Linear potentiometer as stand in for dial indicator?

I have a project that requires measuring the thickness of an object at several locations and taking the average of those measurements.
You can get software that will take measurements from digital dial indicators, but it is limited, and for my application, digital dial indicators are too bulky and won’t fit together closely enough.

I am wondering if spring loaded linear potentiometers would work well as a stand in for dial indicators. I am not familiar with these devices and don’t know what kind of precision they have. I would most likely be using them with an arduino or something similar and would need about .002" or .003" resolution.

If anyone has any input or advice I’d really appreciate it!

AFAIK, a linear potentiometer that can resolve that small a of a distance accurately will be a custom part that costs a thousand dollars per unit. It’s been 40 years since I worked in the precision potentiometer industry but things have only gotten more expensive and harder to find since I moved on.

A linear optical encoder is much better choice however that may be far more expensive than an off the shelf measuring device.