Reverse Engineering 15 yr old electronics

While I, like a lot in this group, tinker with old computers, I have started another project that involves more than old computers. Hope this is close to being on topic, some of you may find it interesting. I purchased parts of a Nicolet Fourier Transform Spectrometer with the goal of putting together a working Michaelson Interferometer. What I have is the beamsplitter/moving mirror portion (essentially the optical/mechanical portion of a Michaelson Interferometer) and the electronics which controlled the moving mirror, counted laser fringes and triggered the A/D. What I don't have is circuit schematics that tell me how to connect power to these parts and what voltages, and how to cable the electronics to the interferometer portion. Any tips on how to efficiently reconstruct circuit diagrams from inspection of the electronics? There are two cards, with standard TTL and analog parts. The printed circuit has a design date of 1985, while the IC's have 88-89 dates. Doug