Search

Article

x

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

Design of monocentric wide field-of-view and high-resolution computational imaging system

Liu Fei Wei Ya-Zhe Han Ping-Li Liu Jia-Wei Shao Xiao-Peng

Design of monocentric wide field-of-view and high-resolution computational imaging system

Liu Fei, Wei Ya-Zhe, Han Ping-Li, Liu Jia-Wei, Shao Xiao-Peng
PDF
HTML
Get Citation
  • Imaging systems with a wide field-of-view (FOV) and high-resolution, which can provide abundant target information, are always desired in various applications including target detection, environment monitoring, marine rescue, etc. Various approaches to realizing the wide FOV and high-resolution imaging have been developed, for example, fisheye lens imaging system, and panoramic optical annular staring imaging technology. In these single aperture imaging systems, the maximum resolution and FOV are determined by either the geometric aberration or the diffraction limit of the optics. Multi-scale monocentric ball-lens imaging system is of particular importance due to its high real-time ability, small image distortion, and wide FOV. The complete geometrical symmetry of multilayer monocentric ball-lens makes it possible to compensate for the geometric aberration with no need of additional assistance. However, the major problem in designing imaging system based on multi-scale monocentric ball-lens is that there are too many variables needed to be set for a ball-lens imaging structure and the problems of high time cost and computation complexity.For simplifying the design process, in this manuscript, we apply the computational imaging theory to optical system design, thereby developing a geometric aberration optimization function to determine the initial values of the desired system by the sound computation rather than repetitive iterations by using the optical system design software. Function development starts from the aberration theory. Since the monocentric ball lens does not bring in the aberrations relating to FOV, only spherical aberration and chromatic aberration are needed to be considered. The optimization function is then founded according to the principle of minimizing the spherical aberration and chromatic aberration. And then with the determined initial parameters, ZEMAX is employed to globally optimize the residual geometric aberrations, which is time-efficient. After required parameters are finally determined, the system performance is evaluated via the modulation transmission function, the spot diagram distribution, the field-curve and distortion value and the ray fan curve. Favorable results are obtained, which demonstrates the feasibility of the developed system designing approach. Imaging results from the finished prototype system are pretty satisfactory with wide FOV and high resolution which is captured through only one frame. The multi-scale wide FOV and high-resolution computation imaging system not only solves the conflict between the wide FOV and high resolution, but also provides the research foundation for computational imaging.
      Corresponding author: Shao Xiao-Peng, xpshao@xidian.edu.cn
    [1]

    Claire S K, Jeffrey R H, Timothy K L, Joi W, Raymond G F, Bryan Z, Takahiro I, Allen B, Seung J, John P C, Amit C, Markus W C, Tannishtha R 2016 Nat. Commun. 7 1

    [2]

    Jisoo K, Doo J P, Sun J B, Jaeho L, Soo B C, Seongjun P, Sung W H 2014 Opt. Express 22 31875

    [3]

    Brady D J, Gehm M E, Stack R A, Marks D L, Kittle D S, Golish D R, Vera E M, Feller S D 2012 Nature 486 386

    [4]

    Golish D R, Vera E M, Kelly K J, Gong Q, Jansen P A, Hughes J M, Kittle D S, Brady D J, Gehm M E 2012 Opt. Express 20 22048

    [5]

    闫阿奇, 祝青, 曹剑中, 周泗忠, 杨正, 刘宇波 2008 光子学报 37 1975

    Yan A Q, Zhu Q, Cao J Z, Zhou S Z, Yang Z, Liu Y B 2008 Acta Photon. Sin. 37 1975

    [6]

    Matthew J L, George B, Michael F 2012 Remote Sensing 4 3006

    [7]

    Wang X, Li L, Hou G Q 2016 Appl. Opt. 55 2580

    [8]

    Yu H, Wan Q H, Lu X R, Du Y C, Yang S W 2017 Appl. Opt. 56 755

    [9]

    Tremblay E J, Marks D L, Brady D J, Ford J E 2012 Appl. Opt. 51 4691

    [10]

    Wang S, Heidrich W 2004 Comput. Graphics Forum 23 441

    [11]

    Donggyun K, Jinho P, Joonki P 2014 Opt. Lett. 39 6261

    [12]

    Antonino F, Giovanni M F, Arcangelo R B, Sebastiano B 2017 IEEE Trans. Image Process. 26 696

    [13]

    Mo Z, Robert H C, Juliet T G 2016 Opt. Express 21 23798

    [14]

    Huang Z, Bai J, Lu T X, Hou X Y 2013 Opt. Express 21 10810

    [15]

    Yan J L, Kong L S, Diao Z H, Liu X F, Zhu L L, Jia P 2018 Appl. Opt. 3 396

    [16]

    Lohmann A W 1989 Appl. Opt. 28 4996

    [17]

    Cossairt O S, Nayar S K 2010 Proceeding on 2010 IEEE International Conference on Computational Photography (ICCP) Pittsburgh, USA, March 29–30, 2010 p1

    [18]

    Brady D J, Hagen H 2009 Opt. Express 13 10659

    [19]

    Marks D L, Llull P R, Philips Z, Anderson J G, Feller S D, Vera E M, Son H S, Youn S, Kim J, Gehm M E, Brady D J, Nichols J M, Judd K P, Duncan M D, Waterman J R, Stack R A, Johnson A, Tennill R, Olson C C 2014 Appl. Opt. 53 C54

    [20]

    Patrick L, Lauren B, Zachary P, Kyle D, Marks D L, Brady D J 2015 Optica 2 1086

    [21]

    Cossairt O S, Miau D, Nayar S K 2011 J. Opt. Soc. Am. A 28 2540

    [22]

    Born M, Wolf E 2016 Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7nd Edition (Cambridge: Cambridge University Press) p210

    [23]

    Luke P L, Robert S 2005 Science 310 1148

    [24]

    Sasian J 2010 Appl. Opt. 49 D69

    [25]

    Lijun L, Yiqing C 2017 Appl. Opt. 56 8570

  • 图 1  基于共心球透镜的广域高分辨率成像原理图

    Figure 1.  Schematic of monocentric wide field of view (FOV) and high-resolution computational imaging system.

    图 2  共心球透镜成像光路图

    Figure 2.  Ray diagram of themonocentric multi-scale ball-lens.

    图 3  (a)共心球透镜二维成像结构图; (b)调制传递函数曲线图; (c)共心球透镜点列图; (d)共心球透镜光线像差图

    Figure 3.  (a) Structure of the designed monocentric ball-lens; (b) MTF curves; (c) the spot diagram; (d) the ray fan curves.

    图 4  相邻小尺度相机视场重叠对应关系示意图

    Figure 4.  Schematic showing the FOV overlapping betweenthe adjacent micro cameras.

    图 5  小尺度相机排布示意图

    Figure 5.  Distribution of the small-scale micro camera.

    图 6  光学系统结构图

    Figure 6.  Structure of the whole optical system.

    图 7  (a)系统MTF曲线图; (b)系统点列图; (c)系统场曲和畸变图; (d)系统光线像差图

    Figure 7.  (a) MTF curves of the whole system; (b) the spot diagram; (c) the field-curve and distortion; (d) the ray fan of the system.

    图 8  不同公差分配时的MTF叠加曲线

    Figure 8.  MTF curves at different tolerance values.

    图 9  多尺度广域高分辨率计算成像系统结构图

    Figure 9.  Prototype of the multi-scale wide FOV high-resolution computational imaging system.

    图 10  (a)测试平台结构示意图; (b)测试平台实物; (c)靶标板图像; (d)分辨率图案参数表

    Figure 10.  (a) Test platform structure diagram; (b) test platform; (c) the image of target plate; (d) resolution pattern parameters table

    图 11  系统成像效果图(部分)

    Figure 11.  Imaging results of the designed system (partial result).

    表 1  共心球透镜初始结构参数

    Table 1.  Structural parameters of the monocentric ball-lens.

    面序号曲率半径/mm厚度/mm玻璃半口径/mm
    156.9031.89H-ZF1251.516
    225.0125.01H-BAK823.238
    STOInfinity32.20H-BAK86.4240
    4–32.2024.70H-ZF1228.975
    5–56.9040.13550.247
    DownLoad: CSV
  • [1]

    Claire S K, Jeffrey R H, Timothy K L, Joi W, Raymond G F, Bryan Z, Takahiro I, Allen B, Seung J, John P C, Amit C, Markus W C, Tannishtha R 2016 Nat. Commun. 7 1

    [2]

    Jisoo K, Doo J P, Sun J B, Jaeho L, Soo B C, Seongjun P, Sung W H 2014 Opt. Express 22 31875

    [3]

    Brady D J, Gehm M E, Stack R A, Marks D L, Kittle D S, Golish D R, Vera E M, Feller S D 2012 Nature 486 386

    [4]

    Golish D R, Vera E M, Kelly K J, Gong Q, Jansen P A, Hughes J M, Kittle D S, Brady D J, Gehm M E 2012 Opt. Express 20 22048

    [5]

    闫阿奇, 祝青, 曹剑中, 周泗忠, 杨正, 刘宇波 2008 光子学报 37 1975

    Yan A Q, Zhu Q, Cao J Z, Zhou S Z, Yang Z, Liu Y B 2008 Acta Photon. Sin. 37 1975

    [6]

    Matthew J L, George B, Michael F 2012 Remote Sensing 4 3006

    [7]

    Wang X, Li L, Hou G Q 2016 Appl. Opt. 55 2580

    [8]

    Yu H, Wan Q H, Lu X R, Du Y C, Yang S W 2017 Appl. Opt. 56 755

    [9]

    Tremblay E J, Marks D L, Brady D J, Ford J E 2012 Appl. Opt. 51 4691

    [10]

    Wang S, Heidrich W 2004 Comput. Graphics Forum 23 441

    [11]

    Donggyun K, Jinho P, Joonki P 2014 Opt. Lett. 39 6261

    [12]

    Antonino F, Giovanni M F, Arcangelo R B, Sebastiano B 2017 IEEE Trans. Image Process. 26 696

    [13]

    Mo Z, Robert H C, Juliet T G 2016 Opt. Express 21 23798

    [14]

    Huang Z, Bai J, Lu T X, Hou X Y 2013 Opt. Express 21 10810

    [15]

    Yan J L, Kong L S, Diao Z H, Liu X F, Zhu L L, Jia P 2018 Appl. Opt. 3 396

    [16]

    Lohmann A W 1989 Appl. Opt. 28 4996

    [17]

    Cossairt O S, Nayar S K 2010 Proceeding on 2010 IEEE International Conference on Computational Photography (ICCP) Pittsburgh, USA, March 29–30, 2010 p1

    [18]

    Brady D J, Hagen H 2009 Opt. Express 13 10659

    [19]

    Marks D L, Llull P R, Philips Z, Anderson J G, Feller S D, Vera E M, Son H S, Youn S, Kim J, Gehm M E, Brady D J, Nichols J M, Judd K P, Duncan M D, Waterman J R, Stack R A, Johnson A, Tennill R, Olson C C 2014 Appl. Opt. 53 C54

    [20]

    Patrick L, Lauren B, Zachary P, Kyle D, Marks D L, Brady D J 2015 Optica 2 1086

    [21]

    Cossairt O S, Miau D, Nayar S K 2011 J. Opt. Soc. Am. A 28 2540

    [22]

    Born M, Wolf E 2016 Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7nd Edition (Cambridge: Cambridge University Press) p210

    [23]

    Luke P L, Robert S 2005 Science 310 1148

    [24]

    Sasian J 2010 Appl. Opt. 49 D69

    [25]

    Lijun L, Yiqing C 2017 Appl. Opt. 56 8570

  • [1] Design and analysis of polarization imaging lidar and short wave infrared composite optical receiving system. Acta Physica Sinica, 2020, (): . doi: 10.7498/aps.69.20200920
    [2] Pei Lin-Lin, Lü Qun-Bo, Wang Jian-Wei, Liu Yang-Yang. Optical system design of the coded aperture imaging spectrometer. Acta Physica Sinica, 2014, 63(21): 210702. doi: 10.7498/aps.63.210702
    [3] Wang Fang, Zhu Qi-Hua, Jiang Dong-Bin, Zhang Qing-Quan, Deng Wu, Jing Feng. Optimization of optical design of the master amplifier in multi-pass off-axis amplification system. Acta Physica Sinica, 2006, 55(10): 5277-5282. doi: 10.7498/aps.55.5277
    [4] Feng Wei, Zhang Fu-Min, Wang Wei-Jing, Qu Xing-Hua. Adaptive high-dynamic-range imaging method and its application based on digital micromirror device. Acta Physica Sinica, 2017, 66(23): 234201. doi: 10.7498/aps.66.234201
    [5] Yao Wei-Qiang, Huang Wen-Hao, Yang Chu-Ping. Theoretical analysis of spectrum reconstruction imaging using single-pixel detection. Acta Physica Sinica, 2017, 66(3): 034201. doi: 10.7498/aps.66.034201
    [6] Cao Chao, Liao Zhi-Yuan, Bai Yu, Fan Zhen-Jie, Liao Sheng. Initial configuration design of off-axis reflective optical system based on vector aberration theory. Acta Physica Sinica, 2019, 68(13): 134201. doi: 10.7498/aps.68.20190299
    [7] Shen Ben-Lan, Chang Jun, Wang Xi, Niu Ya-Jun, Feng Shu-Long. Design of the active zoom system with three-mirror. Acta Physica Sinica, 2014, 63(14): 144201. doi: 10.7498/aps.63.144201
    [8] Lü Xiang-Bo, Zhu Jing, Yang Bao-Xi, Huang Hui-Jie. An approach for calculating the optical structure based on ybar-y diagram. Acta Physica Sinica, 2015, 64(11): 114201. doi: 10.7498/aps.64.114201
    [9] Local hybrid optical encryption system based on double random phase encoding. Acta Physica Sinica, 2020, (): . doi: 10.7498/aps.69.20200478
    [10] Li Yong-Da, Ge Zhen-Jie, Sun Qiang, Zhang Yun-Cui, Wang Jian, Sun Jin-Xia, Liu Jian-Zhuo, Dong Ke-Yan. Design of a refractive/diffractive hybrid infrared bifocal optical system. Acta Physica Sinica, 2006, 55(9): 4602-4607. doi: 10.7498/aps.55.4602
    [11] Wen Chang-Li, Ji Jia-Rong, Dou Wen-Hua, Feng Xiang-Hua, Xu Rong, Men Tao, Liu Chang-Hai. Improvement of the technology of making multi-mode polysiloxane waveguides. Acta Physica Sinica, 2012, 61(9): 094202. doi: 10.7498/aps.61.094202
    [12] Wang Zhao-Qi, Mu Guo-Guang, Yu Bin, Lu Zhen-Wu, Sun Qiang. Study on hyperspectral detection system with the harmonic diffractive element in infrared dual-band. Acta Physica Sinica, 2004, 53(3): 756-761. doi: 10.7498/aps.53.756
    [13] Ren Hong-Liang. Design and error analysis for optical tweezers based on finite conjugate microscope. Acta Physica Sinica, 2013, 62(10): 100701. doi: 10.7498/aps.62.100701
    [14] Xu Ping, Yang Wei, Zhang Xu-Lin, Luo Tong-Zheng, Huang Yan-Yan. Two-dimensional distribution design of micro-prism for partial integrated light guide plate. Acta Physica Sinica, 2019, 68(3): 038502. doi: 10.7498/aps.68.20181684
    [15] Feng Shuai, Chang Jun, Niu Ya-Jun, Mu Yu, Liu Xin. A method of designing asymmetric double-sided off-axis aspheric mirror detection compensation zoom light path. Acta Physica Sinica, 2019, 68(11): 114201. doi: 10.7498/aps.68.20182253
    [16] Liu Yan, Li Jian-Jun, Gao Dong-Yang, Zhai Wen-Chao, Hu You-Bo, Guo Yuan-Yuan, Xia Mao-Peng, Zheng Xiao-Bing. Research on the time-correlation characterisrtic of correlated photon circles generated by the type-I spontaneous parametric down-conversion. Acta Physica Sinica, 2016, 65(19): 194211. doi: 10.7498/aps.65.194211
    [17] Zhang Xu-Lin, Yang Wei, Luo Tong-Zheng, Huang Yan-Yan, Lei Lei, Li Gui-Jun, Xu Ping. Two-dimensional distribution expressions of micro-prism on bottom surface of partial integrated light guide plate. Acta Physica Sinica, 2019, 68(21): 218501. doi: 10.7498/aps.68.20190854
    [18] Zhang Juan, Jiao Zhi-Qiang, Yan Hua-Jie, Chen Fu-Dong, Huang Qing-Yu, Kang Liang-Liang, Liu Xiao-Yun, Wang Lu, Yuan Guang-Cai. Influence of microcavity effect on the performance of top emission tandem blue organic light emitting devices. Acta Physica Sinica, 2020, 69(9): 096104. doi: 10.7498/aps.69.20191576
    [19] Xiang Liang-Zhong, Xing Da, Guo Hua, Yang Si-Hua. High resolution fast digital photoacoustic CT for breast cancer diagnosis. Acta Physica Sinica, 2009, 58(7): 4610-4617. doi: 10.7498/aps.58.4610
    [20] Zhao Gui-Min, Lu Ming-Zhu, Wan Ming-Xi, Fang Li. Study of vibro-acoustography with high spatial resolution based on sector array transducers. Acta Physica Sinica, 2009, 58(9): 6596-6603. doi: 10.7498/aps.58.6596
  • Citation:
Metrics
  • Abstract views:  1215
  • PDF Downloads:  39
  • Cited By: 0
Publishing process
  • Received Date:  18 December 2018
  • Accepted Date:  15 January 2019
  • Available Online:  01 April 2019
  • Published Online:  20 April 2019

Design of monocentric wide field-of-view and high-resolution computational imaging system

    Corresponding author: Shao Xiao-Peng, xpshao@xidian.edu.cn
  • 1. School of Physics and Optoelectronic Engineering, Xidian University, Xi'an 710071, China
  • 2. State Key Laboratory of Applied Optics, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China

Abstract: Imaging systems with a wide field-of-view (FOV) and high-resolution, which can provide abundant target information, are always desired in various applications including target detection, environment monitoring, marine rescue, etc. Various approaches to realizing the wide FOV and high-resolution imaging have been developed, for example, fisheye lens imaging system, and panoramic optical annular staring imaging technology. In these single aperture imaging systems, the maximum resolution and FOV are determined by either the geometric aberration or the diffraction limit of the optics. Multi-scale monocentric ball-lens imaging system is of particular importance due to its high real-time ability, small image distortion, and wide FOV. The complete geometrical symmetry of multilayer monocentric ball-lens makes it possible to compensate for the geometric aberration with no need of additional assistance. However, the major problem in designing imaging system based on multi-scale monocentric ball-lens is that there are too many variables needed to be set for a ball-lens imaging structure and the problems of high time cost and computation complexity.For simplifying the design process, in this manuscript, we apply the computational imaging theory to optical system design, thereby developing a geometric aberration optimization function to determine the initial values of the desired system by the sound computation rather than repetitive iterations by using the optical system design software. Function development starts from the aberration theory. Since the monocentric ball lens does not bring in the aberrations relating to FOV, only spherical aberration and chromatic aberration are needed to be considered. The optimization function is then founded according to the principle of minimizing the spherical aberration and chromatic aberration. And then with the determined initial parameters, ZEMAX is employed to globally optimize the residual geometric aberrations, which is time-efficient. After required parameters are finally determined, the system performance is evaluated via the modulation transmission function, the spot diagram distribution, the field-curve and distortion value and the ray fan curve. Favorable results are obtained, which demonstrates the feasibility of the developed system designing approach. Imaging results from the finished prototype system are pretty satisfactory with wide FOV and high resolution which is captured through only one frame. The multi-scale wide FOV and high-resolution computation imaging system not only solves the conflict between the wide FOV and high resolution, but also provides the research foundation for computational imaging.

    • 广域高分辨率光电成像系统能够捕捉到大空间范围内的目标信息, 且作为最直接的信息获取手段能提供符合人眼视觉特性的直观探测结果[1-3], 在无人机侦察与防控、环境监控及海上搜救等众多领域应用广泛[4-9].

      传统广域光电成像系统所采用的小视场高分辨率扫描成像方式[10]主要依靠转台的机动性和灵活性来增大成像系统的侦测和监视范围, 以实现系统广域高分辨成像. 然而受光机结构所限, 该类系统普遍存在实时性差的问题, 无法对空间信息进行实时获取和精确判读. 相比之下, 凝视型广域成像系统在实时性方面性能更佳, 但由于凝视型光电成像系统中广域范围成像和高分辨率信息的获取本身存在一定程度的相互制约关系, 即凝视型成像系统在增大光学系统成像视场的同时提高成像分辨率较难实现. 目前同时实现广域和高分辨率成像需求的凝视型光电成像系统主要为鱼眼透镜凝视成像系统[11, 12]、环带凝视全景成像系统等新型光学成像系统[13-15]. 上述成像方式虽然能一定程度上解决广域和高分辨率相互制约这一问题, 但场景信息损失率高、视场受杂散光影响较大、图像畸变大及图像存在中心盲区等问题依然存在, 难以实现光电成像装备的实际应用, 因此发展新体制凝视型广域高分辨率成像系统是新型光电成像装备的迫切需求.

      利用中心对称结构的球透镜大视场、小几何畸变且不易产生轴外像差的特点, 文献[1620]中提出利用球透镜和球面探测器阵列实现大视场高分辨率凝视成像. 但上述系统中大面阵球面探测器拼接难度大, 光学设计过分依赖设计软件, 导致系统设计难度大, 成像质量受限. 针对以上问题, 本文设计了一种基于共心球透镜的多尺度广域高分辨率计算成像系统, 该系统不仅有效地解决了凝视型光电成像系统中大视场和高分辨率难以统一的问题, 而且通过引入计算成像技术有效地简化了传统光学系统的设计难度.

      基于共心球透镜的多尺度广域高分辨率计算成像系统从光学系统设计原则出发, 以像差优化理论为基础, 充分利用球透镜视场大、各轴外视场成像效果一致性好的特点, 设计以球透镜为大尺度主物镜、小尺度相机阵列为次级成像系统的多尺度成像结构. 此外, 利用计算成像方法构建系统像差优化函数, 通过求解最优化函数快速获取系统的结构参数. 系统稳定性分析结果及样机最终成像效果证明, 该成像系统不仅实现了大视场和高分辨率的统一, 而且具有良好的成像稳定性.

    2.   多尺度广域高分辨率计算成像系统设计
    • 多尺度广域高分辨率计算成像系统主要利用大尺度球透镜对称性好且与视场相关的几何像差小的特点[3, 21], 实现场景的大视场成像和高效率能量收集; 而小尺度相机阵列所具有的中继转换能力则能够将球透镜所成的像转接到二次像面, 为广域高分辨率成像提供了新的可能. 基于上述原理, 本文设计了由一级大尺度四层共心球透镜(主成像系统)和次级中继小尺度相机阵列(次级成像系统)级联构成的二级广域高分辨率计算成像系统, 系统成像原理如图1所示. 该系统集成了球透镜的大视场能量收集能力和次级中继小尺度相机阵列的局部视场校正能力, 共心球透镜将观测场景成像于球形一次像面, 通过球形排布的小尺度相机阵列进行转接形成一系列子图像, 结合计算成像方法将共心球透镜所获取的场景信息重建为一幅广域高分辨率图像.

      Figure 1.  Schematic of monocentric wide field of view (FOV) and high-resolution computational imaging system.

    • 光学系统中的几何像差会影响系统最小可分辨光斑尺寸, 并决定系统的成像分辨率及最终成像质量. 根据Seidel像差理论, 基于共心球透镜的广域高分辨率光学成像系统的单色初级像差系数(球差(B )、像散(C )、场曲(D )、畸变(E )和彗差(F ))可表示为[22]

      式中各项参数见图2所示, ${r_i}$为共心球透镜成像系统的曲率半径; ${n_2}$${v_2}$分别为外层玻璃的折射率和阿贝常数; ${n_3}$${v_3}$分别为内层玻璃的折射率和阿贝常数, ${b_i}$为常数[22, 23]; ${h_i}$为物方高度; ${s_i}$${s_i}^{'} $分别表示第$i$个曲面顶点到物平面和第$i$个像面的距离, ${H_i} = {{{t_i}} / {{n_{i - 1}}}}$表示入射光瞳中心出射光线与第$i$个面交点的高度; ${t_i}$${t_i}^{'} $分别表示第$i$个曲面顶点到入射光瞳和第$i$个面入瞳所成像的距离; ${K_i}$${L_i}$表示如下:

      Figure 2.  Ray diagram of themonocentric multi-scale ball-lens.

      图2所示, 共心球透镜的光阑位于球心, 以实现其结构对称性. 为便于计算, 利用(3)式所示的Seidel波像差系数表示共心球透镜的像差[24, 25],

      其中$\rho \in \left[ { - 1,1} \right]$, $\phi \in \left[ {0,{\text{π}}} \right]$构成表示光程差OPD(optical path difference)的二维极坐标函数, ${W_{\lambda jk}}$为像差系数, R为径向坐标, $\lambda $, $j$$k$是非负整数, $\lambda $表示径向坐标参量, $j$表示径向分量最高阶数, $k$为正弦分量的角向频率数. 由于共心球透镜具有对称性且一次像面与主物镜为共心球面, 故轴外像差较小[23]. 因此, 影响球透镜成像质量的因素主要为球差以及复色光成像过程中由光波波长差异所引起的系统色差.

      由于光学成像系统中的光线参数无法直观衡量系统优化结果, 因此在设计中用光学系统的结构参数代替光线参数. 通过(4)式中平行光线追迹法实现光线参数与光学系统结构参数间的转化,

      其中${d_i}$表示透镜表面i$i + 1$间的距离, 对于共心球透镜则存在${d_1} = {d_3} = {r_1} - {r_2}$, ${d_2} = {r_2}$. 因此, 对文中系统从位置${h_1} = f \times NA$${\alpha _1} = 0$处开始光线追迹分析残留像差, 其中系统像方焦距$f$如(5)式所示. 对该系统中的多层共心球透镜的每个光学表面应用阿贝不变式, 利用透镜的结构参数来代替物像参数, 并通过(4)式和(5)式迭代可得球差的波像差系数如(6)式所示.

      同理, 系统色差可表示为

      上述分析表明, 共心球透镜系统的设计参数直接决定了其像差分布情况, 因此建立如(8)式所示的像差优化函数进行全局像差最优化计算.

      该像差评价函数为一阶连续函数且只存在一个最小值, 求解可得共心球透镜的曲率半径${r_1}$, 结合(5)式可计算球透镜的曲率半径${r_2}$, ${r_3}$${r_4}$, 即通过上述计算可以确定该多尺度广域高分辨率计算成像系统中共心球透镜的初始设计参数.

    • 通过2.1.1节中建立的像差优化函数可以确定多尺度广域高分辨率计算成像系统中的多层共心球透镜参数的最佳理论设计值, 结果如表1所列.

      面序号曲率半径/mm厚度/mm玻璃半口径/mm
      156.9031.89H-ZF1251.516
      225.0125.01H-BAK823.238
      STOInfinity32.20H-BAK86.4240
      4–32.2024.70H-ZF1228.975
      5–56.9040.13550.247

      Table 1.  Structural parameters of the monocentric ball-lens.

      图3(a)为利用表1所列数据确定的共心球透镜二维成像结构图, 其像面为与所有光学表面共心的球面. 图3(b)为共心球透镜的调制传递函数曲线, 各个视场MTF (modulation transmission function)曲线平直, 且趋势基本一致, 即各视场像差近似相同, 从而可用相同小尺度相机校正不同视场处残余像差, 并实现中继成像.

      Figure 3.  (a) Structure of the designed monocentric ball-lens; (b) MTF curves; (c) the spot diagram; (d) the ray fan curves.

      图3(c)为共心球透镜的点列图, 各个视场弥散斑80%能量均在艾里斑内, 表明共心球透镜各视场成像效果相近, 且具有较好的能量收集能力. 图3(d)为共心球透镜的光线像差图, 各视场曲线均通过坐标零点, 不存在离焦; 各曲线两端点连线与坐标轴交于原点, 不存在子午彗差. 以上结果表明, 本文提出的基于计算成像原理建立像差优化函数来获取光学系统设计参数的方法能够快速有效地获得良好的光学系统设计结果.

    • 球透镜将场景成像于与自身共心的球形一次像面上, 此时通过探测器直接接收将会由于探测器在像面位置占空比过低导致目标场景信息丢失, 故设计与球透镜共心的二次小尺度相机阵列转接系统, 将一次像面中继成像至多个探测器从而获取完整目标场景信息, 实现广域高分辨率成像. 此外, 由图3(c)可见, 经优化设计后球透镜与视场相关的像差较小, 主要影响成像质量的为球差和色差, 且像差优化函数已确保仅存在小部分残余像差, 降低了后续像差校正难度. 可通过对小尺度相机阵列进行特定设计同时校正中继成像过程中球透镜所产生的残余像差, 其结构如图4所示. 为实现二次中继成像系统自身像差及球透镜残余像差的校正, 本文采用具有对称结构的双高斯系统. 该系统能够通过正负透镜组合设计校正球差, 而通过在厚透镜中引入胶合面来校正色差.

      Figure 4.  Schematic showing the FOV overlapping betweenthe adjacent micro cameras.

      此外, 二次成像系统的口径、视场、焦距及二次成像系统与球透镜的中心距离等均是影响像面拼接的制约条件, 因此需在小尺度相机阵列设计时考虑系统像差与视场重叠的平衡问题. 为保证相邻小尺度相机间的视场重叠并提高视场利用率, 相机阵列采用正六边形几何排布方式, 各镜头物方视场重叠情况如图5所示, 其中$M$$N$分别表示物方横向和纵向有效视场长度.

      Figure 5.  Distribution of the small-scale micro camera.

      相邻小尺度相机视场重叠关系可简化为图4所示形式, 图中$l$表示成像距离, $d$表示球透镜中心到小尺度相机的距离, $h$表示相邻小尺度相机的中心距离, $D$表示小尺度相机的封装口径.

      根据成像视场与分辨率需求, 取小尺度相机有效全视场为${\theta _0} \times {\theta _1}$, 单个小尺度相机对应物方视场范围为$2l \cdot \tan \displaystyle\frac{{{\theta _0}}}{2} \times 2l \cdot \tan \displaystyle\frac{{{\theta _1}}}{2}$, 要实现相邻小尺度相机视场重叠, 各参数需满足下述条件:

      (9)式等号成立的条件为相邻小尺度相机视场恰好重叠, 此外还需满足$h > D$, 以保证相邻小尺度相机有足够的排列空间. 满足视场重叠条件和成像质量需求时, 物方横向和纵向有效视场长度为:

      若需达到的物方成像视场范围为$m \times n$, 则所需小尺度相机的数量为

      结合上述约束条件并优化光学系统, 最终确定小尺度相机封装后口径$D = 14\;{\rm{mm}}$, 相机到球透镜中心距离$d = 175.9\;{\rm{mm}}$. 当成像距离$l = 2\;{\rm{km}}$时, 通过 (9)式—(11)式计算可得, 横向张角${4.5614^ {\circ} } < $$\theta < {6.4829^ {\circ} }$, 纵向张角${3.9500^ {\circ} } < {\theta _1} < {5.6138^ {\circ} }$, 相邻相机中心间距$14.0000\;{\rm{mm}} < h < 19.9240\;{\rm{mm}}$. 为保证120° × 90°成像视场下分辨率为6 cm, 所需小尺度相机数量至少19 × 17个, 最多25 × 23个.

      基于共心球透镜的多尺度广域高分辨率计算成像系统整体光学结构如图6所示, 整体光学系统长295 mm, 其中共心球透镜直径为113.8 mm, 二级成像系统为6组9片、长度为62 mm的双高斯结构. 该系统球透镜焦距103.02 mm, 小尺度相机焦距20.83 mm, 像方F#为3.30, 入瞳直径约14.24 mm, 单路次级小尺度相机全视场8°. 由小尺度相机构成的二级光学系统将共心球透镜视场均分为若干个等大的子视场, 通过子视场拼接设计实现获取共心球透镜大视场范围内的高分辨率图像.

      Figure 6.  Structure of the whole optical system.

      为明确系统的整体成像情况, 分析系统MTF曲线、点列图、及表征各个小视场内成像差异性的场曲畸变图和光线像差图分布情况, 结果如图7所示. 图7(a)表明该系统在截止频率357 lp/mm处, 系统的MTF值在0.2左右, 且全波段MTF曲线变化趋势一致, 均接近衍射极限; 系统的零度视场、半视场和全视场MTF曲线变化趋势一致且均接近系统衍射极限, 表明各视场成像质量良好. 图7(b)所示的系统点列图中, 全波段的系统弥散斑均方根半径RMS的最大值为$ 1.145\;{\text{μ}}{\rm{m}}$, 恒小于探测器像元尺寸$ 1.4 \;{\text{μ}}{\rm{m}}$, 满足系统与探测器匹配的要求. 图7(c)所示的系统场曲和畸变曲线显示系统的场曲值在 ± 0.04范围内, 畸变值保持在0.5%以内, 二者都控制在光学系统设计有效范围内, 表明系统设计合理有效. 图7(d)为系统整体光线像差图, 结果显示各视场中子午和弧矢方向上曲线变化情况较小, 且整体变化贴合坐标轴, 球差和像散校正效果较好, 且该曲线在坐标原点附近曲线斜率为0, 说明像面无离焦现象. 上述分析结果表明, 优化后的多尺度广域计算成像系统各参数均满足设计要求, 成像效果良好.

      Figure 7.  (a) MTF curves of the whole system; (b) the spot diagram; (c) the field-curve and distortion; (d) the ray fan of the system.

    3.   系统性能分析
    • 为避免光学系统在加工时由于公差分配而导致的成像性能下降的问题, 本文利用反敏感度分析法对多尺度广域高分辨率计算成像系统的成像稳定性进行分析, 以确保该光学成像系统的MTF曲线分布满足成像需求. 图8所示为利用1000次Monte Carlo分析方法在不同公差分配情况下该成像系统MTF曲线分布情况, 以此来分析多尺度广域高分辨计算成像系统的成像稳定性.

      Figure 8.  MTF curves at different tolerance values.

      Monte Carlo仿真结果表明系统MTF在截止频率357 lp/mm处取值不低于0.05, 其中超过0.053的概率可达98%, 而该系统MTF值在截止频率处大于等于0.2的概率约为75%, 表明系统具有良好的成像稳定性.

      经光机电联合调试, 加工完成基于共心球透镜的多尺度广域高分辨率计算成像系统, 整机实物如图9(a)所示. 图9(b)为半径R = 56.8 mm的系统主物镜, 为四层三胶合共心球透镜. 实际中为了便于装配, 外侧两层结构设计为扇面结构. 根据设计需求, 在球透镜一次像面后设计次级成像系统, 由呈六边形排布的399个小尺度相机构成, 实现视场拼接获取大视场高分辨率图像, 如图9(c)所示. 小尺度相机阵列外观和工作方式如图9(d)图9(e)所示, 每个相机单独封装为独立单元, 方便装调. 考虑到其相邻视场重叠, 采用如图9(c)中橘色六边形框所示的正六边形排布设计, 这种排布不仅能够充分利用光能量, 还可以减少次级成像光学系统引入的像差, 简化整体设计和装调的复杂度, 提升最终成像质量.

      Figure 9.  Prototype of the multi-scale wide FOV high-resolution computational imaging system.

      为验证该光学成像系统的可靠性, 搭建图10所示实验测试平台, 图10(a)为测试平台结构示意图, 图10(b)为测试平台实物实际测量光学系统整机分辨率信息, 采用550 mm平行光管和N3靶标板对所设计系统分辨率进行测量, 拍摄到的靶标板图像如图10(c)所示, 实际测量时可以清晰分辨23组线对. 查阅如图10(d)所示的分辨率图案参数表中单元号与板号对应的空间频率(lp/mm)可得, N3靶标板中23组对应44.5 lp/mm, 其中所设计光学系统的焦距为47 mm, 因此系统成像分辨率约520.7 lp/mm, 由图7(a)光学系统仿真MTF曲线可知系统成像理论截止频率在520 lp/mm左右, 系统实测分辨率与理论设计基本相符.

      Figure 10.  (a) Test platform structure diagram; (b) test platform; (c) the image of target plate; (d) resolution pattern parameters table

      基于共心球透镜的多尺度广域高分辨率计算成像系统的部分成像效果图如图11所示, 该成像系统在5 km探测距离时具有15.4 km × 7.5 km的成像幅宽, 整幅照片像素数量可达32亿. 图11所示的成像结果取自本系统整体成像结果的1/10, 视场范围约为70° × 17.5°. 以距离覆盖范围从近距0.6 km到远距4.1 km处为例, 在该范围内分别选择四个不同距离处的建筑物作为目标, 目标的距离通过地图距离测量工具得到, 从而分析该系统成像质量情况. 图中给出的三列成像结果分别对应原图(下), 一级放大效果(中)和二级放大效果(上). 首先以0.6 km处近目标为例, 一级放大效果图中清晰显示了建筑物中的窗户等结构, 二级放大后则能够清晰分辨长度20 cm、高度7 cm左右的墙砖信息, 表明该系统在近景范围内成像效果良好; 当目标距离较远时, 以距离2.1 km处建筑物为例, 一级放大图像提供了清晰的目标建筑物的整体结构信息和包括窗户、文字标语等在内的细节信息, 而同样观测距离下人眼视觉系统已无法分辨此量级信息, 经二级放大后, 系统成像结果甚至能够准确提供置于建筑物顶部的直径10 cm左右的避雷针的形状轮廓信息; 在远距离成像中, 以4.1 km处建筑物为例, 此时人眼仅能捕捉有限的建筑物轮廓, 而系统成像结果经过一级放大仍能提供建筑物目标的窗户等细节信息, 在经过二级放大的图像中清晰可辨大小约为0.5 m × 0.4 m的空调外挂机, 并能够辨别其左侧墙壁上直径5 cm左右的空调排水管, 该结果表明该系统能够在远距离条件下获得良好的成像结果. 对于图中选取的不同距离分布的目标, 该系统均能实现高清晰度、高分辨率成像, 系统稳定性良好、适应性强. 此外, 如图所示的视场跨度约为7 km的成像结果中, 任意视场位置和成像距离处均不存在视觉可见的图像畸变, 主要原因在于系统主物镜的对称结构无固定光轴、轴外像差相对较小, 因此具有所见即所得、无需校正畸变的优势.

      Figure 11.  Imaging results of the designed system (partial result).

    4.   结 论
    • 为适应大视场、高分辨率实时成像探测需求, 针对传统光电成像探测系统大视场和高分辨率难以同时获得这一不足, 利用共心球透镜的结构对称性, 提出了一种基于共心球透镜的多尺度广域高分辨率计算成像系统. 该系统利用四层共心球透镜有效减小了与视场有关的像差, 通过计算成像原理构建像差优化函数对光学系统的设计参数进行计算, 并结合基于球形分布的次级相机阵列的设计有效地消除了残余像差. 此外, 利用反敏感度分析法对于不同公差分配时系统的稳定性进行分析可知, 在截止频率357 lp/mm处的MTF值几乎都能稳定在系统衍射极限0.2以上, 且弥散斑RMS半径恒小于探测器像元尺寸, 满足设计要求. 系统成像结果也证明, 该成像系统能够对不同距离的目标实现高清晰度、高分辨率无视觉可见畸变成像, 系统稳定性良好、适应性强.

Reference (25)

Catalog

    /

    返回文章
    返回