  Mathematical methods previously used (Phillies, J. Chem. Phys., 122 224905
(2005)) to interpret quasielastic light scattering spectroscopy (QELSS) spectra
are here applied to relate diffusing wave spectroscopy (DWS) spectra to the
moments \bar{X^{2n}} of particle displacements in the solution under study. DWS
spectra of optical probes are like QELSS spectra in that in general they are
not determined solely by the second moment \bar{X^{2}}. In each case, the
relationship between the spectrum and the particle motions arises from the
field correlation function g^{(1)}_{s}(t) for a single quasi-elastic scattering
event. In most physically interesting cases, g^{(1)}_{s}(t) receives except at
the shortest times large contributions from higher moments \bar{X(t)^{2n}}, n
>1. As has long been known, the idealized form g^{(1)}_{s}(t) =\exp(-2 q^{2}
\bar{X(t)^{2}}), sometimes invoked to interpret DWS and QELSS spectra, only
refers to (adequately) monodisperse, noninteracting, probes in purely Newtonian
liquids and is erroneous for polydisperse particles, interacting particles, or
particles in viscoelastic complex fluids. Furthermore, in DWS experiments
fluctuations (for multiple scattering paths of fixed length) in the number of
scattering events and the total-square scattering vector significantly modify
the spectrum.
