中文摘要：

为准确有效地检测大型非球面光学元件的面形,研究了接触式测量光学元件的测量点分布方式。使用不同密度的径向分布及均匀分布的测量点分别对以不同Zernike多项式表示的面形偏差进行采样,然后计算采样所得面形相对给定面形PV值及RMS值的最大相对误差,并对计算结果进行了分析。对1.8m抛物面镜面形实测结果表明：在镜面加工的成型及粗磨阶段,由于面形偏差主要呈旋转对称分布,低密度径向分布测量点即可满足继续加工的检测需求;在精磨及初抛阶段,面形偏差主要为像散或其它非对称面形偏差,测量点均匀分布是提升测量精度的有效手段。此分析方法可以指导测量点的排布方式,从而确保由测量点分布引入的测量误差小于镜面本身面形误差的1/5,提高检测效率。

英文摘要：

Measurement point distribution in contact measuring large aspheric optical surface was researched.By the radial and uniform measurement points with different density distributions,various surface deviations represented by different Zernike polynomials were sampled respectively.Then,the maximum PV and RMS errors were calculated and analyzed.Measurement results of a 1.8 m parabolic mirror were taken as examples,and it indicates that the low density radial measurement point distribution can meet the measurement needs at the forming and coarse grinding stages because the surface deviations show large rotate-symmetrical forms.Moreover,the uniform distribution of measurement points is an effective way to improve measurement accuracy at fine grinding and initial polishing stages,for the main surface deviations are astigmatism or other asymmetrical aberrations.This method can guide the measurement point distribution,control the measurement error caused by distribution to be less than 1/5 of surface error,and can improve measurement accuracy efficiently.