Simple digital phase-measuring algorithm for low-noise heterodyne interferometry

We present a digital algorithm for measuring the phase difference between two sinusoidal signals that combines the modified fringe-counting method with two-sample zero crossing to enable sequential signal processing. This technique can be applied to a phase meter for measuring dynamic phase differences with high resolution, particularly for heterodyne interferometry. The floor noise obtained from a demonstration with an electrical apparatus is $5\times10^{-8} \mathrm{rad/\sqrt{Hz}}$ at frequencies above approximately 0.1 Hz. In addition, by applying this method to a commercial heterodyne interferometer, the floor-noise level is confirmed to be $7\times10^{-14} \mathrm{m/\sqrt{Hz}}$ from 4 kHz to 1 MHz. We also confirm the validity of the algorithm by comparing its results with those from a standard homodyne interferometer for measuring shock-motion peak acceleration greater than 5000 m/s^2 and a 10 mm stroke.