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The Fluorescence Correlation Spectroscopy (FCS) spectrum G(t) and RasterImage Correlation Spectroscopy (RICS) spectrum R(t) of dilute diffusingparticles are determined by the displacement distribution function P(x,t) ofthe particles and by the experimental parameters of the associated opticaltrains. This letter obtains the general relationships between P(x,t) and thesespectra. For dilute diffusing molecules in simple liquids, P(x,t) is a Gaussianin the displacement x; the corresponding G(t) is a Lorentzian in(<(x(t))^2>)^(1/2). In complex fluids such as polymer solutions, colloid andprotein solutions, and the interior of living cells, P(x,t) may have anon-Gaussian dependence on x, for example an exponential in |x|. We comparetheoretical forms for FCS and for RICS spectra of two systems in which P(x,t)is a Gaussian or an exponential in x, but in which the mean-squaredisplacements are precisely equal at all times. If the G(t) and R(t) arisingfrom an exponential P(x,t) are interpreted by using the forms for G(t) and R(t)that are appropriate for a Gaussian P(x,t), the inferred diffusion coefficientmay be substantially in error.

FCS and RICS Spectra of Probes in Complex Fluids