基于窗口傅里叶变换剪切干涉法波前检测

提出了一种利用二维窗口傅里叶变换从径向剪切干涉条纹中准确得到波前的重建技术。首先对剪切干涉条纹做二维窗口傅里叶变换，设置阈值和频率积分范围后，进行二维窗口傅里叶逆变换，然后对包裹相位做去载频和相位展开处理得到相位差分布，最后使用波前迭代算法从相位差中复原实际波前。模拟计算表明，使用该方法最大相位复原误差为0.82%，均方根值为0.020 9 rad，实验结果验证了该方法的有效性。同时也对窗口傅里叶变换的关键参数，如窗函数的选择、窗口大小的确定以及阈值的选取等进行了简要讨论。与传统傅里叶变换法(FFT)相比，基于窗口傅里叶变换的剪切干涉波前检测法有更高的精度和稳定性，为波前检测提供一种新的处理方法。

Wavefront measurement based on windowed Fourier transform by use of radial shearing interferometer

A wavefront reconstruction technique which obtains wavefront from a radial shearing interferometer with high precision based on two-dimensional windowed Fourier transform (WFT) is presented. First, the radial shearing fringe is processed by WFT, and by inverse WFT after setting threshold and frequency range of integration. Then wavefront phase difference distribution is obtained by the treatment of removal-carrier frequency and phase unwrapping. Finally, the actual wavefront can be reconstructed from phase difference by wavefront iterative algorithm. The simulations show that the maximum phase reconstruction error is 0.82%, RMS is 0.020 9 rad. Also corresponding experiments are conducted for comparison. In addition, window function selection, window size and threshold setting are briefly discussed. Compared with the traditional Fourier transform method (FFT), shearing interferometer wavefront measurement based on windowed Fourier transform has higher precision and stability, which provides a new processing method for wavefront measurement.