kingofwoods:
Pololu Carrier with Sharp GP2Y0D805Z0F Digital Distance Sensor 5cm Could this do? it says it doesn't show distance
No.
Google linear displacement sensor
There are a number of different types of linear displacement sensors (non-contact eddy current or capacitive, contact LVDT...) that may work depending on details you haven't shared. At 0.01mm resolution or better, none of them will be cheap.