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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。
A method of generating normalized Zernike basis in a square region is provided. Based on the Gram-Schimdt orthogonal group construction method of linear unrelated group, the standard Zernike polynomials are orthogonalized according to the related concepts of linear algebraic inner product, Euclidean space, orthogonality and norm, and a new set of new Orthogonal Polynomials - Z-square polynomials. Using this orthogonal basis, the wavefront mode fitting in the square region can be realized. It can not only represent the wavefront directly from the set of Z-square modes, but also represent the wave front by linear inverse transform. The linear combination of Zernike modes makes the decomposed wavefront modes have a clear correspondence with the aberrations. Experiments show that it can not only effectively fit the wavefront aberration function in the lens design, but also fit the actual phase data obtained from the Hartmann-Shack wavefront sensor test.