Measuring a very fine wire with 10 µm precision

robtillaart:
Lets try to design the sensor you need,

design 1: - conductive wire

imagine a V shaped sensor that guides the wire.
depending on the thickness of the wire it will be higher or lower in the V shape
make the sides of the V of a conducting material with known (relative to wire high) resistance
The place of the wire will change the resistance of the V as the level where the wire is short-cuts the current.

You do know the wire is insulated (and not BARE). It's a "magnet" wire, the kind used to make coils. If you strip the insulation just so you can measure it's resistance, well, you just made your coil useless.

I think the OP needs to visit an audio transformer manufacturer so he can see how it's done. These guys don't measure their wire diameters to micron precision or use lasers or microscopes as they wind. But they do measure their inductance and DC resistance values. They don't care where the loop ends. Overwind a few extra turns, measure, unwind, measure, tap it, then tape it. Done.

Have you guys seen the insides of an audio transformer?