二维剪切干涉波前的最小二乘法重建

提出了一种可以快捷地重建原始的二维波前的新算法。对于分别在相互垂直方向上横向切干涉获得的两个差分波前，用快速傅里叶变换首先计算出待测原始波前存x和y方向的估计分布，然后利用误差计算的最小二乘法进行二维拟合，可以恢复出待测波前的二维分布。提出的理论可以应用于剪切量大于1个采样间隔的二维波前重建问题，解决了已有的二维剪切干涉波前重建技术中要求剪切量等于采样间隔的限制。研究了剪切量和噪声对重建精度的影响．和其它算法进行了比较．给出了数值实验结果和分析讨沦。结果表明该算法速度快，对噪声有较强的抵抗力．有望在实际的剪切干涉测量中获得应用。

Wave Front Reconstruction from Shearing Interferograms Using Least Square Fitting

Authors propose a novel technique to reconstruct two-dimensional wave front from two difference wave fronts that are measured in shearing interferometers. Firstly, two one-dimensional wavefront estimates are computed using Fourier transform. The two-dimensional wave front distribution is then derived by use of least square fitting. The proposed method is applicable to cases in which the shear amount is larger than one sampling interval, and can alleviate the limitation on the shear amount imposed by conventional algorithm. Investigation into the influences of shear amount and noise level on reconstruction accuracy is made, and comparisons with other methods are also provided. Numeric simulations to confirm the proposed algorithm are carried out, and corresponding analyses and discussions are given. The results show that the method is relatively immune to noises and is promising in practical shearing interferomertry.