaussian laser excitation of fluorescence, (2) the effect of a small number of fluorescent molecules in the observation volume, (3) the shot noise effect due to random emission of fluorescent photons, and (4) a hyperbolic form for the fluorescence autocorrelation function obtained in the case of diffusion. Based on these assumptions, the results differ from the earlier work in several respects, in particular, the dependence of the signal-to-noise ratio on sample concentration and the understanding of shot noise in fluorescence fluctuation moments.