Shi Zhenguang, Sui Yongxin, Liu Zhenyu, Peng Ji, Yang Huaijiang
State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, Jilin, China.
Appl Opt. 2012 Jun 20;51(18):4210-4. doi: 10.1364/AO.51.004210.
Zernike functions are orthogonal within the unit circle, but they are not over the discrete points such as CCD arrays or finite element grids. This will result in reconstruction errors for loss of orthogonality. By using roots of Legendre polynomials, a set of points within the unit circle can be constructed so that Zernike functions over the set are discretely orthogonal. Besides that, the location tolerances of the points are studied by perturbation analysis, and the requirements of the positioning precision are not very strict. Computer simulations show that this approach provides a very accurate wavefront reconstruction with the proposed sampling set.
泽尼克函数在单位圆内是正交的，但在诸如电荷耦合器件（CCD）阵列或有限元网格等离散点上并非如此。这将因正交性的丧失而导致重建误差。通过使用勒让德多项式的根，可以在单位圆内构造一组点，使得在该集合上的泽尼克函数是离散正交的。除此之外，通过微扰分析研究了这些点的位置公差，并且对定位精度的要求不是非常严格。计算机模拟表明，该方法利用所提出的采样集能够提供非常精确的波前重建。
