Zoom into picometer: A picoscale equivalent phase-difference-generating method for testing heterodyne interferometers without ultraprecision stages

A simple and low-budget method aiming to generate phase difference equivalent to picoscale-measured displacements of heterodyne interferometers is proposed. By changing the length of an interference arm in an interferometer-like optical configuration, a small phase difference between the two wavelengths is generated for creating the same effect as a picoscale-measured displacement of the heterodyne interferometer. It is derived and experimentally demonstrated that the zoom factor, defined as the ratio of displacements in a heterodyne interferometer and the proposed method leading to the same phase difference, is proportional to the beat frequency and generally in a scale of 10^-9. Thus, instead of ultraprecision piezo-stages, only a commercial linear guide rail is equipped in the method, and rigorous vibrating isolation is not necessary. The method has been already used to evaluate signal-processing electronics of a heterodyne grating interferometer.