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

Abstract

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