Tian Chao, Chen Xuefeng, Liu Shengchun
Opt Express. 2016 Feb 22;24(4):3572-83. doi: 10.1364/OE.24.003572.
Wavefront reconstruction in radial shearing interferometry with general aperture shapes is challenging because the problem may be ill-conditioned. Here we propose a Gram-Schmidt orthogonalization method to cope with off-axis wavefront reconstruction with any aperture type. The proposed method constructs a set of orthogonal basis functions and computes the corresponding expansion coefficients, which are converted into another set of expansion coefficients to reproduce the original wavefront. The method can effectively alleviate the ill-conditioning of the problem, and is numerically stable compared with the classic least-squares method, especially for non-circular apertures and in the presence of noise. Computer simulation and experimental results are presented to demonstrate the performance of the algorithm.
对于具有一般孔径形状的径向剪切干涉测量中的波前重建具有挑战性，因为该问题可能是病态的。在此，我们提出一种Gram-Schmidt正交化方法来处理任何孔径类型的离轴波前重建。所提出的方法构造了一组正交基函数并计算相应的展开系数，这些系数被转换为另一组展开系数以再现原始波前。该方法可以有效地缓解问题的病态性，并且与经典最小二乘法相比在数值上更稳定，特别是对于非圆形孔径以及存在噪声的情况。给出了计算机模拟和实验结果以证明该算法的性能。
