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300 mm,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 limitations of current interferogram reduction software with circular Zernike polynomials in analyzing obstructed interferogram are illuminated. The Zernike circle polynomials are no longer orthogonal over an annular region and have no explicit physical meanings. The Zernike annular polynomials are discussed and illustrated,which have orthogonality and the similar natures with the Zernike circle polynomials. The experiment is carried out with a Φ 300 mm aspherical mirror with 0.23 obscuration by null-compensation,and the obstructed wavefronts are fitted with Zernike annular polynomials. The first four terms are regarded as misalignment errors and eliminated from the original phase distribution directly,and thus an accurate surface map is gained,which provides a guarantee for the superprecision fabrication.