For thrust position probes and radial vibration probes on rotating machinery we use a spindle micrometer to check accuracy and linearity over the full range. The probes we use are manufactured by Bently Nevada. I believe we buy the spindle micrometers from them as well. These probes have a linear range from about 0.010" to about 0.075" and are normally gapped at 0.050".
if you select tech manuals, then select E308 will be a dislay that gives detail.
you'll notice the generic cal procedure doesnot give full scale travel as a given, but is user defined. for my use i want my display to be in inches. but if it is in a control loop, the actual bump to bump travel is set for 0 to 100%
adding to my previous post, I have used a standard nut as calibration block, and my calipers to determine what actual displacement was.
to determine your actual lineartiy, you can use incremental shims and record output. I think you'll find the linearity of most off the shelf sensors better than you're ability to measure