The fluorescent particles used in FCS are small and thus experience thermal motions in solution. The simplest FCS experiment is thus normal 3D diffusion, for which the autocorrelation is:
where is the ratio of axial to radial radii of the measurement volume, and is the characteristic residence time. This form was derived assuming a Gaussian measurement volume. Typically, the fit would have three free parameters—G(0), and --from which the diffusion coefficient and fluorophore concentration can be obtained.
With the normalization used in the previous section, G(0) gives the mean number of diffusers in the volume
where the effective volume is found from integrating the Gaussian form of the measurement volume and is given by:
- gives the diffusion coefficient:
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