The correlator has an input signal which is multiplied by some filter in the Fourier domain.
So the correlation can then be calculated by inverse Fourier transforming the result.
According to Fresnel Diffraction theory a convex lens of focal length
So that complex amplitudes are multiplied, the light source must be coherent and is typically from a laser.
The input signal and filter are commonly written onto a spatial light modulator (SLM).
This is Fourier transformed with a lens and this is then modulated with a second SLM containing the filter.
Some have been proposed to address hardware limitations, others were developed to optimize a merit function or to be invariant under a certain transformation.