Zernike多项式拟合干涉面方法研究

本文就专著和文献中关于Zernike多项式拟合干涉波面几乎都建设采用Gram-Schimdt正交化方法,而不采用比较简单的传统经典的最小二乘法问题进行了深入研究,从理论和实践上严格地证明了两种方法的等价性。实践中发现,用最小二乘法求解Zernike多项式拟合系数的速度比用Gram-Schimdt正交化方法提高了三倍之多。由于在精密光测技术中,Zernike多项式已被广泛采用,因此,“等价性”的证明具有重要意义,并对于其它类似问题也有着普遍的参考价值。

THE RESEACH INTO THE METHOD TO FIT INTERFEROGRAM WITH ZERNIKE POLYNOMIALS

The Method of fitting the fringes to Zernike polynomials to process an interferogram is thoroughly reseached in this paper, The equivalence of Gram-Schimdt orthogonalization and classical least-squares method to determine the Zernike coefficients is expounded and strictly proved in many ways. It is discovered in the practice that the speed of classical least-squares method adopt ed by us to determine the Zernike coefficients is about three times of that of Gram-Schimdt orthogonalizatipn method usually used by others. For the Zernike polynomial has come into wide use, the method to fit interferogram with the Zernike polynomials and the prove of the equivalence is of important significance and reference value for other similar problems.