用方形区域内的标准正交多项式重构波前  

Wavefront Reconstruction with Orthonormal Polynomials in a Square Area

作　　者：李萌阳[1] 李大海[1] 王琼华[1,2] 赵霁文[1] 章辰[1] 陈盈锋[1] 张充[1] 

机构地区：[1]四川大学电子信息学院,四川成都610065 [2]视觉合成图形图像技术国家重点学科实验室,四川成都610064

出　　处：《中国激光》2012年第11期148-155,共8页Chinese Journal of Lasers

基　　金：国家自然科学基金(60877004)资助课题

摘　　要：提供了一种方形区域上归一化Zernike正交基的生成方法。它采用线性无关组Gram-Schimdt正交组构造方法,根据线性代数内积、欧氏空间及其正交性和范数的相关概念,对标准Zernike多项式进行正交处理,得到了一组新的正交多项式——Z-square多项式。采用该正交基实现了方形区域内波前模式的拟合,它不仅可由Z-square模式的集合直接对波前进行表示,而且也可以通过线性反变换,将Z-square多项式表示成标准的Zernike模式的线性组合,使被分解的波前模式与像差之间有明确的对应关系。实验表明,它不仅可以对透镜设计中的波前像差函数进行有效的拟合,而且也能对Hartmann-Shack波前传感器测试得到的实际相位数据进行拟合。An orthonormal square Zernike basis set is generated from circular Zernike polynomial apodized square mask by use of the linearly independent set Gram-Schmidt orthogonalization technique. Based on the concepts of inner product, Euclidean space and norm in the linear algebra, a standard Zernike polynomial set is made orthogonal and a new orthonormal basis of polynomials named Z-square polynomial is established. Wavefront data in square aperture can be fitted with our new orthonormal set. It can not only fit the wavefront data with Z-square basis set itself, but also can be linearly composed of standard Zernike basis set by linear reverse transform and endows the decomposed wavefront modes with a correspondent aberration meaning. The experimental results show that the Z- square polynomial set can fit the wavefront aberration data in lens design efficiently and can also fit the practical wavefront phase data of Hartmann-Shack wavefront sensor testing, it provides a method of wavefront data analysis.

关 键 词：测量 波前重构 ZERNIKE多项式 方形区域 Z—square多项式 

分 类 号：TN247[电子电信—物理电子学]