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分析了用干涉仪检测中心遮拦光学元件时仍采用圆泽尼克(Zernike)多项式表述相位和求解赛德尔像差的弊端,在环形域上,圆泽尼克多项式不再具有正交性和明确的物理意义。给出了环域泽尼克多项式的求解方式和表达形式,这些表达式具有和圆泽尼克同样的性质和意义。利用Zygo数字干涉仪对口径为300mm,中心遮拦比为0.23的非球面进行了零位补偿检验,用编制的计算程序对其进行环域泽尼克多项式波面拟合,得到的前4项分布可以作为调整误差而消去,进而获得较准确的面形信息,从而为超精加工提供了依据。
The disadvantages of using the Zernike polynomial to represent the phase and solving the Seidel aberration with the interferometer detecting the optical element in the center are also discussed. In the ring domain, the circular Zernike polynomial no longer has orthogonality and explicit physics significance. The solutions and expressions of Zernike polynomials in the ring are given, and these expressions have the same properties and meanings as those of RZ. Zygo digital interferometer is used to test the zero compensation of aspheric surface with a diameter of 300mm and a center obscuration ratio of 0.23. The zernike polynomial wavefront is fitted to the wavefront by the programmed program. The first four distributions can be used as Adjust the error and eliminate, and then get more accurate shape information, thus providing the basis for the super-finishing.