  The Fluorescence Correlation Spectroscopy (FCS) spectrum G(t) and Raster
Image Correlation Spectroscopy (RICS) spectrum R(t) of dilute diffusing
particles are determined by the displacement distribution function P(x,t) of
the particles and by the experimental parameters of the associated optical
trains. This letter obtains the general relationships between P(x,t) and these
spectra. For dilute diffusing molecules in simple liquids, P(x,t) is a Gaussian
in the displacement x; the corresponding G(t) is a Lorentzian in
(<(x(t))^2>)^(1/2). In complex fluids such as polymer solutions, colloid and
protein solutions, and the interior of living cells, P(x,t) may have a
non-Gaussian dependence on x, for example an exponential in |x|. We compare
theoretical 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-square
displacements are precisely equal at all times. If the G(t) and R(t) arising
from 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 coefficient
may be substantially in error.
