Aberration coupling characteristics of axial and lateral misalignments of off-axis three-mirror telescopes
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摘要:
为了保证离轴三反空间望远镜地面装调阶段及在轨调整阶段的成像质量，本文基于矢量像差理论从内在机理层面揭示了轴向失调与横向失调对像差影响的耦合特性，重点分析了两类失调耦合特性产生的补偿关系：（1）针对轴向失调补偿横向失调，揭示了装调过程中系统像质可能处于局部极值的一类工况；（2）针对横向失调补偿轴向失调，提出利用在轨横向失调引入的像散、彗差补偿轴向失调引入的像散、彗差的补偿策略（离焦不能补偿）。本文以实验室现有的一套离轴三反系统为例，充分验证了解析关系的准确性。仿真和实验证明：当系统同时存在轴向失调和横向失调时，系统成像质量也可能达到衍射极限（1/14λ），但系统像质处于局部极小值；望远镜在轨处于失调状态且离焦较小时，可以优先通过校正横向失调以完成系统像质校正，RMS波前误差改变量小于0.02λ。
Abstract:To ensure the imaging quality of the off-axis three-mirror space telescope during the ground adjustment and on-orbit adjustment stages, we reveal the coupling characteristics of the effect of the axial misalignment and the lateral misalignment on aberration based on the Nodal aberration theory from the internal mechanism level. This paper focuses on the compensation relationship generated by the coupling characteristics of two types of misalignments: (1) axial misalignment compensates for lateral misalignment, which reveals a type of working condition where the system image quality may be at a local extreme during the alignment process on the ground; (2) lateral misalignment compensates for axial misalignment. A compensation strategy wherein astigmatisms and comas introduced by in orbit lateral misalignment can compensate for astigmatisms and comas induced by axial misalignment is proposed (defocus cannot be corrected). Taking the off-axis three-mirror system in the laboratory as an example, the accuracy of the analytical relationships can be verified. Simulations and experiments have proven that the imaging quality of the system may reach the diffraction limit (1/14λ), but the system’s image quality is at a local minimum in the presence of both axial and lateral misalignment. When the telescope is misaligned in orbit and the defocus is small, the system image quality can be corrected by properly aligning the lateral misalignment first. The RMS wavefront error after compensation changes less than 0.02λ compared with the design state (the best state of installation and alignment).
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图 1500 mm离轴三反光路图。（a）示意图及（b）实验图
Figure 1.(a) Schematic diagram and (b) experiment device of the 500 mm off-axis three-mirror system
图 5以彗差场改变量最小为目标进行补偿时像差场分布
Figure 5.Aberration field distribution when the minimized coma field change is set as the goal for compensation
图 4以像散场改变量最小为目标进行补偿时像差场分布
Figure 4.Aberration field distribution when the minimized astigmatism field change is set as the goal for compensation
图 6利用轴向自由度补偿横向失调过程中不同状态全视场波前误差RMS分布
Figure 6.Full-field distributions of RMS wavefront error for different states in the process of compensating the aberrations induced by lateral misalignments using axial mialignments
图 7横向失调补偿轴向失调时不同阶段像差场分布
Figure 7.Aberration field distribution in different states when the lateral misalignment compensates for the axial misalignment
图 8利用横向位姿自由度补偿轴向失调（ZDE_SM=1mm）前后全视场RMS分布
Figure 8.Full-field distributions of RMS wavefront error before and after compensating the aberrations induced by axial misalignments (ZDE_SM=1mm) using lateral mialignments
图 9用横向位姿自由度补偿轴向失调（ZDE_SM=−1mm）前后全视场RMS分布
Figure 9.Full-field distributions of RMS wavefront error before and after compensating the aberrations induced by axial misalignments (ZDE_SM=−1mm) using lateral misalignments
图 10不同状态下干涉仪测量结果（去除部分高频量）
Figure 10.Measurement results with interferometer under different conditions (remove some high frequency)
表 1波像差系数对主次镜间距的敏感度
Table 1.Sensitivity of the wavefront aberration coefficient to the distance between primary and secondary mirrors (632.8 nm/mm)
像差系数 像差系数对主次镜间距的敏感度 $ {K_{040{d_1}}} $ 0.080 $ {K_{222{d_1}}} $ 0.239 $ {K_{131{d_1}}} $ −0.119 
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表 2波像差系数对次三镜间距的敏感度
Table 2.Sensitivity of the wavefront aberration coefficient to the distance between the secondary and tertiary mirrors (632.8 nm/mm)
像差系数 像差系数对次三镜间距的敏感度 $ {K_{040{d_2}}} $ −0.006 $ {K_{222{d_2}}} $ −0.016 $ {K_{131{d_2}}} $ 0.028 下载:
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表 3不同方法获得的像散系数差值
Table 3.The difference in the astigmatism coefficient obtained by different methods (λ=632.8 nm)
视场 Zernike 像差系数 仿真软
件获取值公式
计算值（0.3°，−0.8°） $ \Delta {C_5} $ −0.0038 −0.0026 $ \Delta {C_6} $ −0.0495 −0.0388 （−0.3°，−0.8°） $ \Delta {C_5} $ 0.0109 0.0118 $ \Delta {C_6} $ −0.0659 −0.0618 下载:
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表 4不同方法获得的彗差系数差值
Table 4.The difference in the coma coefficient obtained by different methods (λ=632.8 nm)
视场 Zernike 像差系数 仿真软件获取值 公式
计算值（0.3°，−0.8°） $ \Delta {C_7} $ −0.0107 −0.0108 $ \Delta {C_8} $ 0.0115 0.0108 （−0.3°，−0.8°） $ \Delta {C_7} $ −0.0136 −0.0134 $ \Delta {C_8} $ 0.0113 0.0110 下载:
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表 5像差系数对失调量的敏感度
Table 5.Sensitivity of the aberration coefficient to misalignment (632.8 nm/mm and 632.8 nm/°)
C5 C6 C7 C8 XDE 0.053 1.419 0.290 -0.001 YDE −1.410 0.051 −0.0001 0.276 ZDE −0.240 0.031 0.0129 0.139 ADE 8.394 −2.396 −0.014 −2.600 BDE 2.351 8.190 2.522 −0.0165 下载:
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