Non-invertibility of Multiple-Scattered QELSS Spectra

We consider the spectrum S(q,t) and field correlation function f(q,t) of light quasielastically scattered from diffusing optical probes in complex viscoelastic fluids. Relationships between the single-scattering f_1(q,t) and the multiple-scattering f_m(t) are examined. We show that it is fundamentally impossibly to invert f_m(t) to obtain f_1(q,t) or particle displacement moments <X^{2n}>, except with assumptions that are certainly not correct in complex, viscoelastic fluids. For diffusing dilute probes in viscoelastic fluids, f_1(q,t) is determined by all even moments <X^{2n}>, n > 0$, of the particle displacement X; this information is lost in f_m(t). In the special case of monodisperse probes in a true simple fluid, f_1(q,t) can be obtained from f_m(t), but only because the functional form of f_1(q,t) is already known.