Iskander D R, Collins M J, Davis B
Centre for Eye Research, Queensland University of Technology, Victoria Park Rd, Kelvin Grove Q4059, Australia.
IEEE Trans Biomed Eng. 2001 Jan;48(1):87-95. doi: 10.1109/10.900255.
Zernike polynomials are often used as an expansion of corneal height data and for analysis of optical wavefronts. Accurate modeling of corneal surfaces with Zernike polynomials involves selecting the order of the polynomial expansion based on the measured data. We have compared the efficacy of various classical model order selection techniques that can be utilized for this purpose, and propose an approach based on the bootstrap. First, it is shown in simulations that the bootstrap method outperforms the classical model order selection techniques. Then, it is proved that the bootstrap technique is the most appropriate method in the context of fitting Zernike polynomials to corneal elevation data, allowing objective selection of the optimal number of Zernike terms. The process of optimal fitting of Zernike polynomials to corneal elevation data is discussed and examples are given for normal corneas and for abnormal corneas with significant distortion. The optimal model order varies as a function of the diameter of the cornea.
泽尼克多项式常用于角膜高度数据的展开以及光波前分析。使用泽尼克多项式对角膜表面进行精确建模需要根据测量数据选择多项式展开的阶数。我们比较了可用于此目的的各种经典模型阶数选择技术的有效性，并提出了一种基于自助法的方法。首先，模拟结果表明自助法优于经典模型阶数选择技术。然后，证明了在将泽尼克多项式拟合到角膜高度数据的背景下，自助技术是最合适的方法，它允许客观地选择泽尼克项的最佳数量。讨论了将泽尼克多项式最佳拟合到角膜高度数据的过程，并给出了正常角膜和严重变形异常角膜的示例。最佳模型阶数随角膜直径而变化。
