非球面度梯度均方根法确定最佳比较球面及应用

Calculation and application of the best-fit sphere in root mean square of the gradient of the asphericity method

非球面度是非球面光学元件的重要参数,其值大小及其分布情况将影响到所采用的加工工艺、加工余量大小等。非球面度梯度值可以表征非球面的加工难度,在分析近似公式法、最大非球面度最小化法、最大非球面度梯度最小化法计算非球面最佳比较球面基础上,提出了非球面度梯度均方根值最小化法优化非球面最佳比较球面,从非球面整个镜面非球面度的梯度值考虑了加工的难度,特别适用于大口径高陡度非球面最佳比较球面的确定。以一个有效口径φ1000 mm、F/1.44的非球面为例,分析比较了4种方法的计算结果,结果表明非球面度梯度均方根值最小化法是一种综合考虑非球面加工难度和材料去除量的非球面最佳比较球面确定方法,得到的非球面度分布拐点在整个镜面口径的0.82位置附近。按照非球面度均方根值评价加工难度,均方根值最小化法的非球面度的均方根值为传统最大非球面度最小化法的2/3,显著的降低了加工的难度,对加工工艺的确定及表面全频误差段质量控制具有一定的指导意义。

Asphericity,which affects the manufacturing process and the grinding quantity,is an important parameter of the aspherics.The gradient of the asphericity is used to figure the fabrication difficulty.Based on the analysis of the approximate formula method,minimizing the maximum asphericity method and minimizing the maximum the gradient of the asphericity method,the minimizing the root mean square（RMS） of the gradient of the asphericity method is given for calculating the best-fit sphere of the asphericity,which is the best for the large and fast aspheric to calculate the best-fit sphere.For an aspheric with the aperture 1 000 mm and F/1.44,the best-fit sphere,asphericity and asphericity gradient calculated by the four methods are analyzed.The result shows that minimizing RMS of the gradient of the asphericity method is based on the difficulty and the material removal quantity to calculate the best-fit sphere,and the inflexion point of the asphericity distribution is at the place of the 0.82 aperture.According to RMS of the gradient of the asphericity to evaluate the fabrication difficulty,the RMS of the gradient of the asphericity calculated by the minimizing RMS of the gradient of the asphericity method is 2/3 of that calculated by minimizing the maximum asphericity method,so the fabrication difficulty is observably reduced,and it is important for the manufacture and the all-frequency surface error quality controlling.