Ideas to measure 2D position of an object constrained to X-Y plane
Idea 4: This will give you the best accuracy. You will need the following:


2x Precision linear slides.
2x Precision linear encoders.
2x Metal linkages.




Attach a linear encoder to each linear slide. Arrange the two slides 90º apart, and attach the object to the sliders using the linkages. Linear encoders like this are used for precision measurement applications. Using this method you could easily achieve 0.01mm resolution, and 0.1mm accuracy, and will probably do much better than that.