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基于Zernike模型系数优化的椭球型窗口光学系统像差校正

梁殿明 王超 史浩东 刘壮 付强 张肃 战俊彤 余益欣 李英超 姜会林

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基于Zernike模型系数优化的椭球型窗口光学系统像差校正

梁殿明, 王超, 史浩东, 刘壮, 付强, 张肃, 战俊彤, 余益欣, 李英超, 姜会林

Aberration correction for ellipsoidal window optical system based on Zernike mode coefficient optimization

Liang Dian-Ming, Wang Chao, Shi Hao-Dong, Liu Zhuang, Fu Qiang, Zhang Su, Zhan Jun-Tong, Yu Yi-Xin, Li Ying-Chao, Jiang Hui-Lin
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  • 传统的半球形窗口难以满足高速飞行器气动力学的需求, 采用流线型外表面的非球面光学窗口技术应运而生. 这种窗口会随着扫描视场角的变化产生大量动态像差, 校正这类像差成为高速飞行器光电成像系统发展的关键问题. 对于扫描视场为±60°的椭球形窗口光学系统, 研究了静态校正和无波前探测器的自适应光学技术相结合的大扫描视场像差校正方法. 设计时, 首先以减少系统像差种类为导向, 进行初始结构设计, 消除五阶Zernike像差, 从而减少后续自适应优化控制变量数. 利用Zernike多项式系数与变形镜驱动器电压之间的转换矩阵, 将优化变量由140个驱动器电压减少至Zernike多项式2—9项系数. 最后利用基于Zernike模型的遗传算法对变形镜面形进行控制, 校正残余像差. 仿真结果表明, 各典型扫描视场点的优化速度提升95%以上, 且光学像质接近衍射极限. 该优化方法不仅可以修正异形光学窗口引起的像差, 同时还能够校正光学系统装调、加工时引起的误差, 具有较强的实用性.
    The traditional window of high-speed aircraft is hemispherical, and the aberration produced by such a window is constant. However, the hemispherical window is difficult to meet the requirements of a high speed flight of aircraft. Aspheric windows are usually used to replace hemispherical windows to increase the aerodynamic performance. However, the aspheric window will introduce dynamic aberrations that fluctuate with the change of scanning field-of-view (FOV), which becomes the key issue of the development of optoelectronic imaging systems for high-speed aircraft. For the ellipsoidal window optical system with scanning FOV of ±60°, an aberration correction method in large FOV combined with the static correction and non-wavefront-sensor adaptive optical correction is studied. In the initial optical structure design, the types of system aberration are reduced and the fifth-order Zernike aberration is eliminated during initial aberration correction, thus, the number of the subsequent adaptive optimization control variables is reduced. According to the characteristics of the deformable mirror, the driving voltage of the driver is generally taken as a variable of the genetic algorithm. However, when the deformable mirror used has many units, too many variables will directly lead the optimization speed of the algorithm to greatly decrease. So, according to the aberration characteristics of the ellipsoidal optical window, using the conversion matrix between the Zernike polynomial coefficients and the voltages of the deformable mirror driver, the optimization variable is reduced from 140 driver voltages to 2−9 Zernike stripe polynomial coefficients in number. Finally, the genetic algorithm based on Zernike model is used to control the shape of the deformable mirror and correct the residual aberration. Taking 2−9 Zernike mode coefficients, 2−16 Zernike mode coefficients and 140 driver voltages as the variables of genetic algorithm respectively, the optimization generations of genetic algorithm under different variables are obtained. The simulation results show that the optimization speed of each typical scanning field of view is increased more than 95% by changing the variable from 140 driver voltages to 2−9 Zernike mode coefficients, and the imaging quality is close to the diffraction limit. This optimization method can not only correct the aberrations caused by the special-shaped optical window, but also compensate for the error caused by processing and aligning the optical system.
      通信作者: 王超, Nicklo19992009@163.com
    • 基金项目: 国家自然科学基金(批准号: 61805028, 61805027, 61705019, 61701045, 61890960)、科工局专项(批准号: KJSP2016010202)、国家自然基金天文联合基金(批准号: U1731240)、吉林省教育厅基金(批准号: JJKH20190563KJ)、吉林省自然科学基金(批准号: 20180101338JC)和应用光学国家重点实验室开放基金(批准号: SKLA02020001A11)资助的课题
      Corresponding author: Wang Chao, Nicklo19992009@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61805028, 61805027, 61705019, 61701045, 61890960), the Special Fund for The State Administration of Science, Technology and Industry for National Defense (Grant No. KJSP2016010202), the Project supported by the Joint Funds for astronomy of the National Natural Science Foundation of China (Grant No. U1731240), the Scientific Research Foundation of the Education Department of Jilin Province, China (Grant No. JJKH20190563KJ), the Natural Science Foundation of Jilin Province, China (Grant No. 20180101338JC), and the Open Fund for State Key Laboratory of Applied Optics, China (Grant No. SKLA02020001A11)
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    王超, 张新, 王灵杰, 曲贺盟, 王超 2013 红外与毫米波学报 32 260Google Scholar

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    Lu J G, Li Q, Wang H, Cao Y J 1997 Principle of Genetic Algorithm and its Engineering Application (Xuzhou: China University of Mining and Technology Press) p8 (in Chinese)

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    王超 2014博士学位论文 (北京: 中国科学院大学)

    Wang C 2014 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)

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  • 图 1  椭球形窗口和观测系统的示意图

    Fig. 1.  Schematic diagram of ellipsoid window and observation system.

    图 2  Zernike系数随视场变化

    Fig. 2.  Variation of Zernike coefficients with field of view.

    图 3  椭球形窗口光学系统光路图

    Fig. 3.  Optical path diagram of ellipsoid window optical system.

    图 4  优化后Zernike系数随视场变化

    Fig. 4.  Variation of Zernike coefficients with field of view after optimization.

    图 5  变形镜驱动器排布

    Fig. 5.  Actuator arrangement of deformable mirror.

    图 6  遗传算法流程图

    Fig. 6.  Flow chart of genetic algorithm.

    图 7  不同变量下的优化代数

    Fig. 7.  Optimization generations with different variables.

    图 8  不同变焦位置的MTF图 (a) 0°; (b) 20°; (c) 40°; (d) 60°

    Fig. 8.  MTF for different zoom positions: (a) 0°; (b) 20°; (c) 40°; (d) 60°.

  • [1]

    Zhang Y Q, Chang J, Dang F Y, Bai X D, Pan G Q 2020 Chin. Opt. Lett 18 072201Google Scholar

    [2]

    Knapp D 2002 Proc. SPIE 4832 394Google Scholar

    [3]

    薛文慧, 王惠, 包春慧, 范志刚 2017 应用光学 38 1000Google Scholar

    Xue W H, Wang H, Bao C H, Fan Z G 2017 J. Appl. Opt. 38 1000Google Scholar

    [4]

    史要涛, 翟金龙, 陈守谦, 范志刚 2016 航空兵器 1 51Google Scholar

    Shi Y T, Zhai J L, Chen S Q, Fan Z G 2016 Aero. Weap. 1 51Google Scholar

    [5]

    张运强, 常军, 潘国庆 2019 应用光学 40 965Google Scholar

    Zhang Y Q, Chang J, Pan G Q 2019 J. Appl. Opt. 40 965Google Scholar

    [6]

    张旺, 汪东生 2014 光学学报 34 61Google Scholar

    Zhang W, Wang D S 2014 Acta Opt. Sin. 34 61Google Scholar

    [7]

    李衍璋, 黄长春, 张运强, 牛亚军, 宋大林, 常军 2017 红外与激光工程 46 11Google Scholar

    Li H Z, Huang C C, Zhang Y Q, Niu Y J, Song D L, Chang J 2017 Infraed Laser Eng. 46 11Google Scholar

    [8]

    常军, 刘莉萍, 程德文, 赵楠 2009 红外与毫米波学报 28 204Google Scholar

    Chang J, Liu L P, Cheng D W, Zhao N 2009 J. Infrared Milli. Waves 28 204Google Scholar

    [9]

    常军, 何伍斌, 冯树龙 2011 北京理工大学学报 31 333Google Scholar

    Chang J, He W B, Feng S L 2011 J. B. Inst. Techno. 31 333Google Scholar

    [10]

    Song D, Chang J 2013 Optik 124 2455Google Scholar

    [11]

    Morgan D, Cook L 1996 US Patent 6018424

    [12]

    Chen C 1997 US Patent 6091548

    [13]

    Yu J Q, Chen S Q, Dang F Y, Li X S, Shi X T, Ju L, Wang H, Xu X M, Fan Z G 2020 Opt. Commun. 463 125121Google Scholar

    [14]

    王超, 张新, 王灵杰, 曲贺盟, 王超 2013 红外与毫米波学报 32 260Google Scholar

    Wang C, Zhang X, Wang L J, Qu H M, Wang C 2013 J. Infrared Milli. Waves 32 260Google Scholar

    [15]

    Dong B, Li Y, Han X L, Hu B 2016 Sensors 16 1414Google Scholar

    [16]

    李东熙, 卢振武, 孙强, 刘华, 张云翠 2007 物理学报 56 5766Google Scholar

    Li D X, Lu Z W, Sun Q, Liu H, Zhang Y C 2007 Acta Phys. Sin. 56 5766Google Scholar

    [17]

    孙金霞, 孙强, 李东熙, 卢振武 2007 物理学报 56 3900Google Scholar

    Sun J X, Sun Q, Li D X, Lu Z W 2007 Acta Phys. Sin. 56 3900Google Scholar

    [18]

    Crowther B, McKenney D, Mills J 1998 Proc. SPIE 3482 4861Google Scholar

    [19]

    郭爱林, 朱海东, 杨泽平, 唐仕旺, 谢兴龙, 朱建强 2013 光学学报 33 11Google Scholar

    Guo A L, Zhu H D, Yang Z P, Tang S W, Xie X L, Zhu J Q 2013 Acta Opt. Sin. 33 11Google Scholar

    [20]

    陆金桂, 李谦, 王浩, 曹一家 1997 遗传算法原理及其工程应用 (徐州: 中国矿业大学出版社) 第8页

    Lu J G, Li Q, Wang H, Cao Y J 1997 Principle of Genetic Algorithm and its Engineering Application (Xuzhou: China University of Mining and Technology Press) p8 (in Chinese)

    [21]

    王超 2014博士学位论文 (北京: 中国科学院大学)

    Wang C 2014 Ph. D. Dissertation (Beijing: University of Chinese Academy of Sciences) (in Chinese)

    [22]

    杨华峰 2008 博士学位论文 (长沙: 国防科学技术大学)

    Yang H F 2008 Ph. D. Dissertation (Changsha: National University of Defense Technology) (in Chinese)

    [23]

    周仁忠, 阎吉祥, 赵达尊, 曹根瑞, 俞信 1996 自适应光学 (北京: 国防工业出版社) 第320页

    Zhou R Z, Yan J X, Zhao D Z, Cao D Z, Yu R 1996 Adaptive Optics (Beijing: National Defense Industry Press) p320 (in Chinese)

    [24]

    周仁忠, 阎吉祥 1996 自适应光学理论 (北京: 北京理工大学出版社) 第371页

    Zhou R Z, Yan J X 1996 Adaptive Optics Theory (Beijing: Beijing Institute of Technology Press) p371 (in Chinese)

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出版历程
  • 收稿日期:  2020-06-17
  • 修回日期:  2020-07-28
  • 上网日期:  2020-12-05
  • 刊出日期:  2020-12-20

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