One of the primary tools for precision surfaces is the interference microscope, which came out commercially in the 1950's. Computer technology had come far enough by the early 1980's that the technique was revived as viable for non-PhD's to use.
One of the big names in interferometry is Zygo, of which I received the head of one of the old, (but not too old) heads for one of their interference microscopes, the Maxim 3D 5600 or 5700, it looks like. Here are some pictures!
Opening up the top cover reveals a bunch of stuff.
First, we see that the handles on the right side actuate the head to tip/tilt it as needed
for navigation!