19-picometer mechanical step displacement measurement using heterodyne interferometer with phase-locked loop and piezoelectric driving flexure-stage

In this paper, we discuss 20-picometer-order mechanical step displacement measurements using a heterodyne interferometer with a phase-locked loop (PLL) and two piezoelectric (PZT) driving flexure-stages. First, the phase meter for heterodyne interferometry using one simple digital PLL is developed. Two inputs and one output of the single PLL are the reference and measurement signals of the heterodyne interferometer and the phase shift due to the movement of the target mirror, respectively. The PLL includes an active phase shifter, a mixer (multiplier), a low-pass filter combined with an averaging operation, and an integrator. In electronics evaluation of the PLL, the PLL shows a phase resolution of 174 mu rad with 4.2 mu rad noise (standard deviation) and a phase noise floor of 3 mu rad/ root Hz above 0.2 Hz with an output sampling rate of 200 Hz. Using the single PLL, a four-pass normal commercial heterodyne interferometer, and high-stiff-parallel spring stage driven by PZT actuator, we demonstrate the actuations and measurements of mechanical step displacements of 19 pm (1.5 mrad) and a displacement noise floor of 1.1 pm/ root Hz (90 mu rad/ root Hz) above 1 Hz in normal air. In the paper, the principle, instrumentation, and experimental results are discussed. (C) 2020 Elsevier B.V. All rights reserved.