留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

采用五棱镜扫描法检测大口径平面镜的面形

袁理 张晓辉

袁理, 张晓辉. 采用五棱镜扫描法检测大口径平面镜的面形[J]. 中国光学, 2019, 12(4): 920-931. doi: 10.3788/CO.20191204.0920
引用本文: 袁理, 张晓辉. 采用五棱镜扫描法检测大口径平面镜的面形[J]. 中国光学, 2019, 12(4): 920-931. doi: 10.3788/CO.20191204.0920
YUAN Li, ZHANG Xiao-hui. Surface shape measurement of large flat mirrors using a scanning pentaprism method[J]. Chinese Optics, 2019, 12(4): 920-931. doi: 10.3788/CO.20191204.0920
Citation: YUAN Li, ZHANG Xiao-hui. Surface shape measurement of large flat mirrors using a scanning pentaprism method[J]. Chinese Optics, 2019, 12(4): 920-931. doi: 10.3788/CO.20191204.0920

采用五棱镜扫描法检测大口径平面镜的面形

doi: 10.3788/CO.20191204.0920
基金项目: 

国家自然科学基金项目 61675198

详细信息
    作者简介:

    袁理(1983-), 男, 四川泸州人, 硕士, 副研究员, 2006年、2008年于天津大学分别获得学士、硕士学位, 主要从事光学检测技术方面的研究。E-mail:yuanli83130@163.com

    张晓辉(1967-), 女, 吉林长春人, 硕士, 研究员, 1991年于中国科学院长春光学精密机械与物理研究所获得硕士学位, 主要从事光学检测、像质评价技术等方面的研究。E-mail:xhz861@outlook.com

  • 中图分类号: O439

Surface shape measurement of large flat mirrors using a scanning pentaprism method

Funds: 

National Natural Science Foundation of China 61675198

More Information
  • 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。
  • 图  1  表面倾斜角ε测量原理示意图

    Figure  1.  Measurement schematic of the tilt angle ε of surface

    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  3  距离dD的定义

    Figure  3.  Definitions of the distances d and D

    图  4  扫描路径

    Figure  4.  Scanning paths

    图  5  两个配对点的极坐标

    Figure  5.  Polar coordinates of two matching points

    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  7  各个光学组件的倾斜角

    Figure  7.  Tilt angles of the optical components

    图  8  检测系统

    Figure  8.  Measurement system

    图  9  表面倾角的测量结果

    Figure  9.  Results of the tilt angles of surface

    图  10  表面倾角差值的测量结果

    Figure  10.  Results of the surface tilt angle difference

    图  11  检测1.5 m口径平面镜的面形

    Figure  11.  Surface shape detection of a 1.5 m flat mirror

    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  13  5次检测的标准偏差

    Figure  13.  Standard deviation of 5 times of measurements

    图  14  Ritchey-Common法的检测光路

    Figure  14.  Light path of Ritchey-Common method

    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)

    图  16  图 15作低通滤波后的面形图(PV=43.8 nm,RMS=11.9 nm)

    Figure  16.  Surface shape of Fig. 15 after low pass filtering (PV=43.8 nm, RMS=11.9 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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV
  • [1] 赵维谦, 李文宇, 赵齐, 等.被测件随机移相干涉面形测量方法[J].光学 精密工程, 2016, 24(9):2167-2172. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201609010

    ZHAO W Q, LI W Y, ZHAO Q, et al.. Surface measurement by randomly phase shifting interferometry of measured element[J]. Opt. Precision Eng., 2016, 24(9):2167-2172.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201609010
    [2] ZHU SH, ZHANG X H. Eliminating alignment error and analyzing Ritchey angle accuracy in Ritchey Common test[J]. Optics Communications, 2013, 311:368-374. doi: 10.1016/j.optcom.2013.08.024
    [3] 林冬冬, 胡明勇, 李金鹏, 等.大口径平面镜局部采样瑞奇-康芒检验[J].激光与光电子学进展, 2018, 55(3):031202. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jgygdzxjz201803038

    LIN D D, HU M Y, LI J P, et al.. Local sampling Ritchey-Common test for large aperture flat mirror[J]. Laser & Optoelectronics Progress, 2018, 55(3):031202.(in Chinese) http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=jgygdzxjz201803038
    [4] 王孝坤.大口径离轴凸非球面系统拼接检验技术[J].中国光学, 2016, 9(1):130-136. http://www.chineseoptics.net.cn/CN/abstract/abstract9396.shtml

    WANG X K. Measurement of large off-axis convex asphere by systemic stitching testing method[J]. Chinese Optics, 2016, 9(1):130-136.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9396.shtml
    [5] 郭福东, 唐锋, 卢云君, 等.子孔径拼接干涉的快速调整及测量[J].光学 精密工程, 2017, 25(10):2682-2688. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201710019

    GUO F D, TANG F, LU Y J, et al.. Rapid adjustment and measurement for subaperture stitching interferometry[J]. Opt. Precision Eng., 2017, 25(10):2682-2688.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201710019
    [6] 于瀛洁, 齐特, 武欣.大尺寸光学元件在位动态干涉拼接测量系统[J].光学 精密工程, 2017, 25(7):1764-1770. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201707009

    YU Y J, QI T, WU X. On-line dynamic interference stitching measurement system for large optical elements[J]. Opt. Precision Eng., 2017, 25(7):1764-1770.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201707009
    [7] 张磊, 刘东, 师途, 等.光学自由曲面面形检测技术[J].中国光学, 2017, 10(3):283-299. http://www.chineseoptics.net.cn/CN/abstract/abstract9523.shtml

    ZHANG L, LIU D, SHI T, et al.. Optical free-form surfaces testing technologies[J]. Chinese Optics, 2017, 10(3):283-299.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9523.shtml
    [8] GECKELER R D, ARTEMIEV N A, BARBER S K, et al.. Aperture alignment in autocollimator-based deflectometric profilometers[J]. Review of Scientific Instruments, 2016, 87(5):051906. doi: 10.1063/1.4950734
    [9] SIEWERT F, ZESCHKE T, ARNOLD T, et al.. Linear chirped slope profile for spatial calibration in slope measuring deflectometry[J]. Review of Scientific Instruments, 2016, 87(5):051907. doi: 10.1063/1.4950737
    [10] QIAN J, SULLIVAN J, ERDMANN M, et al.. Performance of the APS optical slope measuring system[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment, 2013, 710:48-51.
    [11] QIAN SH N, GECKELER R D, JUST A, et al.. Approaching sub-50 nanoradian measurements by reducing the saw-tooth deviation of the autocollimator in the Nano-Optic-Measuring Machine[J]. Nuclear Instruments and Methods in Physics Research Section A:Accelerators, Spectrometers, Detectors and Associated Equipment, 2015, 785:206-212. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=310dabb1d03d9d36f183d4aaad684b52
    [12] ALCOCK S G, NISTEA L, SAWHNEY K. Nano-metrology:the art of measuring X-ray mirrors with slope errors < 100 nrad[J]. Review of Scientific Instruments, 2016, 87(5):051902. doi: 10.1063/1.4949272
    [13] MALLIK P C V, ZHAO CH Y, BURGE J H. Measurement of a 2-meter flat using a pentaprism scanning system[J]. Optical Engineering, 2007, 46(2):023602. doi: 10.1117/1.2700386
    [14] YELLOWHAIR J, BURGE J H. Analysis of a scanning pentaprism system for measurements of large flat mirrors[J]. Applied Optics, 2007, 46(35):8466-8474. doi: 10.1364/AO.46.008466
    [15] QI E H, HU H X, HU H F, et al.. The application of pentaprism scanning technology on the manufacturing of M3MP[J]. Proceedings of SPIE, 2016, 9682:96821A.
    [16] 袁理, 张晓辉, 韩冰, 等.五棱镜转动时出射光角度的变化[J].中国光学, 2015, 8(6):1035-1043. http://www.chineseoptics.net.cn/CN/abstract/abstract9358.shtml

    YUAN L, ZHANG X H, HAN B, et al.. Changes of output light's angles with pentaprism rotation[J]. Chinese Optics, 2015, 8(6):1035-1043.(in Chinese) http://www.chineseoptics.net.cn/CN/abstract/abstract9358.shtml
    [17] 朱硕.大口径光学平面镜面形检测技术研究[D].北京: 中国科学院大学, 2014.

    ZHU SH. Study on technology for large optic flat mirror testing[D]. Beijing: University of Chinese Academy of Sciences, 2014.(in Chinese)
    [18] GECKELER R D. Optimal use of pentaprisms in highly accurate deflectometric scanning[J]. Measurement Science and Technology, 2007, 18(1):115-125. doi: 10.1088/0957-0233/18/1/014
    [19] 费业泰.误差理论与数据处理[M]. 6版.北京:机械工业出版社, 2010.

    FEI Y T. Error Theory and Data Processing[M]. 6th ed. Beijing:China Machine Press, 2010.(in Chinese)
    [20] 赖丽萍, 梁德娟, 庄其仁.聚合物光栅生物传感器光信号检测滤波电路[J].光学与光电技术, 2013, 11(1):56-59. http://d.old.wanfangdata.com.cn/Periodical/gxygdjs201301014

    LAI L P, LIANG D J, ZHUANG Q R. Filter circuits used for optical signal detection in the polymer grating biosensors[J]. Optics & Optoelectronic Technology, 2013, 11(1):56-59.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxygdjs201301014
    [21] 孟浩玉, 王彦, 汪诚伟, 等.基于锁相放大原理的微弱光信号检测系统设计[J].光学与光电技术, 2014, 12(6):88-91. http://d.old.wanfangdata.com.cn/Periodical/gxygdjs201406021

    MENG H Y, WANG Y, WANG CH W, et al.. Design of the weak fluorescence signal detection system based on the principle of lock-in amplifier[J]. Optics & Optoelectronic Technology, 2014, 12(6):88-91.(in Chinese) http://d.old.wanfangdata.com.cn/Periodical/gxygdjs201406021
  • 加载中
图(16) / 表(5)
计量
  • 文章访问数:  629
  • HTML全文浏览量:  149
  • PDF下载量:  72
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-02-05
  • 修回日期:  2018-03-05
  • 刊出日期:  2019-08-01

目录

    /

    返回文章
    返回