Heterodyne interferometry, an alternative? I am trying to setup an interferometer to monitor displacements and tilts between two surfaces. I am quite struggling because I never studied optics deeply.
I have found in this paper (https://iopscience.iop.org/article/10.1088/0957-0233/25/7/075205/meta) a way to measure three degrees of freedom (yaw, pitch, spacing) using heterodyne interferometry.

In this picture, the red beam is the reference and the blue one is the measuring beam. Tilts and displacements are then computed throug (D)PLL.
My goal is to minimise the costs of the system, and acousto-optic modulator (AOM) seem to be quite pricy. Would it work the same with two laser sources at different wavelenghts (red and green)?
Would the beams interfere? How would the beams behave?
What's the typical frequency difference in heterodyne signals?
 A: Yes, you could use two different laser sources for such a experiment.
Ideally in a heterodyne interferometer the interfering beams will have a fixed frequency offset, giving rise to a fixed-frequency beatnote signal from whose phase variations you can extract the interferometric phase.
This is readily achievable using a single laser source and one or two AOMs driven by an rf source. With two separate laser sources you would in principle get a beatnote signal whose frequency varies according to the free-running frequency noise of your two sources, likely not suitable. You could however implement an offset phase lock between your two sources, for which you could use similar electronics to those used for the phase readout. Having done this, your interferometer will be optically equivalent to one built with a single laser source and two AOMs.
As for the typical frequencies, that would depend on the electronics used for the phase readout. Normally this is in the tens of kHz to hundreds of MHz range. Since the frequency offset is so tiny compared to the optical frequency, you want to use laser sources of the same nominal frequency.
AOMs are much less expensive than your average laser source, though, and they simplify the electronics setup, so they are a typical resource in heterodyne interferometry.
