Application of the continuous wavelet transform in periodic error compensation
Application of the continuous wavelet transform in periodic error compensation
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DOI：
10.1016/j.precisioneng.2016.01.008
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发表时间：
2016-04
影响因子：
3.6
通讯作者：
Chao Lu;John R. Troutman;T. Schmitz;J. Ellis;Joshua A. Tarbutton
中科院分区：
文献类型：
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作者：
Chao Lu;John R. Troutman;T. Schmitz;J. Ellis;Joshua A. Tarbutton
介绍了一种新的基于离散时间连续小波变换（DTCWT）的外差位移测量干涉测量算法，该算法能够实时量化和补偿等速和非等速运动的周期误差。该方法通过测量不同阶位的相位和幅值信息来识别周期误差（周期误差建模为纯正弦信号的和），通过将各阶位的幅值组合重建周期误差，并通过从干涉仪测量的位移信号中减去重建误差来补偿周期误差。通过将补偿结果与传统的等速运动频域方法进行比较，验证了该算法的有效性。该算法成功地将一阶周期误差幅度从4 nm减小到0.24 nm（减小94%），将二阶周期误差幅度从2.5 nm减小到0.3 nm（减小88%）。该算法还克服了现有方法的局限性，降低了非等速运动的周期误差。
This paper introduces a new discrete time continuous wavelet transform (DTCWT)-based algorithm, which can be implemented in real time to quantify and compensate periodic error for constant and non-constant velocity motion in heterodyne displacement measuring interferometry. It identifies the periodic error by measuring the phase and amplitude information at different orders (the periodic error is modeled as a summation of pure sine signals), reconstructs the periodic error by combining the magnitudes for all orders, and compensates the periodic error by subtracting the reconstructed error from the displacement signal measured by the interferometer. The algorithm is validated by comparing the compensated results with a traditional frequency domain approach for constant velocity motion. The algorithm demonstrates successful reduction of the first order periodic error amplitude from 4 nm to 0.24 nm (a 94% decrease) and a reduction of the second order periodic error from 2.5 nm to 0.3 nm (an 88% decrease). The algorithm also reduces periodic errors for non-constant velocity motion overcoming limitations of existing methods.