A Transducer, sometimes termed Probe is a device that converts one form of energy into another form of energy, be it mechanical, electrical, magnetic or chemical.
IMT devices mostly consist of the mechanical to electrical conversion.
The Half Bridge in it’s simplest form consists of two opposed coils which are energised with an ac signal, an armature with high magnetic properties, when equidistance between the coils, induces an equal and opposite output voltage phase from the coils, which cancel each other out. The output is thus zero.
Movement of the armature in any direction would move the balance of output, and thus the phase.
The output would normally be in proportion to the movement in a near linear curve over a set distance. The direction can be ascertained from the output phase. Non-linearity of IMT transducers can vary from type to type, but generally a typical value would be 0.3% over it’s given range.