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全偏振大气偏振模式成像系统的设计与优化分析

王成 范之国 金海红 汪先球 华豆

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全偏振大气偏振模式成像系统的设计与优化分析

王成, 范之国, 金海红, 汪先球, 华豆

Design and optimization analysis of imaging system of polarized skylight pattern of full polarization

Wang Cheng, Fan Zhi-Guo, Jin Hai-Hong, Wang Xian-Qiu, Hua Dou
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  • 全偏振成像能够获取目标更为丰富的信息, 在目标探测、大气特性研究和医学诊断等领域具有广阔的应用前景. 为了实现大视场天空区域全偏振信息的快速获取, 设计了一套全偏振大气偏振模式成像系统; 针对因系统传输矩阵“性态”的不同使得求解的目标Stokes矢量存在误差的问题, 通过分析传输矩阵的特性并建立目标函数, 将传输矩阵的优化转化为目标函数在多组条件下的求解, 确定了最优系统传输矩阵; 并对系统的四分之一波片的延迟量、偏振片的消光比以及传输矩阵进行标定. 通过开展优化前后偏振信息的对比实验, 结果表明: 优化后偏振角误差较优化前降低了10%以上; 偏振度和线偏振度中最大偏振度带的误差和中性区域的误差较优化前也有不同程度的下降. 在此基础上开展了外场全偏振信息测量实验, 结果表明系统满足设计要求, 能够有效地获取天空全偏振信息.
    Full polarization imaging can obtain more information about target, which has a broad application prospect in the target detection, researches of atmospheric characteristics, and medical diagnosis. This paper develops an imaging system of polarized skylight pattern of full polarization for obtaining the information about full polarization rapidly. Meanwhile, aiming at the problem that the error of the light intensity image obtained by the system due to the different “behavior” of the system transmission matrix is brought into the solution of the target Stokes vector, this paper analyzes the condition number and determinant of the system transmission matrix. Firstly, an objective function is established by combining the three sets of condition numbers and the determinant. Therefore, the problem of solving the optimal transmission matrix is transformed into a multi-condition extremal problem. And then the objective function is minimized to determine the optimal angle of the transmission matrix when the 1 norm condition number, 2 norm condition number and ∞ norm condition number reach the minimum value and the determinant reaches the maximum value. In addition, in order to improve the measurement accuracy, the delay components of quarter wave plate, extinction ratio of polarizer, and the transmission matrix of the system are calibrated. Optimization contrast experiment and outfield experiment are performed. The entropy, mean, and standard deviation are used to quantify the optimized results of the angle of polarization, degree of polarization, and degree of linear polarization. ∆Aop is defined as the difference in absolute value of angle of polarization between the two sides of the symmetry axis to verify the optimization performance of angle of polarization. Experimental results show that the polarization angle error after optimization is reduced by more than 10% compared with that before optimization; the error of the band of maximum polarization and the error of the neutral zone in the degree of polarization and linear polarization also decline to different degrees compared with before optimization. On this basis, an experiment on measuring external field full polarization information is carried out. The results show that the system meets the design requirements and can effectively obtain the sky full polarization information.
      通信作者: 金海红, hellen8228@163.com
    • 基金项目: 国家自然科学基金(批准号: 61571177)和安徽省高校自然科学研究项目(批准号: KJ2018JD12)资助的课题
      Corresponding author: Jin Hai-Hong, hellen8228@163.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61571177) and the Natural Science Foundation of the Anhui Higher Education Institutions of China (Grant No. KJ2018JD12)
    [1]

    高隽, 范之国 2014 仿生偏振光导航方法 (北京: 科学出版社) 第2页

    Gao J, Fan Z G 2014 Bionic polarized light navigation method (Beijing: Science Press) p2 (in Chinese)

    [2]

    Wehner R 2003 J. Comp. Physiol. A 189 579Google Scholar

    [3]

    Kraft P, Evangelista C, Dacke M, Labhart T, Srinivasan M V 2011 Philos. Trans. R. Soc. London, Ser. B 366 703Google Scholar

    [4]

    Reppert S M, Zhu H, White R H 2014 Curr. Biol. 14 155

    [5]

    Homberg U 2015 Front. Behav. Neurosci. 9 346

    [6]

    Liang H J, Bai H Y, Liu N, Sui X B 2020 Math. Probl. Eng. 2020 1

    [7]

    Li J S, Chu J K, Zhang R, Chen J H, Wang Y L 2020 Appl. Opt. 59 2955Google Scholar

    [8]

    Dupeyroux J, Viollet S, Serres J R 2019 J. R. Soc. Interface 16 20180878Google Scholar

    [9]

    胡帅, 高太长, 李浩, 程天际, 刘磊, 黄威, 江诗阳 2016 物理学报 65 014203Google Scholar

    Hu S, Gao T C, Li H, Cheng T J, Liu L, Huang W, Jiang S Y 2016 Acta Phys. Sin. 65 014203Google Scholar

    [10]

    刘敬, 金伟其, 王霞, 鲁啸天, 温仁杰 2016 物理学报 65 094201Google Scholar

    Liu J, Jin W Q, Wang X, Lu X T, Wen R J 2016 Acta Phys. Sin. 65 094201Google Scholar

    [11]

    王晨光, 张楠, 李大林, 杨江涛, 王飞, 任建斌, 唐军, 刘俊, 薛晨阳 2015 光电工程 42 60Google Scholar

    Wang C G, Zhang N, Li D L, Yang J T, Wang F, Ren J B, Tang J, Liu J, Xue C Y 2015 Opto-Electron. Eng. 42 60Google Scholar

    [12]

    Horváth G, Barta A, Gál J, Suhai B, Haiman O 2002 Appl. Opt. 41 543Google Scholar

    [13]

    Pust N J, Shaw J A 2006 Appl. Opt. 45 22Google Scholar

    [14]

    孙洁, 高隽, 怀宇, 毕冉, 范之国 2016 光电工程 43 45Google Scholar

    Sun J, Gao J, Huai Y, Fan Z G 2016 Opto-Electron. Eng. 43 45Google Scholar

    [15]

    戴俊, 高隽, 范之国 2017 中国激光 44 184

    Dai J, Gao J Fan Z G 2017 Chin. J. Las. 44 184

    [16]

    Hsu W L, Myhre G, Balakrishnan K, Brock N, Ibn-Elhaj M, Pau S. 2014 Opt. Express 22 3063Google Scholar

    [17]

    张忠顺 2014 硕士学位论文 (合肥: 合肥工业大学)

    Zhang Z S 2014 M. S. Thesis (Hefei: Hefei University of Technology) (in Chinese)

    [18]

    殷玉龙, 孙晓兵, 宋茂新, 陈卫, 陈斐楠 2019 物理学报 68 024203Google Scholar

    Yin Y L, Sun X B, Song M X, Chen W, Chen F N 2019 Acta Phys. Sin. 68 024203Google Scholar

    [19]

    Kiyohara J, Ueno S, Kitai R, Kurokawa H, Makita M, Ichimoto K 2004 Ground-based Instrumentation for Astronomy (Glasgow: SPIE) p1778

    [20]

    Anan T, Ichimoto K, Oi A, Kimura G, Nakatani Y, Ueno S 2012 Ground-based Instrumentation for Astronomy IV (Glasgow: SPIE) p84461C

    [21]

    Isaacson E, Keller H B 2012 Analysis of numerical methods (Massachusetts: Courier) pp54−55

    [22]

    Iniesta J C D T, Collados M 2000 Appl. Opt. 39 1637Google Scholar

    [23]

    Worster S, Mouritsen H, Hore P J 2017 J. R. Soc. Interface 14 134

  • 图 1  全偏振测量原理图

    Fig. 1.  Principle diagram of full polarization measurement.

    图 2  成像系统光路示意图

    Fig. 2.  Schematic diagram of the optical path of the imaging system.

    图 3  ${{{M}}_{{\rm{tran}}}}$$1/{\rm{Cond}}$与Det变化趋势 (a) $1/{\rm{Con}}{{\rm{d}}_1}$变化趋势; (b) $1/{\rm{Con}}{{\rm{d}}_2}$变化趋势; (c) $1/{\rm{Con}}{{\rm{d}}_\infty }$变化趋势; (d) $Det$变化趋势

    Fig. 3.  The change trend of $1/{\rm{Cond}}$ and Det of the ${{{M}}_{{\rm{tran}}}}$: (a) Change trend of $1/{\rm{Con}}{{\rm{d}}_1}$; (b) change trend of $1/{\rm{Con}}{{\rm{d}}_2}$; (c) change trend of $1/{\rm{Con}}{{\rm{d}}_\infty }$; (d) change trend of Det.

    图 4  系统标定原理框图

    Fig. 4.  Block diagram of system calibration principle.

    图 5  优化前后偏振信息对比 (a)−(d) 优化前Aop, ∆Aop, Dop和Dolp; (e)−(h) 优化后Aop, ∆Aop, Dop和Dolp

    Fig. 5.  Comparisons of polarization information before and after optimization: (a)−(c) Aop, ∆Aop, Dop and Dolp before optimization; (d)−(f) Aop, ∆Aop, Dop and Dolp after optimization.

    图 6  优化前后Dop, Dolp的BMP和NZ对比 (a)−(d) 优化前Dop, Dolp的BMP和NZ; (e)−(h) 优化后Dop, Dolp的BMP和NZ

    Fig. 6.  Comparisons of BMP and NZ of Dop and Dolp before and after optimization: (a)−(d) BMP and NZ of Dop and Dolp before optimization; (e)−(h) BMP and NZ of Dop and Dolp after optimization.

    图 7  目标天空区域光强图与偏振模式分布结果 (a) 偏振光强图; (b) Aop; (c) Dop; (d) Dolp; (e) Docp; (f) I分量图; (g) Q分量图; (h) U分量图; (i) V分量图

    Fig. 7.  The light intensity map and polarization mode distribution results of the target sky area: (a) Polarization intensity diagram; (b) Aop; (c) Dop; (d) Dolp; (e) Docp; (f) I component diagram; (g) Q component diagram; (h) U component diagram; (i) V component diagram.

    表 1  最大Det、最小Cond与β对应表

    Table 1.  Corresponding table of maximum Det, minimum Cond and β.

    条件数(Cond)行列式(Det)角度(β0, β1,
    β2, β3)
    Cond18.60840.0923(最大)Det: (5°, 45°, 120°, 155°)
    Cond23.4864
    Cond7.837
    Cond1(最小)7.94480.0814Cond1: (0°, 30°, 115°, 150°)
    –0.0814Cond1: (25°, 60°, 90°, 120°)
    Cond24.0092
    Cond7.0859
    Cond18.4653
    Cond2(最小)3.3381–0.0919Cond2: (35°, 70°, 100°, 135°)
    Cond7.791
    Cond18.5767
    Cond23.4563
    Cond(最小)6.22750.0911Cond: (0°, 40°, 115°, 150°)
    下载: 导出CSV

    表 2  系统传输矩阵标定结果

    Table 2.  Calibration results of system transmission matrix

    QWP旋转角度m11m12m13m14
    0.500–0.44–0.07750.225
    10°0.500–0.377–0.1370.299
    40°0.5000.01020.05770.497
    45°0.5000.0010.1440.479
    120°0.500–0.0574–0.0994–0.487
    125°0.500–0.00975–0.0268–0.499
    155°0.500–0.2690.32–0.274
    160°0.500–0.3520.295–0.198
    下载: 导出CSV

    表 3  优化前后∆Aop数据离散度对比

    Table 3.  Comparisons of data dispersion of the ∆Aop before and after optimization.

    Index均值标准差
    优化前优化后 优化前优化后 优化前优化后
    ∆Aop1.9961.7956 4.95534.2633 27.703624.709
    下载: 导出CSV

    表 4  优化前后BMP的数据离散度指标对比

    Table 4.  Comparisons of data dispersion index of BMP before and after optimization.

    Index均值标准差
    优化前优化后 优化前优化后 优化前优化后
    $\Delta {\rm{Do}}{{\rm{p}}_{{\rm{BMP}}}}$2.68842.5550 0.74960.7252 0.04760.0359
    $\Delta {\rm{Dol}}{{\rm{p}}_{{\rm{BMP}}}}$2.69332.55640.75080.72560.04810.0361
    下载: 导出CSV

    表 5  优化前后NZ数据离散度指标对比

    Table 5.  Comparisons of data dispersion index of NZ before and after optimization.

    Index均值标准差Poa
    优化前优化后 优化前优化后 优化前优化后 优化前优化后
    $\Delta {\rm{Do}}{{\rm{p}}_{{\rm{NZ}}}}$1.53591.5141 0.04460.0413 0.02460.0222 31.937735.3431
    $\Delta {\rm{Dol}}{{\rm{p}}_{{\rm{NZ}}}}$1.52851.50850.04410.04090.02450.022332.815835.9437
    下载: 导出CSV
  • [1]

    高隽, 范之国 2014 仿生偏振光导航方法 (北京: 科学出版社) 第2页

    Gao J, Fan Z G 2014 Bionic polarized light navigation method (Beijing: Science Press) p2 (in Chinese)

    [2]

    Wehner R 2003 J. Comp. Physiol. A 189 579Google Scholar

    [3]

    Kraft P, Evangelista C, Dacke M, Labhart T, Srinivasan M V 2011 Philos. Trans. R. Soc. London, Ser. B 366 703Google Scholar

    [4]

    Reppert S M, Zhu H, White R H 2014 Curr. Biol. 14 155

    [5]

    Homberg U 2015 Front. Behav. Neurosci. 9 346

    [6]

    Liang H J, Bai H Y, Liu N, Sui X B 2020 Math. Probl. Eng. 2020 1

    [7]

    Li J S, Chu J K, Zhang R, Chen J H, Wang Y L 2020 Appl. Opt. 59 2955Google Scholar

    [8]

    Dupeyroux J, Viollet S, Serres J R 2019 J. R. Soc. Interface 16 20180878Google Scholar

    [9]

    胡帅, 高太长, 李浩, 程天际, 刘磊, 黄威, 江诗阳 2016 物理学报 65 014203Google Scholar

    Hu S, Gao T C, Li H, Cheng T J, Liu L, Huang W, Jiang S Y 2016 Acta Phys. Sin. 65 014203Google Scholar

    [10]

    刘敬, 金伟其, 王霞, 鲁啸天, 温仁杰 2016 物理学报 65 094201Google Scholar

    Liu J, Jin W Q, Wang X, Lu X T, Wen R J 2016 Acta Phys. Sin. 65 094201Google Scholar

    [11]

    王晨光, 张楠, 李大林, 杨江涛, 王飞, 任建斌, 唐军, 刘俊, 薛晨阳 2015 光电工程 42 60Google Scholar

    Wang C G, Zhang N, Li D L, Yang J T, Wang F, Ren J B, Tang J, Liu J, Xue C Y 2015 Opto-Electron. Eng. 42 60Google Scholar

    [12]

    Horváth G, Barta A, Gál J, Suhai B, Haiman O 2002 Appl. Opt. 41 543Google Scholar

    [13]

    Pust N J, Shaw J A 2006 Appl. Opt. 45 22Google Scholar

    [14]

    孙洁, 高隽, 怀宇, 毕冉, 范之国 2016 光电工程 43 45Google Scholar

    Sun J, Gao J, Huai Y, Fan Z G 2016 Opto-Electron. Eng. 43 45Google Scholar

    [15]

    戴俊, 高隽, 范之国 2017 中国激光 44 184

    Dai J, Gao J Fan Z G 2017 Chin. J. Las. 44 184

    [16]

    Hsu W L, Myhre G, Balakrishnan K, Brock N, Ibn-Elhaj M, Pau S. 2014 Opt. Express 22 3063Google Scholar

    [17]

    张忠顺 2014 硕士学位论文 (合肥: 合肥工业大学)

    Zhang Z S 2014 M. S. Thesis (Hefei: Hefei University of Technology) (in Chinese)

    [18]

    殷玉龙, 孙晓兵, 宋茂新, 陈卫, 陈斐楠 2019 物理学报 68 024203Google Scholar

    Yin Y L, Sun X B, Song M X, Chen W, Chen F N 2019 Acta Phys. Sin. 68 024203Google Scholar

    [19]

    Kiyohara J, Ueno S, Kitai R, Kurokawa H, Makita M, Ichimoto K 2004 Ground-based Instrumentation for Astronomy (Glasgow: SPIE) p1778

    [20]

    Anan T, Ichimoto K, Oi A, Kimura G, Nakatani Y, Ueno S 2012 Ground-based Instrumentation for Astronomy IV (Glasgow: SPIE) p84461C

    [21]

    Isaacson E, Keller H B 2012 Analysis of numerical methods (Massachusetts: Courier) pp54−55

    [22]

    Iniesta J C D T, Collados M 2000 Appl. Opt. 39 1637Google Scholar

    [23]

    Worster S, Mouritsen H, Hore P J 2017 J. R. Soc. Interface 14 134

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出版历程
  • 收稿日期:  2021-01-17
  • 修回日期:  2021-02-16
  • 上网日期:  2021-05-15
  • 刊出日期:  2021-05-20

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