Kowarsch Robert, Rembe Christian
Institute of Electrical Information Technology, Clausthal University of Technology, Leibnizstrasse 28, 38678, Clausthal-Zellerfeld, Germany.
Sci Rep. 2021 Sep 7;11(1):17753. doi: 10.1038/s41598-021-96684-y.
The lateral or transverse resolution of single-point interferometers for vibration measurement is especially critical for microelectromechanical systems (MEMS) vibrating up to the gigahertz range. In this regime, the acoustic wavelengths are typically in the range of the size of the laser focus. Thus, a successful vibration measurement requires distinct knowledge about the lateral resolution limit and its dependencies with instrumentation parameters. In this paper, we derive an analytic approximation formula, which allows for estimation of the systematic measurement deviation of the vibration amplitude and, thus, a definition of the lateral resolution limit of single-point interferometers for vibration measurement. Further, a compensation and an optimum numerical aperture are proposed the reduce the measurement deviation. For this, the model includes a laser-interferometer microscope of Mach-Zehnder type with Gaussian laser beams considering the Gouy effect and wavefront curvature. As a measurement scenario, an unidirectional surface acoustic wave (SAW) is regarded. The theoretic findings have been validated in the experiment with a representative vibration measurement on a SAW filter at [Formula: see text] with our heterodyne laser-Doppler interferometer with offset-locked semiconductor lasers. The provided formulas help instrument designers and users to choose suitable instrument parameters, especially the numerical aperture of the utilized microscope objective.
用于振动测量的单点干涉仪的横向或横向分辨率对于振动频率高达吉赫兹范围的微机电系统（MEMS）尤为关键。在这种情况下，声波波长通常在激光焦点尺寸范围内。因此，成功的振动测量需要明确了解横向分辨率极限及其与仪器参数的相关性。在本文中，我们推导了一个解析近似公式，该公式可用于估计振动幅度的系统测量偏差，从而定义用于振动测量的单点干涉仪的横向分辨率极限。此外，还提出了一种补偿方法和最佳数值孔径以减小测量偏差。为此，该模型包括一个马赫 - 曾德尔型激光干涉显微镜，其具有考虑古依效应和波前曲率的高斯激光束。作为一种测量场景，考虑了单向表面声波（SAW）。通过我们的带有偏置锁定半导体激光器的外差激光多普勒干涉仪，在[公式：见原文]下对SAW滤波器进行代表性振动测量的实验中验证了理论结果。所提供的公式有助于仪器设计者和用户选择合适的仪器参数，特别是所使用显微镜物镜的数值孔径。
