We have developed new measurement methods for the dynamic light scattering in a periodically stationary
system such as the quasi-elastic light scattering with the sinusoidal (ac) electric field (QELS-SEF). Whereas
the usual dynamic light scattering is measured in the stationary system, the scattered light intensity in
QELS-SEF obeys a nonstationary stochastic process, more specifically, a periodically stationary one. Hence,
the autocorrelation function or the power spectrum in QELS-SEF is a bivariable function of two independent
times or frequencies, which cannot be measured by the conventional correlator or spectrum analyzer. We
have designed a new kind of spectrum analyzer for QELS-SEF and obtained two-dimensional power spectrum
of QELS-SEF by use of an extended Wiener−Khinchin theorem. Furthermore, the data analysis formula
for the two-dimensional spectra is calculated to evaluate the complex electrophoretic mobility μ* and the
apparent diffusion constant D
app of polyions from the two-dimensional power spectra. They are in good
agreement with the experimental results of QELS-SEF for a polystyrene latex solution.