基于连续小波变换的激光外差干涉非线性误差补偿  

Nonlinear Error Compensation Method for Laser Heterodyne Interferometry Based on Continuous Wavelet Transform

作　　者：王煜[1] 陈洪芳[1] Wang Yu;Chen Hongfang(Beijing Engineering Research Center of Precision Measurement Technology and Instruments,Department of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学材料与制造学部北京市精密测控技术与仪器工程技术研究中心,北京100124

出　　处：《中国激光》2022年第21期139-144,共6页Chinese Journal of Lasers

基　　金：国家自然科学基金(52175491)。

摘　　要：测量分辨率和精度的不断提高是激光外差干涉测量的发展趋势,而抑制激光外差干涉测量精度进一步提升的主要因素是周期性非线性误差。提出了一种基于连续小波变换的激光外差干涉非线性误差补偿方法。对非线性误差函数进行Morlet小波变换,利用小波系数矩阵信息提取小波脊线,分析小波脊线上的特征信息,重构一次谐波非线性误差;利用最小二乘非线性拟合方法迭代拟合出二次谐波非线性误差。实验结果表明,将此方法应用于激光外差干涉测量系统中,非线性误差分量由5.97 nm减小到1.09 nm,非线性误差分量减小至原来的18%。该方法可有效抑制非线性误差的影响,并提高激光外差干涉测量的精度。Objective The development trend of laser heterodyne interferometry is the enhancement of measurement resolution and accuracy. The primary factor that hinders the further enhancement of laser heterodyne interferometry accuracy is the periodic nonlinear error. This research proposes a nonlinear error compensation approach for laser heterodyne interferometry based on wavelet transform. The Morlet wavelet transform is employed for the nonlinear error function, and the wavelet ridge is extracted from the wavelet coefficient matrix’s information. Next, the characteristic information of wavelet ridge line is examined and the first harmonic nonlinear error is rebuilt. After compensating for the first harmonic nonlinear error based on the wavelet transform approach, the second harmonic nonlinear error is fitted iteratively by the least-squares nonlinear fitting approach.Methods First, a nonlinear error compensation approach based on a wavelet transform is proposed. Periodic nonlinear errors in laser heterodyne interference systems can be modeled as the superposition of pure sine waves. The wavelet family is created by changing the time and scale factors of complex Morlet wavelet. The pure sinusoidal model is converted using wavelet transform based on the Morlet wavelet family. By further computation, the wavelet coefficient’s modulus and phase are obtained, so that the wavelet ridge is extracted. When the modulus of the wavelet system is the largest at the ridge position, the corresponding scale corresponds to the first harmonic nonlinear error frequency. The first harmonic nonlinear error phase is the corresponding phase. The second harmonic nonlinear error frequency is twice that of the first harmonic nonlinear error. Additionally, the second harmonic nonlinear error phase is achieved under the corresponding frequency’s scale. Based on this, the first harmonic nonlinear error function’s amplitude is computed, and the rebuilt first harmonic nonlinear error function model is achieved. After compensating for the fi

关 键 词：测量 激光外差干涉 非线性误差 连续小波变换 最小二乘非线性拟合 

分 类 号：TH741[机械工程—光学工程]