Bispectral analysis as a probe of quasielastic light scattering intensity fluctuations

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Abstract
The bispectrum ⟨I(0)I(t)I(τ)⟩ of the intensity I of light scattered quasielastically from a fluid system is shown to be a potentially useful tool for studying complex fluids. Bispectra and time cumulants are calculated, in the time domain, for systems with 1, 2, or many diffusing components, treating separately the consequences of homodyne and heterodyne detection at times 0, t, and τ. The experimentally accessible cumulants of the all‐homodyne bispectrum distinguish between systems with exactly two relaxation times and systems with more than two relaxation times. The signal‐to‐noise ratio in a bispectral measurement is shown to be proportional to T1/2, T being the integration time. Clipped scaling of the heterodyne intensity I(t) allows study of the odd powers ⟨‖ak(0)a∗k(t)ak(τ)‖⟩ of the density correlations