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    Journals >Infrared and Laser Engineering >Volume 51 >Issue 6 >Page 20210617 > Article
    • Infrared and Laser Engineering
    • Vol. 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 Ding1、2、*
    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
    • show less
    DOI: 10.3788/IRLA20210617 Cite this Article
    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 Copy Citation Text show less
    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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    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} $=9.9952 E-4
    Table 1. Comparison of rigid body motion of the optical surface (Rmax=1, c=0.2, k=0.5)
    View in the Article
    No.Deformation errorTest valueCalculation of rigid body motion
    Proposed methodTraditional method
    1Case I (Rigid body motion)$ {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} $=9.9951 E-4
    Table 2. Comparison of rigid body motion of the optical surface (Rmax=10, c=0.02, k=0.5)
    View in the Article
    No.Deformation errorTest valueCalculation of rigid body motion
    Proposed methodTraditional method
    1Case I (Rigid body motion)$ {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} $=9.9950 E-4
    Table 3. Comparison of rigid body motion of the optical surface (Rmax=100, c=0.002, k=0.5)
    View in the Article
    Statistical indicatorsMethod$ {T_x} $$ {T_y} $$ {T_z} $$ {\theta _x} $$ {\theta _y} $$ {\theta _z} $
    R2Proposed method1.00001.00001.00001.00001.00001.0000
    Traditional method0.99980.99980.91180.96830.96581.0000
    RRMSEProposed method2.0356 E-62.1224 E-61.9619 E-63.2531 E-62.4301 E-62.5259 E-6
    Traditional method0.01480.01270.29590.17750.18420.0064
    RMAEProposed method3.0167 E-63.1373 E-62.082 E-67.7869 E-66.2185 E-65.4196 E-6
    Traditional method0.04530.03410.48800.45030.42550.0164
    Table 4. Statistical error analysis for comparison between the proposed method and the traditional method
    View in the Article
    Statistical indexMethod$ {T_x} $$ {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 5. Statistical error analysis for comparison between complete and simplified equations of rigid body motion
    View in the Article
    Number of nodes$ {T_x} $$ {T_y} $$ {T_z} $$ {\theta _x} $$ {\theta _y} $$ {\theta _z} $$ {k_{{\text{37}}}} $Surface error ratio
    971.0007 E-31.9997 E-33.3057 E-39.9999 E-41.9969 E-33.0000 E-31.0000 E-33.7642 E-7
    2611.0002 E-31.9998 E-33.1775 E-39.9999 E-42.0049 E-33.0000 E-31.0000 E-37.9573 E-7
    5211.0002 E-31.9998 E-33.1774 E-39.9999 E-42.0026 E-33.0000 E-31.0000 E-33.9583 E-7
    10931.0001 E-31.9999 E-33.1334 E-39.9999 E-42.0032 E-33.0000 E-31.0000 E-37.6929 E-7
    21911.0001 E-31.9999 E-33.1141 E-39.9999 E-42.0026 E-33.0000 E-31.0000 E-38.6559 E-7
    Table 6. Results for the case of radial distribution of nodes on the optical surface
    View in the Article
    Number of nodes$ {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 7. Results for the case of approximately uniform distribution of nodes on the optical surface
    View in the Article
    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%
    Table 8. Calculated deformation errors of primary mirror and secondary mirror
    View in the Article
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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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