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Infrared and Laser Engineering, Volume. 51, Issue 6, 20210617(2022)

Thermal-structural-optical integrated analysis method based on the complete equations of rigid body motion

Zengwei Wang1...2, Zhicheng Zhao3, Yi Yang1,2, Songtao Lei1,2, and Lei Ding12,* |Show fewer author(s)
Author Affiliations
  • 1Shanghai Institute of Technical Physics, Chinese Academy of Sciences, Shanghai 200083, China
  • 2Key Laboratory of Infrared Detection and Imaging Technology, Chinese Academy of Sciences, Shanghai 200083, China
  • 3School of Optoelectronic Science and Engineering, Soochow University, Suzhou 215000, China
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    AbstractGet PDF(in Chinese)
    Figures&Tables (25)
    Equations (32)
    References (18)
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    Figures & Tables(25)
    Schematic diagram of optical surface vertex coordinate system

    Fig. 1. Schematic diagram of optical surface vertex coordinate system

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    Schematic diagram of light incident area before and after optical surface deformation

    Fig. 2. Schematic diagram of light incident area before and after optical surface deformation

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    Schematic diagram of light incident area before and after optical surface deformation

    Fig. 3. Schematic diagram of light incident area before and after optical surface deformation

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    Flow chart of the proposed optical surface deformation error calculation method

    Fig. 4. Flow chart of the proposed optical surface deformation error calculation method

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    Optical surface - Standard sphere (c=0.2, k=0.5)

    Fig. 5. Optical surface - Standard sphere (c=0.2, k=0.5)

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    The fourth term of Fringe Zernike polynomial (Taking k4=1 as an example)

    Fig. 6. The fourth term of Fringe Zernike polynomial (Taking k4=1 as an example)

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    Radial distribution of nodes on the optical surface. (a) 97 nodes；(b) 261 nodes；(c) 521 nodes；(d) 2191 nodes

    Fig. 7. Radial distribution of nodes on the optical surface. (a) 97 nodes；(b) 261 nodes；(c) 521 nodes；(d) 2191 nodes

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    [in Chinese]

    Fig. 7. [in Chinese]

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    Approximately uniform distribution of nodes on the optical surface. (a) 97 nodes；(b) 258 nodes；(c) 520 nodes；(d) 2193 nodes

    Fig. 8. Approximately uniform distribution of nodes on the optical surface. (a) 97 nodes；(b) 258 nodes；(c) 520 nodes；(d) 2193 nodes

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    Relationship between estimation errors and number of nodes. (a) Rigid body motion；(b) Elastic deformation coefficient

    Fig. 9. Relationship between estimation errors and number of nodes. (a) Rigid body motion；(b) Elastic deformation coefficient

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    Approximately uniform distribution of nodes on the optical surface with X: (a) [−0.1, 0.1]；(b) [−0.3, 0.3]；(c) [−0.5, 0.5]；(d) [−0.7, 0.7]

    Fig. 10. Approximately uniform distribution of nodes on the optical surface with X: (a) [−0.1, 0.1]；(b) [−0.3, 0.3]；(c) [−0.5, 0.5]；(d) [−0.7, 0.7]

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    [in Chinese]

    Fig. 10. [in Chinese]

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    Relationship between estimation errors and the surface range coefficient. (a) Rigid body motion；(b) Elastic deformation

    Fig. 11. Relationship between estimation errors and the surface range coefficient. (a) Rigid body motion；(b) Elastic deformation

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    An optical system with two mirrors. (a) Optical design; (b) Mechanical structure; (c) Finite element model

    Fig. 12. An optical system with two mirrors. (a) Optical design; (b) Mechanical structure; (c) Finite element model

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    Finite element and displacement of optical surfaces. (a) Finite element-primary mirror; (b) Displacement-primary mirror；(c) Finite element-secondary mirror; (d) Displacement-secondary mirror

    Fig. 13. Finite element and displacement of optical surfaces. (a) Finite element-primary mirror; (b) Displacement-primary mirror；(c) Finite element-secondary mirror; (d) Displacement-secondary mirror

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    Elastic deformation and fitting residual. (a) Primary mirror deformation; (b) Deformation fitting residual of primary mirror；(c) Secondary mirror deformation; (d) Deformation fitting residual of secondary mirror

    Fig. 14. Elastic deformation and fitting residual. (a) Primary mirror deformation; (b) Deformation fitting residual of primary mirror；(c) Secondary mirror deformation; (d) Deformation fitting residual of secondary mirror

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    Spot diagram and MTF curve. (a) Original spot diagram; (b) Original MTF；(c) Spot diagram of the deformed system; (d) MTF of the deformed system

    Fig. 15. Spot diagram and MTF curve. (a) Original spot diagram; (b) Original MTF；(c) Spot diagram of the deformed system; (d) MTF of the deformed system

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    • Table 1. Comparison of rigid body motion of the optical surface (Rmax=1, c=0.2, k=0.5)

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      Table 1. Comparison of rigid body motion of the optical surface (Rmax=1, c=0.2, k=0.5)

      No.Deformation errorTest valueCalculation of rigid body motion
      The proposed methodTraditional method
      1Case I (Rigid body motion)$ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=1.0000 E-1 $ {\theta _x} $=0.0000 $ {\theta _y} $=0.0000 $ {\theta _z} $=0.0000 $ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=1.0000 E-1 $ {\theta _x} $=−1.6168 E-8 $ {\theta _y} $=−4.0098 E-9 $ {\theta _z} $=6.5839 E-9 $ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=8.5600 E-2 $ {\theta _x} $=−7.3240 E-10 $ {\theta _y} $=1.4389 E-4 $ {\theta _z} $=−2.6730 E-10
      2Case II (Rigid body motion)$ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=0.0000 $ {\theta _y} $=0.0000 $ {\theta _z} $=0.0000 $ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=9.9999 E-4 $ {\theta _x} $=1.3572 E-8 $ {\theta _y} $=−1.2696 E-8 $ {\theta _z} $=−1.8522 E-9 $ {T_x} $=9.9994 E-4 $ {T_y} $=9.9999 E-4 $ {T_z} $=8.5637 E-4 $ {\theta _x} $=1.7830 E-9 $ {\theta _y} $=1.4343 E-6 $ {\theta _z} $=1.5747 E-10
      3Case III (Rigid body motion)$ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=1.0000 E-3 $ {\theta _y} $=1.0000 E-3 $ {\theta _z} $=1.0000 E-3 $ {T_x} $=1.0000 E-3 $ {T_y} $=9.9999 E-4 $ {T_z} $=9.9999 E-4 $ {\theta _x} $=1.0000 E-3 $ {\theta _y} $=1.0000 E-3 $ {\theta _z} $=9.9999 E-4 $ {T_x} $=9.9672 E-4 $ {T_y} $=1.0000 E-3 $ {T_z} $=8.4683 E-4 $ {\theta _x} $=1. 1101 E-3 $ {\theta _y} $=1.0977 E-3 $ {\theta _z} $=9.9953 E-4
      4Elastic deformation$ {T_x} $=0.0000 $ {T_y} $=0.0000 $ {T_z} $=0.0000 $ {\theta _x} $=0.0000 $ {\theta _y} $=0.0000 $ {\theta _z} $=0.0000 k4=1.0000 E-3 $ {T_x} $=4.9010 E-7 $ {T_y} $=8.7944 E-10 $ {T_z} $=3.2373 E-6 $ {\theta _x} $=−5.4085 E-10 $ {\theta _y} $=−1.4595 E-5 $ {\theta _z} $=−1.3092 E-9 $ {T_x} $=4.9005 E-7 $ {T_y} $=8.8007 E-10 $ {T_z} $=3.2373 E-6 $ {\theta _x} $=−5.4015 E-10 $ {\theta _y} $=−1.4595 E-5 $ {\theta _z} $=−1.3093 E-10
      5Rigid body motion + elastic deformation$ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=1.0000 E-3 $ {\theta _y} $=1.0000 E-3 $ {\theta _z} $=1.0000 E-3 k4=1.0000 E-3 $ {T_x} $=1.0004 E-3 $ {T_y} $=9.9999 E-4 $ {T_z} $=1.0032 E-3 $ {\theta _x} $=9.9994 E-4 $ {\theta _y} $=9.8545 E-4 $ {\theta _z} $=9.9997 E-4 $ {T_x} $=9.9722 E-4 $ {T_y} $=1.0038 E-3 $ {T_z} $=8.5007 E-4 $ {\theta _x} $=1.1101 E-3 $ {\theta _y} $=1.0830 E-3 $ {\theta _z} $=9.9952 E-4

    • Table 2. Comparison of rigid body motion of the optical surface (Rmax=10, c=0.02, k=0.5)

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      Table 2. Comparison of rigid body motion of the optical surface (Rmax=10, c=0.02, k=0.5)

      No.Deformation errorTest valueCalculation of rigid body motion
      Proposed methodTraditional method
      1Case I (Rigid body motion)$ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=1.0000 E-1 $ {\theta _x} $=0.0000 $ {\theta _y} $=0.0000 $ {\theta _z} $=0.0000 $ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=1.0000 E-1 $ {\theta _x} $=1.5220 E-10 $ {\theta _y} $=−1.8239 E-11 $ {\theta _z} $=1.1900 E-10 $ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=8.5600 E-2 $ {\theta _x} $=−5.4967 E-10 $ {\theta _y} $=1.4384 E-5 $ {\theta _z} $=−8.5772 E-11
      2Case II (Rigid body motion)$ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=0.0000 $ {\theta _y} $=0.0000 $ {\theta _z} $=0.0000 $ {T_x} $=9.9999 E-4 $ {T_y} $=9.9999 E-4 $ {T_z} $=9.9999 E-4 $ {\theta _x} $=−9.4591 E-11 $ {\theta _y} $=−1.9287 E-11 $ {\theta _z} $=−4.8523 E-11 $ {T_x} $=9.9995 E-4 $ {T_y} $=9.9999 E-4 $ {T_z} $=8.5637 E-4 $ {\theta _x} $=−3.1314 E-9 $ {\theta _y} $=1.3656 E-7 $ {\theta _z} $=−9.2801 E-11
      3Case III (Rigid body motion)$ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=1.0000 E-3 $ {\theta _y} $=1.0000 E-3 $ {\theta _z} $=1.0000 E-3 $ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=9.9999 E-4 $ {\theta _y} $=1.0000 E-3 $ {\theta _z} $=1.0000 E-3 $ {T_x} $=9.9733 E-4 $ {T_y} $=1.0113 E-3 $ {T_z} $=3.0511 E-4 $ {\theta _x} $=1. 0325 E-3 $ {\theta _y} $=1.0087 E-3 $ {\theta _z} $=9.9951 E-4

    • Table 3. Comparison of rigid body motion of the optical surface (Rmax=100, c=0.002, k=0.5)

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      Table 3. Comparison of rigid body motion of the optical surface (Rmax=100, c=0.002, k=0.5)

      No.Deformation errorTest valueCalculation of rigid body motion
      Proposed methodTraditional method
      1Case I (Rigid body motion)$ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=1.0000 E-1 $ {\theta _x} $=0.0000 $ {\theta _y} $=0.0000 $ {\theta _z} $=0.0000 $ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=1.0000 E-1 $ {\theta _x} $=−7.8975 E-12 $ {\theta _y} $=1.1882 E-11 $ {\theta _z} $=−4.5312 E-12 $ {T_x} $=1.0000 E-1 $ {T_y} $=1.0000 E-1 $ {T_z} $=8.5600 E-2 $ {\theta _x} $=−4.1705 E-10 $ {\theta _y} $=−1.4335 E-6 $ {\theta _z} $=2.0338 E-10
      2Case II (Rigid body motion)$ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=0.0000 $ {\theta _y} $=0.0000 $ {\theta _z} $=0.0000 $ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=9.9999 E-4 $ {\theta _x} $=−3.3836 E-11 $ {\theta _y} $=−1.5327 E-12 $ {\theta _z} $=−1.5605 E-11 $ {T_x} $=9.9995 E-4 $ {T_y} $=9.9999 E-4 $ {T_z} $=8.5636 E-4 $ {\theta _x} $=3.3035 E-10 $ {\theta _y} $=1.0407 E-8 $ {\theta _z} $=−3.1869 E-10
      3Case III (Rigid body motion)$ {T_x} $=1.0000 E-3 $ {T_y} $=1.0000 E-3 $ {T_z} $=1.0000 E-3 $ {\theta _x} $=1.0000 E-3 $ {\theta _y} $=1.0000 E-3 $ {\theta _z} $=1.0000 E-3 $ {T_x} $=9.9987 E-4 $ {T_y} $=1.0000 E-3 $ {T_z} $=9.9973 E-4 $ {\theta _x} $=1.0000 E-3 $ {\theta _y} $=9.9999 E-4 $ {\theta _z} $=9.9999 E-4 $ {T_x} $=1.0000 E-3 $ {T_y} $=1.0525 E-3 $ {T_z} $=−5.8487 E-3 $ {\theta _x} $=1. 0144 E-3 $ {\theta _y} $=9.9060 E-4 $ {\theta _z} $=9.9950 E-4

    • Table 4. Statistical error analysis for comparison between the proposed method and the traditional method

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      Table 4. Statistical error analysis for comparison between the proposed method and the traditional method

      Statistical indicatorsMethod$ {T_x} $$ {T_y} $$ {T_z} $$ {\theta _x} $$ {\theta _y} $$ {\theta _z} $
      R2Proposed method1.00001.00001.00001.00001.00001.0000
      Traditional method0.99980.99980.91180.96830.96581.0000
      RRMSEProposed method2.0356 E-62.1224 E-61.9619 E-63.2531 E-62.4301 E-62.5259 E-6
      Traditional method0.01480.01270.29590.17750.18420.0064
      RMAEProposed method3.0167 E-63.1373 E-62.082 E-67.7869 E-66.2185 E-65.4196 E-6
      Traditional method0.04530.03410.48800.45030.42550.0164

    • Table 5. Statistical error analysis for comparison between complete and simplified equations of rigid body motion

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      Table 5. Statistical error analysis for comparison between complete and simplified equations of rigid body motion

      Statistical indexMethod$ {T_x} $$ {T_y} $$ {T_z} $$ {\theta _x} $$ {\theta _y} $$ {\theta _z} $
      R2Complete equation1.00001.00001.00001.00001.00001.0000
      Simplified equation0.99990.99991.00001.00001.00001.0000
      RRMSEComplete equation1.9457 E-61.9696 E-61.91146 E-63.1742 E-62.3667 E-62.9295 E-6
      Simplified equation0.01210.01141.6050 E-50.00240.00240.0053
      RMAEComplete equation31019 E-63.1034 E-62.7365 E-68.1965 E-67.8133 E-66.6832 E-6
      Simplified equation0.03280.03016.0652 E-50.00640.00660.0149

    • Table 6. Results for the case of radial distribution of nodes on the optical surface

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      Table 6. Results for the case of radial distribution of nodes on the optical surface

      Number of nodes$ {T_x} $$ {T_y} $$ {T_z} $$ {\theta _x} $$ {\theta _y} $$ {\theta _z} $$ {k_{{\text{37}}}} $Surface error ratio
      971.0007 E-31.9997 E-33.3057 E-39.9999 E-41.9969 E-33.0000 E-31.0000 E-33.7642 E-7
      2611.0002 E-31.9998 E-33.1775 E-39.9999 E-42.0049 E-33.0000 E-31.0000 E-37.9573 E-7
      5211.0002 E-31.9998 E-33.1774 E-39.9999 E-42.0026 E-33.0000 E-31.0000 E-33.9583 E-7
      10931.0001 E-31.9999 E-33.1334 E-39.9999 E-42.0032 E-33.0000 E-31.0000 E-37.6929 E-7
      21911.0001 E-31.9999 E-33.1141 E-39.9999 E-42.0026 E-33.0000 E-31.0000 E-38.6559 E-7

    • Table 7. Results for the case of approximately uniform distribution of nodes on the optical surface

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      Table 7. Results for the case of approximately uniform distribution of nodes on the optical surface

      Number of nodes$ {T_x} $$ {T_y} $$ {T_z} $$ {\theta _x} $$ {\theta _y} $$ {\theta _z} $$ {k_{{\text{37}}}} $Surface error ratio
      971.0005 E-31.9997 E-33.2749 E-99.9999 E-42.0000 E-33.0000 E-31.0000 E-31.9526 E-8
      2581.0004 E-31.9998 E-33.1834 E-39.9944 E-42.0000 E-33.0000 E-31.0000 E-31.3288 E-7
      5201.0003 E-31.9998 E-33.1303 E-39.9916 E-42.0000 E-33.0000 E-31.0000 E-32.0133 E-7
      10921.0001 E-31.9999 E-33.0751 E-39.9877 E-42.0006 E-33.0000 E-31.0000 E-33.2122 E-7
      21931.0000 E-31.9999 E-33.0476 E-39.9937 E-41.9999 E-33.0000 E-31.0000 E-32.1161 E-7

    • Table 8. Calculated deformation errors of primary mirror and secondary mirror

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      Table 8. Calculated deformation errors of primary mirror and secondary mirror

      Normalized radius $ {T_x} $/ mm $ {T_y} $/ mm $ {T_z} $/ mm $ {\theta _x} $/ (°) $ {\theta _y} $/ (°) $ {\theta _z} $/ (°) PV/ mm Surface error ratio
      Primary mirror48.7284−1.5587 E-53.3805 E-3−3.8495 E-3−6.1539 E-57.0932 E-82.3137 E-73.4480 E-60.44%
      Secondary mirror74.5760−5.0592 E-56.9241 E-39.2077 E-31.4575 E-4−4.1180 E-87.9050 E-71.9449 E-51.82%
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    Zengwei Wang, Zhicheng Zhao, Yi Yang, Songtao Lei, Lei Ding. Thermal-structural-optical integrated analysis method based on the complete equations of rigid body motion[J]. Infrared and Laser Engineering, 2022, 51(6): 20210617

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    Paper Information

    Category: Optical design

    Received: Aug. 30, 2021

    Accepted: --

    Published Online: Dec. 20, 2022

    The Author Email:

    DOI:10.3788/IRLA20210617

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology