Opto-Electronic Engineering, Volume. 50, Issue 11, 230194-1(2023)
Design theory and method of off-axis four-mirror telescope for space-based gravitational-wave mission
Figures & Tables(14)
Fig. 1. Fraunhofer's diffraction model for transmitting Gaussian beam
Fig. 2. Far-field wavefront. (a) The diffraction intensity distribution; (b) The diffraction phase distribution; (c) The generated phase with wavefront error of λ/40; (d) The diffraction phase distribution of the far field with wavefront error
Fig. 4. Function of the chief ray and marginal ray in pupil imaging
Fig. 5. Schematic diagram of paraxial ray tracing of the initial design
Table 1. Specifications of the TianQin telescope
View tableView in ArticleTable 1. Specifications of the TianQin telescope
系统参数 设计需求 波长 1064 nm 波前质量(设计残余像差) /300 RMS@1064 nm 捕获视场 ±200 µrad 科学视场 ±7 µrad 入瞳直径 220 mm 放大倍率 40× 背向杂散光功率 <10−10 of laser power 光程稳定性 TTL≤0.025 nm/μrad
Table 2. Coaxial initial structure parameters of the TianQin telescope
View tableView in ArticleTable 2. Coaxial initial structure parameters of the TianQin telescope
表面 曲率半径/mm 厚度/mm 圆锥系数 主镜 −643.455 −300 −0.929 次镜 −47.498 350 − 三镜 −188.985 −60 − 四镜 Infinity − − 像面 − − −
Table 3. Fundamental parameters of final off-axial structures
View tableView in ArticleTable 3. Fundamental parameters of final off-axial structures
表面 半径/mm 厚度/mm 圆锥系数 Y偏心/mm X倾斜/(°) 尺寸/mm 主镜 −708.33 −320.02 −0.95 −180 − 230 次镜 −75.09 382.38 −5.41 − − 55 三镜 −195.52 −19.17 16.33 0.09 −8.1 2.5 四镜 49.017 − 18.27 −7.73 −5.5 9.1 像面 − − − − − −
Table 4. Even-order aspheric coefficients of final off-axial structures
View tableView in ArticleTable 4. Even-order aspheric coefficients of final off-axial structures
表面 四阶项 六阶项 八阶项 十阶项 副镜 −1.31E−06 4.63E−10 −1.74E−13 3.73E−17 三镜 5.34E−03 3.05E−03 −3.875E−03 −1.59E−03 四镜 −5.68E−05 −5.64E−05 −4.019E−08 2.31E−10
Table 5. Wavefront error in the form of Zernike Fringe series expansion
View tableView in ArticleTable 5. Wavefront error in the form of Zernike Fringe series expansion
序数 系数ai 多项式Zi 序数 系数 多项式 Z1 −0.0046 1 Z20 0.001969 (5ρ2 − 4) ρ3 sin3θ Z2 0.005705 ρ cosθ Z21 0.001095 (15ρ4 − 20ρ2 + 6) ρ2 cos2θ Z3 −0.01953 ρ sinθ Z22 −3.44E−06 (15ρ4 − 20ρ2 + 6) ρ2 sin2θ Z4 0.008356 2ρ2 − 1 Z23 7.57E−07 (35ρ6 − 60ρ4 + 30ρ2 − 4) ρ cosθ Z5 0.049601 ρ2 cos2θ Z24 −0.0003 (35ρ6 − 60ρ4 + 30ρ2 − 4) ρ sinθ Z6 −0.01931 ρ2 sin2θ Z25 −2.57E−05 70ρ8 − 140ρ6 + 90ρ4 − 20ρ2 + 1 Z7 0.010996 (3ρ2 − 2) cosθ Z26 0.000114 ρ5 cos5θ Z8 0.021988 (3ρ2 − 2) sinθ Z27 −0.00054 ρ5 sin5θ Z9 0.001957 6ρ4 − 6ρ2 + 1 Z28 −0.0001 (6ρ2−5) ρ4 cos5θ Z10 0.022299 ρ3 cos3θ Z29 −1.46E−05 (6ρ2−5) ρ4 sin5θ Z11 0.016406 ρ3 sin3θ Z30 −2.73E−07 (21ρ4 − 30ρ2 + 10) ρ3 cos3θ Z12 −0.00045 (4ρ2 − 3) ρ2 cos2θ Z31 5.70E−05 (21ρ4 − 30ρ2 + 10) ρ3 sin3θ Z13 0.003273 (4ρ2 − 3) ρ2 sin2θ Z32 2.04E−05 (56ρ6 − 105ρ4 + 60ρ2 − 10) ρ2 cos2θ Z14 0.0000082 (10ρ4 − 12ρ2 + 3) ρ cosθ Z33 2.02E−07 (56ρ6 − 105ρ4 + 60ρ2 − 10) ρ2 sin2θ Z15 −0.00074 (10ρ4 − 12ρ2 + 3) ρ sinθ Z34 −5.12E−10 (126ρ8 − 280ρ6 + 210ρ4 − 60ρ2 + 5) ρ cosθ Z16 −0.0006 20ρ6 − 30ρ4 + 12ρ2 − 1 Z35 −4.72E−06 (126ρ8−280ρ6+210ρ4−60ρ2+5) ρ sinθ Z17 −0.00513 ρ4 cos4θ Z36 −3.21E−07 (252ρ10 − 630ρ8 − 560ρ6 − 210ρ4 + 30ρ2 − 1) Z18 −0.00135 ρ4 sin4θ Z37 2.29E−08 924ρ12 − 2772ρ10 + 3150ρ8 − … 1680ρ6 + 420ρ4 − 42ρ2 + 1 Z19 0.000825 (5ρ2 − 4) ρ3 cos3θ
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Zichao Fan, Hao Tan, Yan Mo, Haibo Wang, Lujia Zhao, Huiru Ji, Zhiyu Jiang, Ruyi Peng, Liping Fu, Donglin Ma. Design theory and method of off-axis four-mirror telescope for space-based gravitational-wave mission[J]. Opto-Electronic Engineering, 2023, 50(11): 230194-1
Paper Information
Category: Article
Received: Aug. 8, 2023
Accepted: Oct. 19, 2023
Published Online: Mar. 26, 2024
The Author Email: Donglin Ma (马冬林)
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