Partially coherent processing by optical means

When the coherence time of a signal propagated through a time-varying medium is less than the signal duration, detection methods using conventional coherent correlation processes are not appropriate. Instead, mixed integration techniques can be used, with the coherent integration interval matched to the signal coherence time. A mixed integration can be simulated quite easily in an optical correlator by controlling the degree of coherence of the illumination at the first aperture. A partially coherent optical correlator produces an output light intensity
I(x_{0}) = \int \int \gamma\(x, x')s(x - x_{0})r(x)s(x' - x_{0})r(x')dxdx'
where
\gamma (x, x')
is the coherence factor and
s(x)
and
r(x)
are the received signal and reference. This equation is derived for a partially coherent optical correlator, and the range of output correlation intensities, which are directly related to processing gain, is determined as a function of the coherence width inherent in
\gamma(x, x')
.