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4.19 kHz，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20 μm时，相位差测量误差所产生的位移测量误差小于0.0111 μm，为光栅位移纳米级测量提供了参考。

Moire fringe phase difference measurement is the key technology of grating displacement measurement, when the two gratings are in relative movement, moire fringe signal frequency is offset because there is an angle error between the two gratings, traditional multi-phase fast Fourier transform (MPFFT) algorithm is used to calculate moire fringe phase value at any time, it will produce measurement errors, resulting in phase difference measurement is not accurate. To reduce the phase measurement error caused by frequency offset, a phase measurement algorithm of correcting MPFFT is proposed, and phase correction model of MPFFT spectrum based on phase difference correction method is deduced. Simulation results show that in the absence of noise, when the angle error is 0.1°, moire fringe maximum signal frequency offset is 4.19 kHz, the phase measurement error of traditional MPFFT is more than 100°, phase measurement error is less than 0.2°and the phase difference measurement error is less than 0.004° after correction in the presence of Gaussian noise and harmonics, the phase difference measurement error is less than 0.2°. When the pitch is 20 μm, the corresponding grating displacement measurement error is less than 0.0111 μm, it provides a reference for the grating nanoscale displacement measurement.