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摘要: 为了提高大口径平面镜面形检测的精度和效率，提出了一种新的五棱镜扫描法。该方法采用径向扫描的方式，使用一个扫描的五棱镜和一台自准直仪来测量表面倾斜角的差值，然后将被测平面镜的面形表示为Zernike多项式的线性组合，再利用表面倾斜角的差值建立方程组，最后采用最小二乘法计算得到被测平面镜的面形。在检测过程中，该方法还可以对五棱镜在扫描过程中的倾斜变化量进行自动监视和调整，减小了检测误差。误差分析表明，该方法的面形检测精度为7.6 nm rms(均方根误差)。采用该方法对一块1.5 m口径的平面镜进行了面形检测，并与Ritchey-Common法的检测结果进行了对比，两种方法面形结果的差异为7.1 nm rms，小于五棱镜扫描法的面形检测精度。证明了利用该五棱镜扫描法检测大口径平面镜面形的正确性。Abstract: To improve the accuracy and efficiency of the surface shape measurements of large flat mirrors, a new scanning pentaprism method is proposed. In this method, we use a scanning pentaprism and an autocollimator to radially scan and measure the differences between the tilt angles. The surface shape of the flat mirror under test is expressed by a linear combination of Zernike polynomials and an equation set is established on the basis of the angle differences. Finally, the surface shape of the flat mirror can be derived through a least squares calculation. In the measuring process, this method can automatically accommodate changes in the pentaprism tilts during scans, which can reduce measurement errors. The error analysis indicates that the surface shape measurement accuracy by this method is 7.6 nm rms(root-mean-square). This method is used to measure the surface shape of a 1.5 m flat mirror and the result is compared to that of the Ritchey-Common method. The difference between the two surface shape results is 7.1 nm rms, which is less than the surface shape measurement results of the scanning pentaprism method. This proves that it is feasible using the scanning pentaprism method to measure the topographies of large flat mirrors.
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Key words:
- scanning pentaprism method /
- large flat mirror /
- surface shape /
- tilt angle of surface
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图 2 自准直仪存在倾斜角ω时测量示意图
Figure 2. Measurement schematic when autocollimator has a tilt angle ω
图 6 自准直仪2和返回平面镜监视五棱镜的倾斜变化量示意图
Figure 6. Schematic of using autocollimator 2 and the return mirror to monitor the changes of pentaprism tilts
图 12 5次检测的平均面形(PV=45.3 nm，RMS=13.2 nm)
Figure 12. Average surface shape of 5 times of measurements(PV=45.3 nm, RMS=13.2 nm)
图 15 Ritchey-Common法检测得到的平面镜面形(PV=79.1 nm，RMS=11.5 nm)
Figure 15. Flat mirror surface shape detected by Ritchey-Common method(PV=79.1 nm, RMS=11.5 nm)
表 1 各个倾斜误差角的值
Table 1. Values of tilt angle error
倾斜误差角 来源于初始调整 来源于五棱镜扫描时的倾斜 来源于旋转臂的倾斜 来源于被测平面镜的表面倾斜 方和根 αpp ＜30 μrad ＜45 μrad ＜210 μrad — ＜217 μrad γpp ＜30 μrad ＜45 μrad — — ＜54 μrad αac — — ＜210 μrad — ＜210 μrad βac — — ＜210 μrad — ＜210 μrad γac — — — — 等于0 μrad αst ＜30 μrad — — ＜9 μrad ＜31 μrad Δαpp — 21 μrad rms — — 21 μrad rms Δγpp — 21 μrad rms — — 21 μrad rms Δαst — — — 3 μrad rms 3 μrad rms 
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表 2 计算式(15)的一些组成部分
Table 2. Calculations of some components in Equation (15)(μrad)
组成部分 αpp 2αpp αac αst γpp 方和根 2αpp+αac+αst — ＜434 ＜210 ＜31 — ＜483 αac+αst — — ＜210 ＜31 — ＜212 αac+αpp+γpp ＜217 — ＜210 — ＜54 ＜307
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表 3 计算Eδ的值
Table 3. Calculations of Eδ
式(15)中的项 误差值(nrad rms) Δαpp(2αpp+αac+αst) 10.1 Δγpp(αac+αst) 4.5 Δαst(αac+αpp+γpp) 0.9 方和根 11.1
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表 4 计算光束倾斜带来的测量点位置误差
Table 4. Calculations of the position errors caused by beam tilts
光束倾斜角/μrad rms 五棱镜与被测平面镜的距离/mm 测量点位置误差mm rms 来源于αpp:72 0.036 来源于γpp:18 0.009 来源于βac:70 500 0.035 来源于γac:0 0 来源于V0:15 0.008 来源于H0:15 0.008 方和根 0.052
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表 5 表面倾角差值的误差汇总
Table 5. The combined error of the surface tilt angle difference
误差来源 误差值/nrad rms 倾斜误差 11.1 自准直仪1的测量误差 70.7 测量点的位置误差 1.7 环境变化带来的误差 38.5 方和根 81.3
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