Very precise way of measuring small distances?
If contact is okay, you can use a digital dial indicator. They use an incremental measuring method internally so they need to be zero'd. Accuracy is about 0.001" for the cheap ones and range is typically at least an inch. 

Price ranges from about $25 to $500 depending on brand and performance. 

You can interface to the internal battery-powered electronics- they usually have a proprietary serial interface with 1.5V levels. There are a few standards for the interface- Mitutoyo is one- and the Chinese ones are generally similar to each other (and different from Mitutoyo).