Hi Davek0974,
some good vid's on youtube about them. Reamarkably simple tho, three coils side by side
with the centre one energised by some AC voltage, few kHz is common, mine is 160kHz.
A magnetic core slips down the middle of the coils, if nearer one end than tother the outer coil
gets energised by transformer action, shift the core to the other end and that coil becomes energised.
Little bit of electronics and you have an infinite resolution linear gage with core in the centre
equal zero V.
They are available comercically as rugged contact free transducers. One with 1mm stroke but centre
accuracy of 100nm right through to 200mm and more stroke with centre accuracy of 20um.
I can't afford to buy one but I can make one! My current one offers 38mV/mm sensitivity and a linear
range of plus/minus 2mm. Not great but getting better.
Craig