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I have been struggling in the past weeks to understand how should I setup a laser interferometer for my experiment. I am not a physicist, and I am quite new to optics.

I have a Cassegrain telescope with a primary mirror M1 and a secondary mirror M2 and I want to monitor the relative displacements and tilts between M1 and M2. How can I obtain that output with the minimum number of optical components? I am also not sure about the detector I should need. I was thinking of a simple system that I don't know if it could actually work. I still have to purchase the components, but the budget should be around 2K.

First of all, I thought that cornercube retroreflector on both M1 and M2 would be necessary. With flat mirrors the beam would not be reflected if there is some tilt, right?
The laserbeam passes through a beamsplitter: one half goes to a right angle prism and then toward the retroreflector on M1 (can it count as the reference beam?). The other half goes to the retroreflector on M2. The beams from M1 and M2 are then recombined in the beamsplitter and the interference beam goes to the detector (PSD, quadrant photodiode?)
Would a system like this be able to give me as output the relative displacement (like a classic Michelson interferometer) and maybe the tilts (looking at the current in the quadrant photodiode perhaps)?

enter image description here

In the picture: LS = laser source, BS = beamsplitter, P = prism, R1-2 = retroreflectors, QPD = quadrant photodiode.

Thanks in advance.

EDIT: here's the version with paths of same length enter image description here

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  • $\begingroup$ A laser interferometer is best for measuring relative displacements less than or equal to the wavelength (~1 um). Larger than that, and you need to count fringes, and you wouldn’t necessarily know which direction the mirrors are moving. What is the length scale of the mirror displacements you’re concerned about? Also, measuring displacement and interference simultaneously with the same beams is probably not recommended (analysis would be complicated; usually for interference measurements, the assumption is that the beams remain aligned). $\endgroup$
    – Gilbert
    Nov 22, 2020 at 16:56

2 Answers 2

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There are many ways to measure tilt and separation changes using interferometry. As @Gilbert pointed out, for large displacements you need a way to keep track of the direction in which fringes are moving. Actually, that's not too difficult if a video record is kept of the fringes. An automated way to do it is to make a subsystem that locates the peak of a fringe and "dithers" the system to determine whether a sensor is on the left or right side of the peak via the relative phase of the "dithering" motion and the signal change at the sensor. IMHO, retroreflectors should not be necessary, and might confuse the results because they don't really exactly produce a time-reversed wavefront. It's probably best to simply set up the telescope with a laser to produce fringes that cover the field of view, get the telescope aligned the way you like it, and then monitor the fringes. Interpreting the fringe motion in terms of change of separation, tilt angle and direction will require some assumptions and a lot of math. If you include a sketch of the setup you're contemplating, I or someone else here will gladly comment on the setup.

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  • $\begingroup$ Thank you for your reply. For the retroreflectors, I thought of using them just because the reflected beams perhaps might not interfere in the beamsplitter if I use flat mirrors. Does it make sense? Regarding the tilts, maybe it could be easier to use flat mirrors in this case, and monitor how the reflected laser beam moves on a quadrant photodiode to obtain information on its X and Y coordinates. Moreover, do I need a HeNe laser or a compact laser module would it be fine? Perhaps the diameter of the beam is too wide to accurately monitor its displacement on the sensors? $\endgroup$
    – Gianluca
    Nov 23, 2020 at 10:48
  • $\begingroup$ Flat mirrors will not prevent interference; they just need to be carefully aligned. Practically any red or green laser pointer should have plenty of coherence length for your experiment, as long as the path lengths are essentially the same. If your quadrant detector indicates the differences between the amounts of light received by each quadrant, the beam size should not matter much. $\endgroup$
    – S. McGrew
    Nov 23, 2020 at 13:56
  • $\begingroup$ The thing is that the surfaces themselfes where I intend to mount the flat mirrors/retroreflectors should slightly tilt during the test. In this condition, am I right to think that the reflected beam does not go back on the same direction of the incoming beam? Do you think that a photodiode would be enough to measure the interference beam? $\endgroup$
    – Gianluca
    Nov 23, 2020 at 14:06
  • $\begingroup$ Presumably your tilt will be very small. As long as the beam is coherent and is spread wide enough that the two beams overlap, the beams will interfere. The more tilt there is, the closer together the fringes will be. If you want to count fringes as they drift past, it's best to make sure the detector is smaller than the fringe spacing. $\endgroup$
    – S. McGrew
    Nov 23, 2020 at 14:10
  • $\begingroup$ I'd suggest that you go ahead and set up the interferometer using a red laser pointer and flat mirrors. Get it adjusted until you can see fringes, then adjust more until the fringes are large. Play with placement of your photodiode and watch what happens when the fringes drift across it. You will need to spread the beam, e.g., using a microscope objective and pinhole filter, and then collimate it with a decent lens. There will be a lot of "noise": irrelevant fringes due to dirt on the lens. $\endgroup$
    – S. McGrew
    Nov 23, 2020 at 14:13
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So, this should be the setup of the experiment with the configuration we discussed about (the lens between BS and the sensor is missing): enter image description here

Do you think it could work?

Does it make sense to put sensors also before? Both mirrors (reference on M1 and moving on M2) are actually moving, thus perhaps also the interference between the original laser beam and the splitted beams might be helpful and meaningful?

This should be an absolute measure, while the previous one is relative between M1 and M2. I hope I have been clear enough.

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