A Gaussian laser beam is reflected by a dichroic mirror (reflective at the laser wavelength but transmissive at the fluorescence wavelength) and directed into a high aperture microscope objective. This objective focuses the laser beam into a solution of fluorescent molecules. The excited fluorescence is detected through the same objective (epifluorescence set-up) and directed through the dichroic mirror, and then focused onto a small confocal aperture in front of a sensitive photodetector (usually a photomultiplier tube or a single photon avalanche diode). The main purpose of the confocal aperture is to restrict the detection volume along the optical axis by barring all light coming from above or below the plane of minimum laser diameter. Usually, it is assumed that the thus defined fluorescence detection function F(x,y,z) (convolution of laser excitation profile with collection efficiency function) has an elliptical shape given by

where s is the optical absorption cross section, Ff is the fluorescence quantum yield, k is the maximum value of the light collection efficiency, I is the maximum value of the laser intensity, x and y are the coordinates perpendicular to the optical axis, while z is along that axis, and a and b are parameters describing the spatial extent of the detection volume. A fluorescence measurement registers continuously the detected photon counts, yielding a long file of photon count numbers within subsequent time intervals.

A very clever way of analyzing the measured fluorescence data is the so called autocorrelation analysis. Basically, it calculates the probability to detect a photon at some time t+Dt if there was a photon at time t. Its calculation goes as follows: If the number of detected photons within the kth time interval is denoted by Nk, the autocorrelation function g(Dk) is given by

where the brackets denote averaging over all channels k. The normalizing factor in front of the sum takes into account that, for a given value of Dk, the sum can only run from one through kmax - Dk, where kmax is the last time channel of the measurement.

The usefulness of such an autocorrelation approach can be seen by deriving a theoretical expression for it. Let us assume that one measures the fluorescence of a solution of freely diffusing fluorescing molecules with diffusion constant D. First at all, it is important to understand that the fluorescence photons emitted by different (and supposedly non-interacting) molecules are completely non-correlated. That means that for e.g. two molecules 1 and 2, if Nk1 and Nk2 define the numbers of fluorescence photons in the kth time channel stemming from molecule 1 and 2, respectively, then <Nk1Nk2> = <Nk1><Nk2>.

The non-trivial (non-uniform) contribution to the autocorrelation function is completely defined by the autocorrelation of the fluorescence photons of one and the same molecule. Consider a small volume DxDyDz at position (x, y, z). If the molecules' concentration within the solution is c, there are, on average, cDxDyDz molecules within that volume. These molecules emit, on average, F(x,y,z) Dt photons during the time interval Dt (width of one time channel). After time Dk Dt, the probability that a molecule has diffused to the new position (x', y', z') is given by the solution of the diffusion equation for the given initial condition:

For a molecule at this new position (x', y', z'), the average number of detected photons equals F(x',y',z') Dt.

Now, the non-uniform part of autocorrelation is nothing else than the product of all the above average numbers and probabilities, integrated over all possible initial and final positions of the molecules. The uniform part is simply given by the square of the probability to detect a photon during any time interval (proportional to the average number <N> of detected photons per time interval Dt), accounting for the contribution to the autocorrelation function by photons emitted by different molecules. Thus, the complete autocorrelation reads:

An important property of the autocorrelation function can be seen when it is divided by its uniform part:

This normalized autocorrelation function does no longer depend on anything such as fluorescence quantum yield, detection efficiency, laser intensity etc., and its limiting value for Dt -> 0 is inversely proportional to the absolute concentration c of the fluorescing molecules!

When evaluating experimental data, it is often useful to calculate directly the non-uniform part of the correlation function, which can be done by subtracting from the measured data their average prior to performing the autocorrelation operation:

It is obvious that this renormalized autocorrelation function decays to zero for large values of Dt, thus representing indeed the non-uniform part of g.