The Feynman variational method is applied to a real functional integral representation of a generator for the velocity correlation functions in stationary homogeneous turbulence. The resulting approximation for the two-point correlation differs from that recently obtained by Lucke using a similar approach. It is pointed out that Lucke's approximation is based on a restricted trial function and does not correctly reproduce second-order perturbation theory in the limit of weak non-linearity. The approximation derived here does not suffer from this defect but is more complicated. Some defects of this general approach are discussed.

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We demonstrate silicon-based integration of an optical pulse waveform analyzer using a pulse-induced nonlinear spectral change which succeeded in reconstruction of an optical pulse waveform reflected by a slight chirp change in an optical pulse.