基于矢量像差理论的空间大口径离轴三反望远镜像差补偿机理研究

Space large-aperture off-axis three-mirror anastigmatic (TMA) telescopes have many advantages in astronomical observation. However, the figure of the primary mirror and the pose of each mirror are easily affected by external factors, which will introduce wavefront aberrations to the system. Therefore, wavefront correction technique is needed to maintain the imaging quality. The engineering cost and risk of correcting the figure of the primary mirror and the pose of each mirror together on orbit are extremely high. On the contrary, the aberration compensation technique which only needs to adjust the pose of secondary mirror is more convenient for on-orbit application, and therefore it has a better prospect for development. However, at present, its theoretical support is insufficient and its applicable scope is not clear, which restrict its promotion and application. To solve these problems, this project will present a systematic and in-depth discussion on the aberration compensation mechanism based on nodal aberration theory. The theoretical researches included in this project are presented below. The wavefront aberration function for misaligned off-axis TMA telescopes is first improved to provide a theoretical tool for subsequent researches. The aberration compensation relationship between the mirror perturbations is then established to provide an analytic description for the aberration compensation state of the system. On this basis, the transition law of wavefront aberration constituent in the compensation process is revealed to clarify the internal mechanism of aberration compensation using secondary mirror on the level of aberration component. The quantitative relationship between compensation capability of secondary mirror and the related system parameters is further established to provide a theoretical basis for clarifying the scope of application. This project will lay a theoretical foundation for the application and promotion of this technique, and it will be of guiding significance for maintaining the imaging quality of space large-aperture off-axis TMA telescopes.

空间大口径离轴三反望远镜在天文观测方面具有诸多优势。然而，其主镜面形与各镜面位姿易受外界因素影响而发生改变，引入波前像差，需利用波前校正技术维持像质。对主镜面形与各镜面位姿一同进行在轨校正所需工程代价巨大，风险性高，而仅以次镜位姿调整为实现形式的像差补偿技术便于在轨应用，前景较好。然而，目前其理论支撑不足，适用性尚未明确，制约其推广与应用。本项目以矢量像差理论为基础以解决该问题为重点，系统性进行如下研究：完善失调离轴三反系统波像差表达式，为后续研究提供理论工具；建立各镜面扰动量之间像差补偿关系，对系统像差补偿状态进行解析描述；在此基础上，揭示像差补偿过程中波前像差构成的转变规律，从像差成分层面阐明次镜像差补偿机理；揭示次镜像差补偿能力与相关系统参数之间量化关系，为明确其适用范围提供理论依据。本项目将为该技术的应用与推广打下理论基础，对于空间大口径离轴三反天文望远镜像质保持具有指导性意义。

大口径离轴三反空间望远镜在天文观测方面具有诸多突出优势。然而，主镜口径的增大使离轴三反空间望远镜像质更易受失调的影响而发生退化，有必要在轨利用主动光学技术对系统波前进行校正，以恢复并维持系统像质。为降低在轨应用的工程代价，大口径反射式空间望远镜通常采用像差补偿的方式对系统像质进行校正。本项目基于矢量像差理论针对离轴三反空间望远镜像差补偿特性分析、补偿量解算开展相关研究，并对相应研究结论进行了有效验证。.具体来讲，论文主要研究工作包含如下内容：.针对离轴反射式望远镜不同类型失调量之间像差耦合特性进行研究。镜面轴向失调量可产生视场常量0°像散和90°彗差，而部分横向失调量同样产生0°像散和90°彗差，二者存在耦合关系，其耦合强度主要与光瞳偏心矢量、球差系数对轴向失调的敏感度以及彗差系数相关。镜面曲率半径误差通过影响光学系统波像差系数改变像差场分布，产生视场常量0°像散和90°彗差，耦合强度主要与球差系数对两类误差的敏感度相关。.针对离轴三反望远镜不同失调量之间的像差补偿关系进行研究。横向失调量能够补偿轴向失调产生的视场常量0°像散或90°彗差。存在曲率半径误差时，在地面装调阶段，通过调整主镜轴向位姿进行补偿，且所需调整量为曲率半径误差的一半，当主镜曲率半径误差在±1 mm范围内时，补偿残差优于0.003 λ；在轨调校阶段，通过调整次镜轴向位姿进行补偿，当主镜曲率半径误差在±0.2 mm范围内时，补偿残差优于0.005λ。.提出了一种基于任意视场位置处恒星点斑图像特征匹配的补偿量计算方法。通过建立补偿系统波像差所需调整量与任意视场位置处恒星点斑灰度图像特征之间的映射关系，将补偿量求解转化为以其为自变量的最优化问题。以600 mm口径离轴TMA为例，且考虑噪声（峰值信噪比30 dB），1%执行机构误差情况下，补偿后系统补偿残差优于0.02 λ。.本论文对于离轴三反空间望远镜像差场特性分析及像差场校正具有一定的指导意义与参考价值。