用Zernike多项式拟合干涉波面不同算法的等价性研究

通过严格证明在Zernike多项式拟合光学干涉波面时,求解拟合系数的2种典型算法即最小二乘法和Gram-Schimdt算法的等价性,论证了求解Zernike多项式拟合系数的各种算法在求解过程中具有相同的稳定性。研究发现当其中一种算法在求解过程因故中断或拟合的干涉波面出现了突变,则另一种算法同样无法实现对该干涉波面的正确拟合。研究结果表明:用Zernike多项式拟合干涉波面,没有哪一种算法更优于其他算法,仅仅是求解过程不同而已,各种算法的可靠性是等价的。

The Research on Equivalence of the Algorithms in Fitting Interference Wave Surface with Zernike Polynomials

Through strictly proving the equivalence of the least squares method and Gram-Schimdt algorithm in fitting interference wave-front with Zernike polynomials, it is demonstrated that all algorithms of solving Zernike polynomial coefficients in the solving process are the same in stability. That is, when one of these algorithms is interrupted or a mutation appears in fitted interference wave-front in the solving process, then it is also not possible for the other algorithms to fit interference wave-front correctly. The research results show that no algorithm is superior to other algorithms in fitting the interference wave surface with Zernike polynomials. All these algorithms are equivalent in reliability except that their fitting processes are different.