Polydyne displacement interferometer using frequency-modulated light

A radio-frequency Frequency-Modulated (FM) signal is used to diffract a He-Ne laser beam through an Acousto-Optic Modulator (AOM). Due to the modulation of the FM signal, the measured spectra of the diffracted beams comprise a series of phase-synchronized harmonics that have exact integer frequency separation. The first diffraction side-beam emerging from the AOM is selected by a slit to be used in a polydyne displacement interferometer in a Michelson interferometer topology. The displacement measurement is derived from the phase measurement of selected modulation harmonic pairs. Individual harmonic frequency amplitudes are measured using discrete Fourier transform applied to the signal from a single photodetector. Phase signals are derived from the changes in the amplitudes of different harmonic pairs (typically odd-even pairs) with the phase being extracted using a standard quadrature method. In this study, two different modulation frequencies of 5 and 10 kHz are used at different modulation depths. The measured displacements by different harmonic pairs are compared with a commercial heterodyne interferometer being used as a reference for these studies. Measurements obtained from five different harmonic pairs when the moving mirror of the interferometer is scanned over ranges up to 10 μm all show differences of less than 50 nm from the reference interferometer measurements. A drift test was also used to evaluate the differences between the polydyne interferometer and reference measurements that had different optical path lengths of approximately 25 mm and 50 mm, respectively. The drift test results indicate that about half of the differences can be attributed to temperature, pressure, and humidity variations. Other influences include Abbe and thermal expansion effects. Rough magnitude estimates using simple models for these two effects can account for remaining observed deviations.