Study on sinusoidal estimation deviation of electrostatic actuated MEMS mirror torsion angle

静电MEMS微镜谐振扭转角轨迹正弦估计的偏差研究

¹ China Mobile IoT Company Limited, Chongqing 401121, China
² Ministry of Education Key Lab of Micro/Nano Systems for Aerospace, Northwestern Polytechnical University, Xi'an 710072, China

Received: 22 June 2022

Abstract

Electrostatic MEMS micromirrors usually work in resonant state to obtain large amplitude of torsion angle. The real-time prediction of MEMS micromirror torsion angle is calculated according to the measured resonant amplitude and phase under the assumption that the relationship between the torsion angle and time is sinusoidal. However, there are few reports on the deviation of this torsion angle predication based on sinusoidal assumption. In this paper, the real resonant torsion trajectory of C1100 MEMS micromirror under different driving frequencies and voltages is measured by using microscopic laser Doppler method, and the deviation between the real trajectory and the trajectory fitted by sinusoidal curve is compared. The results show that the real trajectory of the MEMS micromirror driven by square wave is not completely consistent with the sinusoidal estimation, and the deviation increases with the increase of the torsional angle amplitude. By obtaining the frequency domain components of the torsion angle signal using FFT method, the main reason of this prediction deviation is due to composition of harmonic signals on base frequency signal. The research results reveal that the sinusoidal assumption method is only suitable for situations when the optical angle accuracy is less than 0.1°.

摘要

静电MEMS微镜扭转角实时获取通常是通过测量出微镜的谐振幅值和相位, 按照正弦关系去估计任意时刻的扭转角数值, 但关于这种正弦轨迹的假设存在多大的偏差的相关报道很少。使用显微激光多普勒方法, 对C1100型MEMS微镜在不同驱动频率和驱动电压下的真实谐振扭转角轨迹进行了测量, 并对比了真实轨迹和用正弦曲线拟合轨迹的偏差。结果证明, 方波驱动下的MEMS微镜, 其真实轨迹和正弦拟合轨迹并不完全符合, 存在随扭转角振幅增大而增大的偏差。通过对真实轨迹时域信号进行快速傅里叶变换和频域分析, 可以证明偏差存在的主要原因是实测轨迹除了有频率为驱动方波频率1/2倍的正弦信号以外, 还叠加了频率为驱动方波频率1倍和3/2倍等高频正弦信号。研究结果表明, 按照正弦曲线来估计光学角的方法仅适用于光学扫描角精度要求低于0.1°的场景。