The panchromatic principle in optical filtering

The panchromatic optical correlator is a coherent correlator which uses a slightly broadened light spectrum to correlate simultaneously a number of receiver channels against a continuous range of Doppler distortions of the transmitted signal. The relation between spatial frequency
\omega_{x}
and aperture distance
x
in a coherent optical correlator is
\omega_{x} = - 2 \pi x/ \lambda f
, wherein
\lambda
is the light wavelength and
f
is the lens focal length. Since signals reflected from a target moving with uniform radial velocity undergo a scale factor adjustment of the signal spectrum, the Doppler distortions resulting from target motion can be simulated by a range of
\lambda
. The panchromatic correlator is actually a superposition of many monochromatic correlators with each
\lambda
corresponding to a particular Doppler distortion. The correlator output can be color separated by a prism to resolve Doppler information, or left unresolved to provide a Doppler invariant correlation regardless of the invariance properties of the chosen signal. Inserting a diffraction grating in the proper aperture changes the relation above to
\omega_{x} = -2 \pi x/ \lambda f - \omega_{h}
, where
\omega_{h}
is a frequency shift. This form permits correlation against a Doppler-distorted signal, heterodyned an amount
\omega_{h}
to use the time-bandwidth product of the correlator more efficiently.