Research Article

2-dimensional in-plane displacement measurement system at fast sampling rate of 5 kHz using sinusoidal phase modulation interferometer

¹ National Institute of Technology, Gunma College, 850, Toriba Maebashi, Gunma, 371-8530, Japan
² Nagaoka University of Technology, 1603-1, Kamitomioka, Nagaoka, Niigata 940-2188, Japan

^* Corresponding author: masatoaa@vos.nagaokaut.ac.jp

Received: 31 January 2025
Accepted: 6 June 2025

Abstract

Dynamic and high-resolution air fluctuation (wavefront aberration) measurements are necessary for precision interferometry and astronomical observations. In this paper, to solve the problem, we propose a measurement system that uses sinusoidal phase modulation interferometry to observe 2-dimensional (2-D) in-plane displacements with sub-nm resolution and fast speed sampling rate of 5 kHz. The interferometer consists of a Michelson type interferometer incorporating an electric-optic modulator with a modulation frequency of 5 kHz and a high-speed camera synchronized to a clock signal at a frequency of 60 kHz, 12 times the modulation frequency. Phase demodulation of each pixel in the camera is performed by acquiring the interference signal to that pixel synchronously with the sampling signal and performing a specific addition and subtraction between the signals obtained synchronously. By applying this procedure to all pixels in the camera, 2-D in-plane displacements can be obtained. In this paper, we report on the measurement equipment, the demodulation principle, the pre-filter for noise reduction and experimental results. In the experiments, 2-D in-plane displacements with sub-nm resolution are confirmed at a sampling rate of 5 kHz. This technique has the potential to measure fast, dynamic deformation of object surfaces and dynamic wavefront aberrations due to air fluctuations. Based on the proposed demodulation method, interferometers with MHz-class sampling rates are possible by using faster electro-optical modulator and high-speed camera.