Dai Fengzhao, Tang Feng, Wang Xiangzhao, Feng Peng, Sasaki Osami
Laboratory of Information Optics and Opto-Electronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai, China.
Opt Express. 2012 Jan 16;20(2):1530-44. doi: 10.1364/OE.20.001530.
A numerical orthogonal transformation method for reconstructing a wavefront by use of Zernike polynomials in lateral shearing interferometry is proposed. The difference fronts data in two perpendicular directions are fitted to numerical orthonormal polynomials instead of Zernike polynomials, and then the orthonormal coefficients are used to evaluate the Zernike coefficients of the original wavefront by use of a numerical shear matrix. Due to the fact that the dimensions of the shear matrix are finite, the high-order terms of the original wavefront above a certain order have to be neglected. One of advantages of the proposed method is that the impact of the neglected high-order terms on the outcomes of the lower-order terms can be decreased, which leads to a more accurate reconstruction result. Another advantage is that the proposed method can be applied to reconstruct a wavefront on an aperture of arbitrary shape from its difference fronts. Theoretical analysis and numerical simulations shows that the proposed method is correct and its reconstruction error is obviously smaller than that of Rimmer-Wyant method.
提出了一种在横向剪切干涉测量中利用泽尼克多项式重建波前的数值正交变换方法。将两个垂直方向上的差分波前数据拟合到数值正交多项式而非泽尼克多项式，然后利用数值剪切矩阵通过正交系数来评估原始波前的泽尼克系数。由于剪切矩阵的维度是有限的，必须忽略原始波前高于某一阶的高阶项。该方法的优点之一是可以减小被忽略的高阶项对低阶项结果的影响，从而得到更精确的重建结果。另一个优点是该方法可应用于从其差分波前重建任意形状孔径上的波前。理论分析和数值模拟表明该方法是正确的，其重建误差明显小于里默 - 怀恩特方法。
