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用高斯光学和三级像差理论求变焦距物镜的初始解

史光辉

史光辉. 用高斯光学和三级像差理论求变焦距物镜的初始解[J]. 中国光学(中英文), 2018, 11(6): 1047-1060. doi: 10.3788/CO.20181106.1047
引用本文: 史光辉. 用高斯光学和三级像差理论求变焦距物镜的初始解[J]. 中国光学(中英文), 2018, 11(6): 1047-1060. doi: 10.3788/CO.20181106.1047
SHI Guang-hui. Find preliminary solution of zoom objective lens using gaussian optics and third-order aberration theory[J]. Chinese Optics, 2018, 11(6): 1047-1060. doi: 10.3788/CO.20181106.1047
Citation: SHI Guang-hui. Find preliminary solution of zoom objective lens using gaussian optics and third-order aberration theory[J]. Chinese Optics, 2018, 11(6): 1047-1060. doi: 10.3788/CO.20181106.1047

用高斯光学和三级像差理论求变焦距物镜的初始解

doi: 10.3788/CO.20181106.1047
详细信息
    作者简介:

    史光辉(1935-), 男, 辽宁本溪人, 研究员, 主要从事光学设计方面的研究。E-mail:51454473@qq.com

Find preliminary solution of zoom objective lens using gaussian optics and third-order aberration theory

More Information
  • 摘要: ZEMAX和CODE V等光学设计软件,虽然有很强的优化功能,但如果想得到好的设计结果,初始解的选择至关重要。求初始解的普遍做法是,将已有的光学系统或其中某一个组元拿来进行缩放。这种办法带有盲目性。另一种方法就是利用高斯光学和三级像差理论求变焦距物镜的初始解。这一方法有助于创新设计,但却很少被应用。本文介绍了作者在运用这一方法过程中产生的观点、理念、经验和成果。本文通过一个十倍变焦距物镜设计实例,详细介绍了求初始解的过程,为了验证该初始解的效果,还用ZEMAX进行了像差优化。为了增加说服力,设计过程的每一步,都给出了具体的数据,包括经ZEMAX优化得到的最后结果。

     

  • 图 1  两个移动组元的变焦距物镜

    Figure 1.  Zoom objective lens with two move components

    图 2  凸轮曲线展开图。实线代表变倍曲线为直线,其升角36°。虚线代表变倍曲线为双曲线。X为焦距由10变化到100时,变倍组移动方向。Y为焦距由10变化到100的滚筒转动方向

    Figure 2.  Unfold curves of the cam. The solid lines express the variable curves in shape of strait line with rise angle of 36°. The dotted lines express the variable curves in shape of bi-curve. X:The moving direction of the zooming groups from F=10 to F=100. Y:The rotation direction of roller.

    图 3  10×变焦距物镜的光学系统结构和传递函数

    Figure 3.  Structure and transfer functions of optical system with 10× zooming objective lens

    表  1  两移动组件的移动量和各组之间间隔

    Table  1.   Movements of two move components and interval between components

    FXYD1D2D3D4
    1000041.8515420
    70-2.579 1-3.983 039.270 913.596 27.983 020
    55-4.850 1-5.851 236.999 913.998 99.851 220
    30-12.547 8-7.931 129.302 219.616 711.931 120
    10-35.599 7-6.306 96.250 344.292 810.306 920
    下载: 导出CSV

    表  2  F=100、F=35和F=10各组元相关参数

    Table  2.   Related parameters of components for F=100, F=35 and F=10

    F前固组变倍组补偿组后固前后固后
    100u′-u0.208 3-0.229 2-0.120 40.266 20
    h12.53.781 34.093 84.658 72.158 7
    hp-9.675 9-1.671 4-0.32201.609 9
    35u′-u0.072 9-0.125 7-0.088 40.266 20
    h4.3752.075 13.065 34.658 72.158 7
    hp-11.702 5-2.847-0.942301.609 9
    10u′-u0.020 8-0.067 8-0.094 20.266 20
    h1.251.119 83.2034.658 72.159 7
    hp-8.205 7-5.475 8-0.829 601.609 9
    下载: 导出CSV

    表  3  解方程后得出的各焦距的像差系数

    Table  3.   Aberration coefficients of zooming groups in each focal length after solving equations

    F10090705540251510
    S100.000 60.000 50-0.000 5-0.000 9-0.000 70
    S20-0.000 3-0.000 300.000 50.000 80.000 50
    S3000000.000 10.000 20
    S5-0.025 9-0.026 4-0.027 6-0.028 3-0.028 6-0.026 4-0.0150.011 3
    下载: 导出CSV

    表  4  去掉无光焦度组四组元的像差系数

    Table  4.   Aberration coefficients of the four groups by removing afocal group

    F10090705540251510
    S10-0.001 5-0.001 300.001 30.0020.001 60
    S200.001 40.001 50-0.001 8-0.002 6-0.001 60
    S30-0.002 1-0.005 2-0.006 1-0.005 6-0.003 6-0.001 50
    下载: 导出CSV

    表  5  采用0点方法时像差的减小量

    Table  5.   Aberration reduction results using zero-point method

    F10090705540251510
    S10-0.001 2-0.001 000.001 00.001 60.001 30
    S200.001 20.001 30-0.001 5-0.001 6-0.001 30
    S30.001 90-0.002 9-0.003 8-0.003 5-0.001 000.001 2
    下载: 导出CSV

    表  6  各组元的pwp0值以及结构

    Table  6.   p, w, p0 and structure of each component

    前固定组变倍组补偿组后固组前后固组后
    p=0.210 1p=1.121 2p=-1.865 3p=-0.262 3p=10.811 9
    w=0.938 8w=1.331 6w=1.802 6w=0.611 2w=1.128 5
    p0=-0.319 4p0=-0.057 3p0=-4.159 7p0=-0.446 6p0=10.011 0
    半径玻璃半径玻璃半径玻璃半径玻璃半径玻璃
    121.917 5ZF7-74.656 9ZK9-19.888 4ZF742.750 3K99.622 6ZK9
    42.715 2K922.115 3-13.023 7-9.897 5ZF75.6437
    -99.809 9-28.057 7ZK9-16.332 4ZK920.121 16.874 5ZK9
    51.853 1LAK213.439 9ZF748.494 317.668 7LAK213.850 3
    411.755 150.519 0141.750 4
    下载: 导出CSV

    表  7  薄透镜系统像差

    Table  7.   System aberrations of thin lenses

    F像差类别S1S2S3S4S5C1C2
    100系数0.001 550.000 479-0.000 03-0.001 195-0.025 8400
    初级0.049 60.000 639-0.002 141-0.038 24-0.034 4600
    实际-0.120 30.005 158-0.443 10.070 15-0.038 97-1.281 60.0126 8
    高级-0.169 90.004 519-0.440 90.108 4-0.000 45-1.281 60.0126 8
    70系数0.002 0780.000 1260-0.001 195-0.027 5400
    初级0.066 510.000 1680-0.038 24-0.036 7200
    实际-0.064 810.001 538-0.365 60.047 67-0.042 19-0.633 30.011 75
    高级-0.131 30.001 37-0.365 60.085 91-0.005 47-0.633 30.011 75
    55系数0.001 5760.000 459-0.000 02-0.001 195-0.028 2300
    初级0.050 440.000 612-0.001 35-0.038 24-0.037 6500
    实际-0.086 990.001 646-0.318 1-0.032 96-0.044 04-0.548 70.010 24
    高级-0.137 40.001 034-0.316 80.005 28-0.006 39-0.548 70.010 24
    30系数0.000 7580.001 1670.000 06-0.001 195-0.027 4900
    初级0.024 260.001 5560.003 952-0.038 24-0.036 6400
    实际-0.121 80.002 586-0.229 10.007 815-0.045 96-0.5460.004 71
    高级-0.146 10.001 030-0.233 10.046 55-0.009 32-0.5460.004 71
    10系数0.001 5790.0004 33-0.000 05-0.001 1950.010 7700
    初级0.050 50.000 578-0.000 303-0.038 240.014 3600
    实际-0.090 470.001 538-0.166 95-0.001 3450.010 15-0.535 7-0.007 35
    高级-0.141 00.000 96-0.166 60.036 90-0.004 21-0.535 7-0.007 35
    注:S2一列中的像差为O.S.C. C1一列中的色差是以波长为单位。
    下载: 导出CSV

    表  8  初始解(厚透镜系统)的像差

    Table  8.   Aberrations of initial solution for thick lens system

    F像差类别S1S2S3S4S5C1C2
    100系数0.014 130.006 1080.000 206-0.001 608-0.022 55-0.000 6070.000 61
    初级0.451 80.008 1460.013 16-0.051 43-0.030 07-0.516 50.004 876
    实际0.429 10.013 126-0.337 430.033 45-0.034 4-1.229 30.015 02
    高级-0.022 70.004 98-0.350 60.085 29-0.004 24-0.712 80.010 14
    70系数0.013 940.003 9550.001 099-0.001 608-0.023 730.000 0180.000 272
    初级0.446 380.005 2730.070 38-0.051 43-0.031 640.001 5310.002 174
    实际0.406 610.007 370-0.217 80.013 77-0.036 53-0.247 10.011 91
    高级-0.039 770.002 106-0.282 20.065 17-0.005 29-0.248 60.009 736
    55系数0.013 010.003 7440.001 569-0.001 608-0.024 090.000 2420.000 088
    初级0.4160.004 9920.100 31-0.051 43-0.032 130.205 90.000 70
    实际0.362 20.006 843-0.141 60.000 06-0.037 66-0.022 80.009 27
    高级-0.052 70.001 851-0.241 90.051 49-0.005 53-0.228 60.008 57
    30系数0.011 660.003 8490.002 441-0.001 608-0.022 570.002 380.000 748
    初级0.373 70.005 1320.156 42-0.051 43-0.030 092.025 30.005 93
    实际0.310 720.007 052-0.004 87-0.024 12-0.037 751.759 50.010 86
    高级-0.062 980.001 92-0.161 290.027 31-0.007 66-0.265 80.004 94
    10系数0.013 1160.002 6260.002 779-0.001 6080.016 890.000 861-0.000 455
    初级0.419 420.003 5020.177 9-0.051 430.022 450.477 4-0.003 635
    实际0.360 360.005 8360.063 51-0.027 650.020 610.478 8-0.010 5
    高级-0.059 060.002 334-0.114 40.023 78-0.001 840.001 4-0.006 865
    下载: 导出CSV

    表  9  初始解结构数据

    Table  9.   Structure data of initial solution

    序号半径间隔玻璃组元焦距
    1121.912 81.5ZF760
    242.713 64K9
    3-99.806 10.1
    451.851 13LAK2
    5411.739 3变焦间隔
    6-78.323 41ZBAF1-16.5
    723.201 42
    8-29.346 01ZK9
    914.057 02ZF7
    1052.838 7变焦间隔
    11-19.607 61.2ZF7-34
    12-12.839 81.5
    13-16.101 81ZK9
    1447.809 6变焦间隔
    1542.797 82.5K917.498 3
    16-9.908 41ZF7
    17-20.143 50.1
    1817.688 32LAK2
    19141.907 920
    209.622 580.7F4-315.43
    215.643 740.3
    226.874 451ZK9
    2311.940 0
    变焦间隔
    Fd5d10d14
    10037.972 012.045 90.871 5
    7035.392 310.611 74.854 8
    5533.121 911.044 86.722 7
    3025.423 616.632 28.802 6
    102.372 341.338 77.178 4
    下载: 导出CSV

    表  10  最终设计结果结构数据

    Table  10.   Structure data of final design results

    序号半径间隔玻璃口径组元焦距
    1134.843 41.5ZF729.860.120 2
    247.075 394K929.38
    3-134.108 20.129.36
    447.300 253LAK228.76
    5413.596 3变焦间隔28.37
    6-66.570 411ZBAF113.9-16.494 9
    719.972 16212.88
    8-41.840 761ZK912.65
    915.549 692ZF712.38
    1054.753 75变焦间隔12.18
    11-18.917 591.2ZF78.38-33.879 8
    12-13.284 991.58.53
    13-15.468 311ZK98.52
    1478.311 92变焦间隔8.69
    1545.045 392.5K98.8517.527 2
    16-9.877 9151ZF79.23
    17-18.838 670.19.76
    1823.768 192LAK210.04
    19-199.390 2209.97
    2012.480 830.7F47.5-586.08
    217.204 5190.37.15
    2210.466 231ZK97.15
    2323.432 314.383 017.04
    变焦间隔
    Fd5d10d14最佳像面
    100.0738.280 1711.728 70.607 7314.382 02
    70.0535.667 310.405 04.544 114.449 3
    55.0233.406 0510.778 186.431 3214.382 02
    30.0225.611 916.608 68.394 914.468 3
    10.032.565 7541.261 786.793 7714.382 02
    下载: 导出CSV
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  • 收稿日期:  2017-09-11
  • 修回日期:  2017-10-13
  • 刊出日期:  2018-12-01

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