Chinese Optics, Volume. 15, Issue 4, 761(2022)
Optical design of space gravitational wave detection telescope
Figures & Tables(16)
Fig. 2. The relative position of the interference beam and the four-quadrant detector
Fig. 3. Combined cosine and sine terms of the tilt aberration. (a) Vertical tilt aberration; (b) horizontal tilt aberration; (c) combined tilt aberration
Fig. 5. The influence of different aberrations on TTL noise in the matrix 矩阵中不同像差对TTL噪声的影响
Fig. 6. The effect of low-order aberration on TTL noise under different proportions
Fig. 8. (a) Wavefront at the exit pupil of the telescope after optimization; (b) calculation results of TTL coupled noise
Fig. 9. Statistical results of coupling coefficient with Monte Carlo tolerance analysis
Table 1. The fourteen Zernike aberrations consist of the first 25 terms of Fringe Zernike polynomials
View tableView in ArticleTable 1. The fourteen Zernike aberrations consist of the first 25 terms of Fringe Zernike polynomials
i n, m j ${\textit{z}_j}\left( {\rho ,\theta } \right)$ Aberration Name 2,3 1,±1 1 ${\text{2} }\rho \cos (\theta - {\theta _{{\rm{TI}}} })$ Tilt (TI) 4 2,0 2 $ \sqrt 3 \left( {2{\rho ^2} - 1} \right) $ Defocus (DE) 5,6 2,±2 3 $\sqrt 6 {\rho ^2}\cos(2\theta - {\theta _{{\rm{PA}}} })$ Primary astigmatism (PA) 7,8 3,±1 4 $\sqrt 8 \left( {3{\rho ^2} - 2\rho } \right)\cos (\theta - {\theta _{{\rm{PC}}} })$ Primary coma (PC) 9 4,0 5 $ \sqrt 5 \left( {6{\rho ^4} - 6{\rho ^2} + 1} \right) $ Primary spherical (PS) 10,11 3,±3 6 $\sqrt 8 {\rho ^3}\cos(3\theta - {\theta _{{\rm{PTR}}} })$ Primary trefoil (PTR) 12,13 4,±2 7 $\sqrt {10} \left( {4{\rho ^4} - 3{\rho ^2} } \right)\cos (2\theta - {\theta _{{\rm{SA}}} })$ Secondary astigmatism (SA) 14,15 5,±1 8 $\sqrt {12} \left( {10{\rho ^5} - 12{\rho ^3} + 3\rho } \right)\cos (\theta - {\theta _{{\rm{SC}}} })$ Secondary coma (SC) 16 6,0 9 $ \sqrt 7 \left( {20{\rho ^6} - 30{\rho ^4} + 12{\rho ^2} - 1} \right) $ Secondary spherical (SS) 17,18 4,±4 10 $\sqrt {10} {\rho ^4}\cos(4\theta - {\theta _{{\rm{PTE}}} })$ Primary tetrafoil (PTE) 19,20 5,±3 11 $\sqrt {12} \left( {5{\rho ^5} - 4{\rho ^3} } \right)\cos (3\theta - {\theta _{{\rm{STR}}} })$ Secondary trefoil (STR) 21,22 6,±2 12 $\sqrt {14} \left( {15{\rho ^6} - 20{\rho ^4} + 6{\rho ^2} } \right)\cos (2\theta - {\theta _{{\rm{TA}}} })$ Tertiary astigmatism (TA) 23,24 7,±1 13 $4\left( {35{\rho ^7} - 60{\rho ^5} + 30{\rho ^3} - 3\rho } \right)\cos (2\theta - {\theta _{{\rm{TA}}} })$ Tertiary coma (TC) 25 8,0 14 $ 3\left( {70{\rho ^8} - 140{\rho ^6} + 90{\rho ^4} - 20{\rho ^2} + 1} \right) $ Tertiary spherical (TS)
Table 2. Average value of TTL coupling noise and probability statistics for TTL coupling noise not exceeding 25 pm/μrad under different proportions of low-order aberrations
View tableView in ArticleTable 2. Average value of TTL coupling noise and probability statistics for TTL coupling noise not exceeding 25 pm/μrad under different proportions of low-order aberrations
占比 λ/60 λ/50 λ/40 λ/30 λ/20 平均值 比例 平均值 比例 平均值 比例 平均值 比例 平均值 比例 20% 4.75 100.00% 5.85 100.00% 7.60 100.00% 10.76 100.00% 18.19 88.10% 30% 6.42 100.00% 7.86 100.00% 10.11 100.00% 14.15 98.92% 23.05 60.86% 40% 8.21 100.00% 10.07 100.00% 12.70 99.96% 17.62 88.50% 28.40 36.12% 50% 10.07 100.00% 11.98 100.00% 15.41 96.50% 21.23 68.92% 34.24 20.76% 60% 11.88 100.00% 14.51 98.54% 18.15 84.20% 25.16 48.26% 39.38 14.84% 70% 13.84 99.32% 16.78 90.80% 21.16 67.80% 29.03 34.62% 45.28 10.78% 100% 19.85 74.20% 24.32 50.98% 30.50 29.94% 41.52 14.30% 64.15 5.36%
Table 3. Indicators of space telescope system
View tableView in ArticleTable 3. Indicators of space telescope system
系统参数 技术指标 入瞳直径/mm 200 工作波长/nm 1064 科学视场/μrad ±8 系统放大倍率 40 系统波像差 ≤ 0.03λ@1064 nm TTL耦合噪声 ≤ 25 pm/μrad
Table 4. Optimized design parameters of the telescope optical system
View tableView in ArticleTable 4. Optimized design parameters of the telescope optical system
望远镜 曲率半径 空气间隔 圆锥系数 主镜 −1212.526 −573.883 −1.00537 次镜 −68.658 676.229 −1.36538 三镜 −760.425 −227.503 − 四镜 736.659 223.794 −
Table 5. High-order term coefficients of even-order aspheric surfaces of the secondary mirror
View tableView in ArticleTable 5. High-order term coefficients of even-order aspheric surfaces of the secondary mirror
项数 4th 6th 8th 10th 12th 系数 2.9010×10−8 −1.2858×10−10 7.6057×10−12 5.8855×10−14 −4.5785×10−16
Table 6. Amplitude and orientation of the wavefront at the exit pupil of the telescope based on Zernike polynomials
View tableView in ArticleTable 6. Amplitude and orientation of the wavefront at the exit pupil of the telescope based on Zernike polynomials
Mag/Ori $A_2^{{\rm{DE}}}$ $A_3^{{\rm{PA}}}/{\theta _{ {\rm{PA} } } }$ $A_4^{{\rm{PC}}}/{\theta _{ {\rm{PC} } } }$ $ A_5^{{\rm{PS}}} $ $ A_6^{{\rm{PTR}}}/{\theta _{{\rm{PTR}}}} $ $ A_7^{{\rm{SA}}}/{\theta _{{\rm{SA}}}} $ $ A_8^{{\rm{SC}}}/{\theta _{{\rm{SC}}}} $ Value/(mm·rad−1) 1.30 3.74/3.14 3.93/4.71 1.15 4.52/4.71 2.08/3.14 8.36/1.57 Mag/Ori $ A_9^{{\rm{SS}}} $ $ A_{10}^{{\rm{PTE}}}/{\theta _{{\rm{PTE}}}} $ $ A_{11}^{{\rm{STR}}}/{\theta _{{\rm{STR}}}} $ $ A_{12}^{{\rm{TA}}}/{\theta _{{\rm{TA}}}} $ $ A_{13}^{{\rm{TC}}}/{\theta _{{\rm{TC}}}} $ $ A_{14}^{{\rm{TS}}} $ − Value/(mm·rad−1) 5.85 9.04/1.57 9.69/4.71 7.64/3.14 4.03/1.57 0.93 −
Table 7. Tolerance allocation of the telescope
View tableView in ArticleTable 7. Tolerance allocation of the telescope
类型 公差项 主镜 次镜 三镜 四镜 加工公差 曲率半径(mm) 0.1 0.02 0.1 0.1 二次曲面系数 0.0005 0.001 − − 面型精度(λ) 1/100 1/100 1/200 1/200 装调公差 X向位移(μm) − 15 20 20 Y向位移(μm) − 15 20 20 Z向位移(μm) − 15 20 20 绕X轴倾斜(″) − 20 20 20 绕Y轴倾斜(″) − 20 20 20 绕Z轴倾斜(″) − 40 60 60
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Jian-cong LI, Hong-an LIN, Jia-xiong LUO, Yan-xiong WU, Zhi WANG. Optical design of space gravitational wave detection telescope[J]. Chinese Optics, 2022, 15(4): 761
Paper Information
Category: Original Article
Received: Jan. 22, 2022
Accepted: Mar. 22, 2022
Published Online: Sep. 6, 2022
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