What about String-pots?
With a little bit of calibration/interpolation, you can probably achieve the accuracy you're after
Or LVDTs?
http://www.lvdt.co.uk/pdf/AML-E.pdf
Or finally magnetic encoders;
http://www.renishaw.com/en/magnetic-linear-encoders-and-magnetic-ring-encoders--9802
Any of those are simpler/easier to implement that optical or US solutions, and should give you the kind of accuracy you're after.
String pots aren't a bad idea, except when you have to worry about humidity changes and string stretch. Good for being able to replace them though, and wouldn't be too hard to implement a centering capability with end cap limit switches. The LVDT's are quite a bit more accurate, IMHO, used them for flight control position sensing on Helicopters. Currently work with encoders and wheels that measure speed/distance for conveyor belts. They work well if you can find the right combination to get the 7.5 degree measurements to equal a specific linear measurement.
String pots aren't a bad idea, except when you have to worry about humidity changes and string stretch. Good for being able to replace them though, and wouldn't be too hard to implement a centering capability with end cap limit switches. The LVDT's are quite a bit more accurate, IMHO, used them for flight control position sensing on Helicopters. Currently work with encoders and wheels that measure speed/distance for conveyor belts. They work well if you can find the right combination to get the 7.5 degree measurements to equal a specific linear measurement.
Regular calibration (yearly) should take care of any stretch in the steel wire used for the pots strings.. not sure how humidity would affect that. (temperature is likely to much bigger effect).
As for the encoders, take a look at the link.. I meant linear magnetic encoders, they use magnetic strips with alternating poles with a moving reader head. the accuracy can be down to a micron if required, 20microns is quite common (0.02mm). Bit more difficult to use but worth it if accuracy and reliability is what you need