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叠栅条纹相位差测量是光栅位移测量中的关键技术,在两块光栅相对运动过程中,叠栅条纹信号的频率会因光栅夹角误差的存在而发生偏移,采用传统多相位快速傅里叶变换(MPFFT)算法计算任意时刻叠栅条纹相位值会产生测量误差,导致相位差测量不准确。为了减少频偏所产生的相位测量误差,提出了一种校正MPFFT相位测量算法,推导出了基于相位差校正法的MPFFT谱校正模型。仿真结果表明,在无噪声情况下,当光栅夹角误差为0.1°时,信号的最大频率偏移量约为4.19kHz,传统MPFFT相位测量误差大于100°,经相位校正后,相位测量误差小于0.2°,相位差测量误差小于0.004°;在高斯噪声和谐波干扰情况下,相位差测量误差小于0.2°,当取栅距为20μm时,相位差测量误差所产生的位移测量误差小于0.0111μm,为光栅位移纳米级测量提供了参考。
The moiré fringe phase difference measurement is the key technology in the measurement of grating displacement. During the relative movement of two rasters, the frequency of the moiré fringe signal will be shifted due to the error of the included angle of the grating. The traditional multi-phase fast Fourier transform The Leaf Transform (MPFFT) algorithm, which calculates the moire fringe phase value at any time, produces measurement errors that result in inaccurate phase measurements. In order to reduce the phase error caused by frequency offset, a correction algorithm for MPFFT phase measurement is proposed and the MPFFT spectral correction model based on phase difference correction is derived. The simulation results show that the maximum frequency offset of the signal is about 4.19kHz when the included angle error of the grating is 0.1 ° and the error of the phase measurement of the conventional MPFFT is greater than 100 °. The phase error after phase correction is less than 0.2 °, and the error of phase difference measurement is less than 0.004 °. In the case of Gaussian noise and harmonic interference, the phase difference measurement error is less than 0.2 °. When the grating pitch is 20 μm, the error of phase measurement error is less than 0.0111 μm , Provides a reference for grating displacement nanometer measurement.