Spatial interference fringes in Hong-Ou-Mandel

[Swamp Thing]

If we can slightly skew the optics in a HOM setup, so that the phase difference between Beam-1 and Beam-2 varies slowly across one of the detection planes, then would we see dark and bright regions in the cumulative pattern (assuming an array type i.e. spatially resolved detector) ??

 

[jfizzix]

I think the HOM interference takes place at the beamsplitter well before the detectors.
That being said, if the two incoming beams completely overlap on a quantum level, then you'll see HOM interference throughout the coincidence detection planes.
Usually HOM interference id done with beams of down-converted light, because the light comes in pairs of photons which can completely overlap each other.

If you're varying the light after the beamsplitter, the light should display HOM interference regardless (i.e., a dip to near zero coincidence counts) over both spatially resolving detectors.

If you shift one of the incoming beams of light into the beam splitter, the photon-photon overlap will decrease, and the number of coincidence counts will rise.
If you perform a spatially varying phase shift on one of the incoming beams (say by a spatial light modulator), while keeping everything else aligned, then you should see a spatially varying HOM interference pattern with a pair of spatially resolving photon counting detectors, and the pattern you see will be an image of the pattern you put on the modulator.