两步式灵敏度矩阵法在卡塞格林望远镜装调中的应用

曹宇泽,马文礼. 两步式灵敏度矩阵法在卡塞格林望远镜装调中的应用[J]. 光电工程,2020,47(2):180536. doi: 10.12086/oee.2020.180536
引用本文: 曹宇泽,马文礼. 两步式灵敏度矩阵法在卡塞格林望远镜装调中的应用[J]. 光电工程,2020,47(2):180536. doi: 10.12086/oee.2020.180536
Cao Y Z, Ma W L. Application of two step sensitivity matrix method in Cassegrain telescope alignment[J]. Opto-Electron Eng, 2020, 47(2): 180536. doi: 10.12086/oee.2020.180536
Citation: Cao Y Z, Ma W L. Application of two step sensitivity matrix method in Cassegrain telescope alignment[J]. Opto-Electron Eng, 2020, 47(2): 180536. doi: 10.12086/oee.2020.180536

两步式灵敏度矩阵法在卡塞格林望远镜装调中的应用

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    作者简介:
    通讯作者: 马文礼(1962-),男,研究员,博士生导师,主要从事光电探测、精密机械、光电探测系统总体技术的研究及大型光电望远镜的研制。E-mail:mawenli@ioe.ac.cn
  • 中图分类号: TH743

Application of two step sensitivity matrix method in Cassegrain telescope alignment

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  • 为了调节视场较大的卡塞格林望远镜的次镜位置,提出了两步式灵敏度矩阵模型的计算机辅助装调方法。在分析了传统的二次模型灵敏度矩阵法的缺陷的基础上,根据灵敏度矩阵的特点加入了精调步骤,对传统的灵敏度矩阵法进行了改进。针对卡塞格林系统,分析了各项泽尼克系数与失调量之间的关系,并对300 mm口径,0.6°视场的卡塞格林系统进行了校正仿真。仿真结果显示,传统的灵敏度矩阵法校正后沿xyz轴偏移及绕xy轴倾斜的失调量的均值分别为:-0.0684 mm、-0.0892 mm、0.0015 mm、0.0498°和-0.0444°,全视场波像差RMS均小于0.1λ(λ=632.8 nm);两步式灵敏度矩阵法校正后的均值分别为-0.0018 mm、-0.0012 mm、0.0002 mm、0.0008°和-0.0012°,全视场RMS均小于0.03λ,明显优于传统的灵敏度矩阵法。

  • Overview: With the development of telescope technology, the aperture and field of view of telescope are becoming larger and larger, the structure of optical system is becoming more and more complex, and the difficulty of fabrication and assembly is also increasing. The speckle pattern of the focal plane of the optical system can be measured by interferometer and other testing equipment, and the Zernike coefficients can be calculated by the speckle pattern. For Cassegrain telescope, in order to obtain good imaging quality, it is necessary to correct the position of its secondary mirror. By using computer-aided alignment technology, the optical system can be real-time detected and compared with the theoretical results. By establishing a mathematical model between Zernike coefficient and misalignment, the misalignment of the components can be corrected accurately. The most widely used computer-aided alignment method is the sensitivity matrix method. Sensitivity matrix method is a method of correcting aberration by establishing mathematical model of misalignment and Zernike coefficient on the basis of analyzing aberration characteristics. The traditional sensitivity matrix method only carries out single correction. According to the meaning of Zernike coefficient, z3z4z5z6z7 and z8 are chosen to construct the sensitivity matrix. Based on the analysis of the shortcomings of the traditional sensitivity matrix method of the two order model, a fine tuning step was added based on the characteristics of the sensitivity matrix. The calculation method of sensitivity is improved. According to the relationship between misalignment and Zernike coefficient, the selection principle of Zernike coefficient for constructing sensitivity matrix is proposed. The traditional sensitivity matrix method is improved. For the Cassegrain system, the relationship between the Zernike coefficients and the misadjustment was analyzed, and the calibration simulation of Cassegrain system with 300 mm aperture and 0.6° field of view was carried out. The simulation results show that after correction by traditional sensitivity matrix method, the mean values of offset along x, y, z axes and tilt around x, y axes are -0.0684 mm, -0.0892 mm, 0.0015 mm, 0.0498° and -0.0444°, respectively, and the full field wavefront aberration RMS is less than 0.1λ (λ=632.8 nm). After correction by two step sensitivity matrix correction method, the mean values are -0.0018 mm, -0.0012 mm, 0.0002 mm, 0.0008° and -0.0012°, respectively, and the full field wavefront aberration RMS is less than 0.03λ. The corrected optical system reaches the diffraction limit and approaches the design position, which is obviously superior to the traditional sensitivity matrix method.

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  • 图 1  卡塞格林系统的光学结构图

    Figure 1.  Layout of Cassegrain system

    图 2  各自由度对泽尼克系数的关系曲线图

    Figure 2.  The relation graph of Zernike coefficient with different degrees of freedom

    表 1  卡塞格林望远镜光学系统参数

    Table 1.  Optical system parameters of Cassegrain telescope

    光学面 曲率半径/mm 间隔/mm 半径/mm 非球面系数
    主镜 -699.512 -250 150 -1.06
    次镜 -269.876 260 45 -3.45
    校正镜1(前) 3722.167 10 20 0
    校正镜1(后) 5147.631 10 20 0
    校正镜2(前) 51.141 10 20 0
    校正镜2(后) 43.322 10 20 0
    校正镜3(前) 43.345 10 20 0
    校正镜3(后) 34.065 30 20 0
    分光棱镜 - 40 20 0
    像面 - - - -
    下载: 导出CSV

    表 2  粗调后的各自由度失调量

    Table 2.  The degree of misalignment of each degree of freedom after coarse tuning

    Dx=0.9058 mm
    Dy=0.127 mm
    Dz=0.8147 mm
    Tx=0.9134°
    Ty=0.6324°
    Dx=0.3689 mm
    Dy=0.5178 mm
    Dz=0.2311 mm
    Tx=-0.1538°
    Ty=0.8126°
    Dx=0.8491 mm
    Dy=0.934 mm
    Dz=0.0357 mm
    Tx=0.6787°
    Ty=0.7577°
    Dx=0.4318 mm
    Dy=0.5625 mm
    Dz=0.1324 mm
    Tx=0.7419°
    Ty=0.8828°
    Dx/mm -0.0602 -0.0111 -0.0509 -0.1282
    Dy/mm -0.102 -0.1722 0.024 0.0125
    Dz/mm 0.0027 0.0011 -0.0043 0.0024
    Tx/(°) 0.0984 0.1362 -0.0213 -0.0081
    Ty/(°) -0.0426 -0.0074 -0.0323 -0.0872
    下载: 导出CSV

    表 3  初始状态的灵敏度矩阵

    Table 3.  Sensitivity matrix of initial state

    Dx/mm Dy/mm Dz/mm Tx/(°) Ty/(°)
    z0 0.23;-0.56 0.22;-0.36 0;-79.55 -4.5;5.3 -4.1;5.6
    z1 0;21.82 0;0.054 0.64;-0.44 0;0.082 0;-33.42
    z2 0;0.054 0;21.84 -0.84;1.01 0;33.34 0;-0.083
    z3 0.24;-0.54 0.24;-0.4 0;-78.53 -4.3;5.2 -4.1;5.54
    z6 0;10.69 0;0.011 0.28;-0.02 0;0.017 0;-16.35
    z7 0;0.011 0;10.75 -0.34;0.48 0;16.38 0;-0.017
    下载: 导出CSV

    表 4  精调后的各自由度失调量

    Table 4.  The degree of misalignment of each degree of freedom after fine tuning

    Dx=0.9058 mm
    Dy=0.127 mm
    Dz=0.8147 mm
    Tx=0.9134°
    Ty=0.6324°
    Dx=0.3689 mm
    Dy=0.5178 mm
    Dz=0.2311 mm
    Tx=-0.1538°
    Ty=0.8126°
    Dx=0.8491 mm
    Dy=0.934 mm
    Dz=0.0357 mm
    Tx=0.6787°
    Ty=0.7577°
    Dx=0.4318 mm
    Dy=0.5625 mm
    Dz=0.1324 mm
    Tx=0.7419°
    Ty=0.8828°
    Dx/mm -0.0003 -0.0034 -0.0025 -0.001
    Dy/mm 0.0016 -0.005 0.0003 -0.0017
    Dz/mm 0.0002 0.0002 0.0002 0.0002
    Tx/(°) -0.0011 0.0032 -0.0002 0.0011
    Ty/(°) -0.0002 -0.0022 -0.0017 -0.0006
    下载: 导出CSV

    表 5  粗调后的灵敏度矩阵

    Table 5.  First-order sensitivity matrix after coarse tuning

    Dx/mm Dy/mm Dz/mm Tx/(°) Ty/(°)
    z0 0.0083 -0.0028 -79.4587 -0.0650 -0.1012
    z1 21.8904 0.0000 -0.0008 0.0001 35.2296
    z2 0.0000 21.8904 0.0014 33.7626 -0.0001
    z3 0.0086 -0.0030 -78.2894 -0.0646 -0.1004
    z6 10.7042 0.0000 -0.0004 0.0000 -16.4869
    z7 0.0000 10.7042 0.0007 16.4869 -0.0000
    下载: 导出CSV

    表 6  精调采用的一阶灵敏度矩阵

    Table 6.  First-order sensitivity matrix for fine tuning

    Dx/mm Dy/mm Dz/mm Tx/(°) Ty/(°)
    z0 -0.0085 -0.0482 -79.4451 0.2625 0.3028
    z1 21.882 0.0002 0.0013 0.0016 -33.7492
    z2 -0.0002 21.8823 -0.0166 33.7494 -0.0016
    z3 -0.0091 -0.0468 -78.2814 0.2629 0.3012
    z6 10.7025 -0.0001 -0.0002 0.0006 -16.4836
    z7 -0.0004 10.7027 -0.0037 16.4839 -0.0008
    下载: 导出CSV

    表 7  传统的灵敏度矩阵法校正后的失调量

    Table 7.  Misalignment after correction by traditional sensitivity matrix method

    Dx=0.9058 mm
    Dy=0.127 mm
    Dz=0.8147 mm
    Tx=0.9134°
    Ty=0.6324°
    Dx=0.3689 mm
    Dy=0.5178 mm
    Dz=0.2311 mm
    Tx=-0.1538°
    Ty=0.8126°
    Dx=0.8491 mm
    Dy=0.934 mm
    Dz=0.0357 mm
    Tx=0.6787°
    Ty=0.7577°
    Dx=0.4318 mm
    Dy=0.5625 mm
    Dz=0.1324 mm
    Tx=0.7419°
    Ty=0.8828°
    Dx/mm -0.0782 0.0669 -0.1189 -0.1432
    Dy/mm -0.024 -0.2072 -0.087 -0.0385
    Dz/mm 0.0067 0.0031 -0.0043 0.0004
    Tx/(°) 0.0094 0.1192 0.0627 0.0079
    Ty/(°) -0.0426 0.0406 -0.0783 -0.0972
    下载: 导出CSV

    表 8  校正前后的泽尼克系数

    Table 8.  Zernike coefficient before and after correction

    z0 z1 z2 z3 z6 z7
    第一组 初始 61.1902 1.7441 -34.3459 60.3361 0.8321 -16.7761
    粗调后 0.1165 -0.1204 -0.2506 0.122 -0.0579 -0.1194
    精调后 -0.0293 -0.0002 0.0021 -0.0212 -0.0001 0.001
    传统校正后 -0.5817 0.2735 0.208 -0.5655 0.1347 0.1019
    第二组 初始 16.3064 19.3113 -6.1533 16.1609 9.4315 -3.0148
    粗调后 -0.0343 -0.0068 0.0101 -0.0268 -0.0032 0.0089
    精调后 -0.0294 -0.0007 -0.0012 -0.0134 -0.0004 -0.0006
    传统校正后 -0.3284 -0.0937 0.5113 -0.3161 -0.0467 0.2527
    第三组 初始 -0.2186 6.8088 -43.1554 -0.2127 3.3268 -21.1387
    粗调后 -0.3907 -0.0406 0.0328 -0.4455 -0.0181 0.0195
    精调后 -0.0293 -0.0027 0.0002 -0.0212 -0.0013 0.0001
    传统校正后 0.2712 -0.0407 -0.2123 0.2747 -0.0181 -0.1024
    第四组 初始 6.0277 20.1141 -37.1608 5.9514 9.8478 -18.2063
    粗调后 0.1262 -0.1376 -0.0001 0.1319 -0.0653 -0.0003
    精调后 -0.0293 0.0016 0.0001 -0.0212 0.0008 0.0001
    传统校正后 -0.1005 -0.1469 0.576 -0.0915 -0.0696 0.2818
    下载: 导出CSV
  • [1]

    周龙峰.大口径反射式望远镜在线调整技术研究[D].成都: 中国科学院研究生院(光电技术研究所), 2016.

    Zhou L F. Study on the alignment technique of large aperture reflecting telescope on-line[D]. Chengdu: University of Chinese Academy of Sciences (Institute of Optics and Electronics), 2016.http://ir.ioe.ac.cn/handle/181551/7990

    [2]

    Figoski J W, Shrode T E, Moore G F. Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor[J]. Proceedings of SPIE, 1989, 1049: 166. doi: 10.1117/12.951421

    [3]

    Egdall I M. Manufacture of a three-mirror wide-field optical system[J]. Optical Engineering, 1985, 24(2): 242285. doi: 10.1117/12.7973470

    [4]

    巩盾, 田铁印, 王红.利用Zernike系数对离轴三反射系统进行计算机辅助装调[J].光学精密工程, 2010, 18(8): 1754–1759. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201008009

    Gong D, Tian T Y, Wang H. Computer-aided alignment of off-axis three-mirror system by using Zernike coefficients[J]. Optics and Precision Engineering, 2010, 18(8): 1754–1759. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201008009

    [5]

    杨晓飞.三反射镜光学系统的计算机辅助装调技术研究[D].长春: 中国科学院长春光学精密机械与物理研究所, 2005.

    Yang X F. Study on the computer-aided alignment of three-mirror optical system[D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, 2005.

    [6]

    Kim S, Yang H S, Lee Y W, et al. Merit function regression method for efficient alignment control of two-mirror optical systems.[J]. Optics Express, 2007, 15(8): 5059–5068. doi: 10.1364/OE.15.005059

    [7]

    王彬, 蒋世磊.卡塞格林系统计算机辅助装调技术研究[J].光学仪器, 2008, 30(1): 50–54. doi: 10.3969/j.issn.1005-5630.2008.01.011

    Wang B, Jiang S L. Study on computer-aided alignment method of Cassegrain system[J]. Optical Instruments, 2008, 30(1): 50–54. doi: 10.3969/j.issn.1005-5630.2008.01.011

    [8]

    孙敬伟, 吕天宇, 姚丽双, 等.发射望远镜的设计与装调[J].光学精密工程, 2014, 22(2): 369–375. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201402018

    Sun J W, Lv T Y, Yao L S, et al. Design and assembly of transmitter-telescope[J]. Optics and Precision Engineering, 2014, 22(2): 369–375. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201402018

    [9]

    张向明, 姜峰, 孔龙阳, 等.卡塞格林系统光学装调技术研究[J].应用光学, 2015, 36(4): 526–530. http://d.old.wanfangdata.com.cn/Periodical/yygx201504006

    Zhang X M, Jiang F, Kong L Y, et al. Research on optical alignment technology for Cassegrain system[J]. Journal of Applied Optics, 2015, 36(4): 526–530. http://d.old.wanfangdata.com.cn/Periodical/yygx201504006

    [10]

    顾志远, 颜昌翔, 李晓冰, 等.改进的灵敏度矩阵法在离轴望远镜装调中的应用[J].光学精密工程, 2015, 23(9): 2595–2604. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201509022

    Gu Z Y, Yan C X, Li X B, et al. Application of modified sensitivity matrix method in alignment of off-axis telescope[J]. Optics and Precision Engineering, 2015, 23(9): 2595–2604. http://d.old.wanfangdata.com.cn/Periodical/gxjmgc201509022

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出版历程
收稿日期:  2018-10-22
修回日期:  2019-03-13
刊出日期:  2020-02-01

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