Error compensation for laser heterodyne interferometric displacement measurement based on Kalman filter
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 was established.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 μm post-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 of the 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.
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