Wu Qiaoyu, Huang Qiushi, Yu Jun, Xu Xudong, Qi Runze, Zhang Zhong, Wang Zhanshan
Appl Opt. 2021 Oct 1;60(28):8694-8705. doi: 10.1364/AO.433143.
To accurately measure the surface figure of curved mirrors with large radius of curvature (RoC) using stitching interferometry methods, three types of measurement errors are systematically studied, including retrace error, defocusing error within a single subaperture, and stitching angle error among different subapertures. It was found that part of the retrace error caused by the mismatch between the reference wavefront and reflected wavefront has little effect, while the overall retrace error, including the influence of the imperfect optical elements, will cause an error of 1-2 nm RMS within a single subaperture. Defocusing error will enlarge the error due to amplification of optical path error caused by the deviation of the position of the CCD. Because the error is mainly in the edge area, a slope threshold, which controls the maximum surface slope of each subaperture, can be optimized to reduce the effect of the defocus on stitching measurement error. Constant angle error among neighboring subapertures has the biggest accumulation effect on the final stitched figure. For the spherical mirror with RoC of 100 m of 80×40, the error of the one-dimensional residual profile is 4.67 nm PV, assuming a constant angle error of 2×10. For the elliptical mirror with RoC of 60-140 m, it is more than 15 nm peak-to-valley (PV). It is because the profile difference caused by constant angle error is closer to a circle, which can be mostly removed after subtraction of a best-fit sphere. Based on the above error analysis, the developed algorithm-based stitching method was used to measure an elliptical cylindrical mirror of 74×40 with RoC of 60-140 m, and the result was compared with a slope measurement instrument from the Beijing Synchrotron Radiation Facility. After removing the best fitting ellipse profile, the one-dimensional difference between the two results is only 0.77 nm RMS, which demonstrated good measurement accuracy.
为了使用拼接干涉测量法精确测量具有大曲率半径（RoC）的曲面镜的表面形状，系统地研究了三种类型的测量误差，包括回程误差、单个子孔径内的离焦误差以及不同子孔径之间的拼接角度误差。结果发现，由参考波前与反射波前不匹配引起的部分回程误差影响较小，而包括不完善光学元件影响在内的整体回程误差在单个子孔径内会导致均方根误差（RMS）为1 - 2纳米的误差。离焦误差会因电荷耦合器件（CCD）位置偏差导致的光程误差放大而增大误差。由于该误差主要在边缘区域，可以优化一个控制每个子孔径最大表面斜率的斜率阈值，以减少离焦对拼接测量误差的影响。相邻子孔径之间的恒定角度误差对最终拼接图形的累积效应最大。对于曲率半径为100米、尺寸为80×40的球面镜，假设恒定角度误差为2×10，则一维残余轮廓的误差为峰谷值（PV）4.67纳米。对于曲率半径为60 - 140米的椭圆镜，峰谷值（PV）超过15纳米。这是因为恒定角度误差引起的轮廓差异更接近圆形，在减去最佳拟合球面后大部分可以消除。基于上述误差分析，使用所开发的基于算法的拼接方法测量了一个尺寸为74×40、曲率半径为60 - 140米的椭圆柱面镜，并将结果与北京同步辐射装置的斜率测量仪器进行了比较。在去除最佳拟合椭圆轮廓后，两个结果的一维差异仅为均方根误差（RMS）0.77纳米，这表明测量精度良好。
