Displacement measurement using an optoelectronic oscillator with an intra-loop Michelson interferometer.

We report on measurement of small displacements with sub-nanometer precision using an optoelectronic oscillator (OEO) with an intra-loop Michelson interferometer. In comparison with conventional homodyne and heterodyne detection methods, where displacement appears as a power change or a phase shift, respectively, in the OEO detection, the displacement produces a shift in the oscillation frequency. In comparison with typical OEO sensors, where the frequency shift is proportional to the OEO oscillation frequency in radio-frequency domain, the frequency shift in our method with an intra-loop interferometer is proportional to an optical frequency. We constructed a hybrid apparatus and compared characteristics of the OEO and heterodyne detection methods.