Non-invertibility of Multiple-Scattered QELSS Spectra
Abstract
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 f1(q,t) and the multiple-scattering fm(t) are examined. We show that it is fundamentally impossibly to invert fm(t) to obtain f1(q,t) or particle displacement moments <X2n>, except with assumptions that are certainly not correct in complex, viscoelastic fluids. For diffusing dilute probes in viscoelastic fluids, f1(q,t) is determined by all even moments <X2n>, n > 0$, of the particle displacement X; this information is lost in fm(t). In the special case of monodisperse probes in a true simple fluid, f1(q,t) can be obtained from fm(t), but only because the functional form of f1(q,t) is already known.
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