Sub-miniature linear sensor

I am asking the impossible, but here goes:
I need a sensor that can sense movement of 0.5mm to a resolution of at least
0.01mm, which is similar resolution to the cheap vernier callipers that are available for $20 or so. The problem is the space available, the moving part fits in a 5mm diameter tube and seperated by 2mm from a PCB. It is possible to fit the signal conditioning electronics remotely, but the actual sensor must fit in the 5mm x 2mm cylindrical space.
Am I dreaming? Even a pointer to a possible technology would help.
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