Building an OCT requires some very high spec interferometry. It is largely based on a Michelson interferometer, so I would first get a Michelson working well, before trying to continue
A basic Michelson is just a light source (laser, discharge lamp, etc), 2 mirrors, a beam splitter, and a screen. If you make sure your source is collimated (beam doesn’t change size as it travels) and fairly broad area (a few mm spot size) then you can just use a piece of paper as a screen to view interference.
What makes the above hard is you need both laser spots (that return from each mirror) very well aligned over each other, so your mirrors need to be very finely adjustable in angle. You also need your mirrors to not distort the “wavefront”, this basically means that if the mirror is bumpy rather than flat then different parts of the beam needed to travel different distances (which destroys the signal). As we are talking about light interference you really need the flatness to be a fraction of an optical wavelength. To do this you normally buy special “front silvered” mirrors where the reflective surface is exposed on top of the glass, these are easier to scratch, can only be cleaned in a special way, but work well. Also if you get a thick-ish beam splitter plate then you will need and extra compensating plate to correct for the extra time the light spent travelling through the beamsplitter. Once this is all correct and nicley aligned you should be able to get a an interference pattern, if you do not have a pattern when the spots overlap it is normally because the length one beam travelled is too different from the other (this is key for OCT). Lasers that have a very thin spectrum (range of colours in the beam) produce interference with more allowance for path difference.
Next before you can start thinking about OCT you will need a way to translate components very accurately. In a Michelson you normally translate one mirror. As it moves you should see the interference pattern move. To get it to move well you need the motion to be small (generally it is good if you can reproducibly move distances of less than 100nm). Also as it moves you need to be as free as possible from wobble and tilt of the mirror. If it wobbles by 100nm or so this will make your signal super noisy, by much more you can’t get useful data. We had some MPhys students build a 3D printed base for a Michelson (unfortunately not well documented as of yet) which you can find here. They got about 20nm steps with a stepper motor, but there was some slight tilt of the mirror that had to be live corrected by tilting the fixed mirror:
Of you get all this working really nicely with good fringes moving reproducible along the screen, you can start using a photo diode to just detect bright vs dark at one place on the pattern, probably done by reducing the width of the input beam. You need to be pretty confident in the reproducibility of you setup here because it is far harder to debug now.
If this all starts working really well then you can start thinking about OCT. We said before that the lower range of wavelengths the larger the length you get interference over (coherence length). For OCT you broaden the optical spectrum, so you use something like a supercontinum (a laser beam that has had its spectrum widened to contain lots of frequencies). This will now only give a signal between beams that have travelled the same distance (this is how you set the depth you are imaging). To image you need to focus the light from one beam with a microscope objective and scan the focused through your sample in all 3 directions. The diagrams I have seen seems to tilt one mirror, and move another, but I don’t see why you cannot just move the sample in 3D (there may well be a reason I am missing). It is worth bearing in mind that the only light that is coming back is light that gets focused through the objective, gets scattered, and then returns through the whole system. To detect this you will probably need some really clever detection scheme and an incredibly stable laser. This would require a lot of thought even for a simple proof of principle. To do the scanning you could use this (better documented) stage we designed for aligning optical fibres:
Sounds like a fun project but I would not underestimate how accurately these things need to be aligned and moved (especially when you get to more broad sources, and detecting only scattered light). You can definitely build a simple Michelson for a reasonable price (I hope we find time to document and write up ours as some point), that is a good starting point to iterate to something more fancy.