面向高动态纳米测量的光栅莫尔条纹信号误差机理及实时补偿研究

In this project, the dynamic characteristics and error mechanism of optical grating moiré fringe signal in measurement will be analyzed for the first time, on the basis of which the real-time compensation theory of moiré fringe signal suitable for high magnification electronic subdivision will be investigated. First, data-driven model identification will be employed to establish the dynamic model of moiré fringe signal and reveal the error mechanism, providing a theoretical basis for using model inversion method to reduce signal nonlinear distortion induced by optoelectronic receiving system and sampling noise. Then, in consideration of the features of moiré fringe signal in dynamic measurement, a correlation function method based on varying sampling rate is proposed to detect the phase difference of frequency-varying signal for its orthogonal deviation compensation. And a fundamental component extraction method combining instant frequency estimation and modified empirical mode decomposition is presented to compensate the sinusoidal deviation of the signal. Using these methods, the signal attenuation and distortion induced by the grating optoelectronic receiving system can be eliminated, so that the quality of the moiré fringe signal in highly dynamic measurement can meet the requirement for 10000 times electronic subdivision to implement nano-precision measurement. This project will provide a theoretical basis for achieving nano-precision in highly dynamic measurement and offer a new idea for the measurement in the future ultra-precision manufacturing equipments.

本项目首次分析光栅莫尔条纹信号在测量过程中的动态特性，对莫尔条纹测量的误差机理进行研究，在此基础上探究适用于高倍电子学细分的莫尔条纹信号实时补偿理论。项目首先运用数据驱动的模型辨识方法建立莫尔条纹信号的动态模型，揭示动态信号的误差机理，为采用模型求逆法消除光电接收系统和采样噪声引入的信号非线性畸变提供理论基础；其次，针对莫尔条纹信号在动态测量过程中的特点，提出基于变采样率的相关函数法检测变频信号的相位差，用来补偿信号的正交偏差；提出基于瞬时频率估计和改进经验模态分解法相结合的基波提取方法，用来补偿信号的正弦偏差。应用上述方法可消除高速测量时光栅光电接收系统引入的信号衰减和畸变，使莫尔条纹的信号质量在高动态测量时满足10000倍电子学细分的要求，进而实现纳米精度的位置测量。本研究可为光栅在高动态测量中实现纳米级精度提供理论支持，为未来超精密加工设备的测量提供一个新的研究思路。

莫尔条纹信号的质量是影响光栅测量分辨率的关键因素。受光电接收系统带宽和采样电路噪声的影响，在动态测量过程中莫尔条纹信号的正交性和谐波成分会发生恶化，引入细分误差。本项目对莫尔条纹测量的误差机理进行了分析，研究了用于高倍电子学细分的莫尔条纹信号补偿理论。首先，建立了莫尔条纹信号的数学模型，提出了模型构建和系数估计的方法。然后，基于变采样率的相关函数法对莫尔条纹信号的正交偏差进行测量，解决了正交性补偿问题。最后，针对莫尔条纹信号的谐波污染问题，提出了基于改进经验模态分解的基波提取方法，解决了正弦性补偿问题。本项目还初步探索了基于参数估计的正交性和正弦性补偿方法。相关仿真与实验验证了上述方法的可行性和有效性。

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