Just build up something like these for your closed loop measurements:
http://www.zygo.com/?/products/zmi/
I found this just typing it in a search engine. These measure to a couple of nm, so well beyond your actual needs. Probably some used ones out there.
Most of these are laser based and use the concept of measuring the constructive and destructive interference of light waves. Basically, you get a "peak" and "trough" brightness in the light signal.
From a practical standpoint, the shorter the wavelength of the laser, the more accurate (and more expensive). Blue light is approx 460nm (about 1/2 micron) and red is nominally 630 ish nm. 1000 nm = 1 micron. Red solid state lasers are practically free now days, while blue / green cost real money.
Just a tidbit, this method is how the official standard meter is defined.
Keep in mind, you only need movement in 1 dimension, over a very short distance. I think the hardest part will be picking your reference points to mount and measure from. Small temperature changes will be both your friend, and your challenge, regardless of movement method selected.