针对非球面光学元件面形检测中的欠采样问题，提出了一种欠采样包裹相位图的恢复方法。首先，将原始欠采样包裹相位图在水平和竖直两个方向进行一个像素的错位相减，得到两个包裹相位差图。其次，对这两个包裹相位差图进行解包裹运算，得到两个解包裹相位差图。最后，应用傅里叶变换和最小二乘法恢复出连续的相位分布。模拟结果表明该方法可以高精度地对欠采样包裹相位图进行恢复重建。该方法与现有干涉仪相结合，有望实现非球面光学元件面形的检测。关键词傅里叶光学；欠采样；包裹相位；剪切干涉； 傅里叶变换；最小二乘法

Aiming at the problem of undersampling in the aspheric testing, a method for phase recovery from a single undersampled wrapped phase map is presented. Firstly, two wrapped phase differences are gained by subtracting the original undersampled wrapped phase with its two sheared copies along two orthogonal directions while the sheared value is 1 pixel. Secondly, the unwrapping is performed for the two wrapped phase differences. Finally, the searched phase is obtained by using the Fourier transform and least square algorithm. The simulation results show that the method can retrieve the wave-front with high accuracy. Using the method, the aspheric surface can be tested by current interferometers.