Linear capacitive displacement sensor with frequency readout

A simple, inherently linear technique for measuring changes in the separation of the mirrors of an optical cavity is reported. The capacitor, made up of the reflective metallic coatings, is part of a feedback loop which adjusts the frequency of an oscillator to be proportional to the mirror separation. A linearity of 0.2 percent full scale was achieved for separations up to 0.5 mm with a resolution of 10 nm.