基于卡尔曼滤波的激光外差干涉位移测量误差补偿

Error compensation for laser heterodyne interferometric displacement measurement based on Kalman filter

针对激光外差干涉仪测量过程中测量镜随被测对象旋转而导致的位移测量误差,提出了一种基于卡尔曼滤波的激光外差干涉位移测量补偿方法。根据测量镜转角和测量光束光斑位置变化对应关系,利用位置敏感探测器(PSD)和位置电压信号卡尔曼滤波方法测得降噪后的光斑位置变化,从而获得更为准确的转角测量结果,最后根据转角与位移的解耦数学模型利用测得的转角进行位移补偿。为验证滤波算法和位移补偿方法的可行性和有效性,搭建激光外差干涉测量实验装置,分别进行光斑位置稳定性测量实验、角度测量验证实验和激光外差干涉位移测量补偿实验。实验结果表明:经卡尔曼滤波降噪后系统装置测得的光斑位置抖动标准差从0.52μm降至0.18μm,测量的转角与索雷博六自由度转台的转角偏差在±1.38×10^(-4°)内,对M-531.DD线性导轨200 mm量程内的位移和转角进行测量,将测得的转角进行位移补偿后,系统的位移测量结果与M-531.DD线性导轨位移的标准差从1.55μm减小到0.29μm。

In laser heterodyne interferometry,displacement measurement errors arise from the rotation of the measuring mirror alongside the measured object.To address this,the paper introduces a compensation technique using a Kalman filter for laser heterodyne interferometric displacement measurements.By analyz⁃ing the correlation between the measuring mirror's rotational angle and the measuring beam spot's position shift,a position sensitive detector(PSD)is employed to gauge the rotational angle.Enhancing angle mea⁃surement precision,the Kalman filter method is utilized to diminish the noise in the PSD's position voltage signal,thereby accurately determining the spot's position shift.Subsequently,displacement is compensat⁃ed based on the measured rotational angle,utilizing a decoupling mathematical model that separates rota⁃tional angle from displacement.To assess the proposed filtering algorithm and displacement measurement compensation method's viability and efficiency, an experimental laser heterodyne interferometric setup wasestablished. Experiments conducted included spot position stability measurement, rotational angle mea⁃surement verification, and laser heterodyne interferometric displacement measurement and compensation.Results demonstrate a reduction in the standard deviation of spot position drifts from 0.52 μm to 0.18 μmpost-Kalman filter denoising. Moreover, the discrepancy between measured angles and the Thorlabs 6-DOF motion stage's rotational angles remain within ±1.38×10^(-4° ). Displacement and rotational angle ofthe M-531. DD linear stage over a 200 mm range are measured. Following compensation with the mea⁃sured angle, the standard deviation between the displacement measurement results and the M-531.DD lin⁃ear stage's positionings decreases from 1.55 μm to 0.29 μm.