含自由曲面光学系统高阶矢量像差理论及失调校正方法和关键技术研究

he introduction of free-form surfaces to traditional off-axis optical path, help to solve field aberration balance problem of large FOV, high resolution optical system. However, the initial alignment accuracy is reduced, and the linear equivalent error of the numerical misalignment correction model such as the sensitivity matrix is magnified, so that it is difficult to obtain the convergence result. In addition, the out-of-axis field high-order aberrations increase proportionally and play a dominant role on the image quality, resulting in the decrease of the sensitivity of the correction strategy based on the third-order nodal aberration theory and the significant increase of the error of the noise introduction. The above problems bring great blindness and uncertainty to the alignment procedure, and new solutions are urgently needed..The subject faces the frontiers of space optical technology, extracts scientific topics in the field of optical alignment and assembly for optical systems with free-form surfaces. The subject hopes to derive the functions of intrinsic and extrinsic aberrations by dividing and describing the misalignment free-form surfaces in the nodal aberration field, which help to perfecting the higher-order nodal aberration theory and building the analytical correction model. The subject is expected to scientifically explain the propagation mechanism of high-order wave aberration fields in complex optical paths, and reveal the law of the interaction between high-order nodal aberrations and misalignment of optical surface. It is of great scientific significance and application value to solve the problem of computer-aided alignment of complex optical path with free-form surfaces.

将自由曲面引入离轴光路，有助于解决大视场、高分辨率空间光学系统像差平衡难题。但由此引起初装调精度下降，使灵敏度矩阵等数值化校正模型线性等效误差放大，难以获得收敛结果。由于轴外高级像差占比激增并对像质起主导作用，使基于三级矢量像差的校正模型敏感度下降，噪声引入的解算误差显著上升。上述问题为装调过程带来较大盲目性和不确定性，亟待探索新的解决途径。.课题面向空间光学技术前沿，凝练含自由曲面光学系统装调领域科学议题，通过在矢量像差场中划分并描述失调自由曲面，逐一推导本征和诱导像差场，为完善高级矢量像差场理论并建立解析形失调校正模型，并据此系统分析测量噪声与失调量解算精度作用关系提供理论基础。课题有望科学解释高阶矢量像差场在复杂光路中传播机理，揭示高阶矢量像差与失调量间作用规律，具有重要科学意义和应用价值。

为拓展视场、提高观测效率、改善光学性能，空间天文望远镜光路设计日趋复杂。一方面，在同轴TMA光路的基础上发展为兼具视场和口径离轴，且采取非共母线设计的偏轴系统。另一方面，为平衡随视场激增的轴外视场像差，将具有复杂表面特征的自由曲面引入光学设计。上述趋势增大了光学系统地面装调的挑战性，导致装调效率低、存在不确定性、且装调残差难以控制。基于现有代理模型的计算机辅助装调算法存在收敛速度慢，难以适应复杂光学系统初装调残差增大引起的算法非线性误差等问题。课题针对上述问题，重点研究含自由曲面偏轴反射式光学系统失调与矢量像差场分布间作用机理等基础理论问题，据此构建复杂光学系统装调理论体系。.课题系统研究了含自由曲面复杂光学系统装调策略制定方法。以失调敏感度单变量分析为基础，分离高敏感失调间耦合作用特性。再针对敏感度耦合关系和敏感度排序，制定光学系统装调策略。提出多CGH辅助区互干涉方法，以提高初装调精度，解决含自由曲面系统光学基准传递精度低等问题。并通过坐标变换算法，构建基于光学特征传递的初装调精度分析模型。以0.6m偏轴反射式光学系统为例，进行模拟初装调并据此计算初装调残差。基于灵敏度矩阵和矢量像差模型分别构建失调量解算方程。采用阻尼系数自适应算法解决最小二乘法收敛性差、对Zernike系数测量误差敏感度高等问题。通过模拟装调实验初步验证了所提算法可在初装调残差阈值内，高效解算各维度失调量。课题在矢量像差理论研究方面重点开展三方面工作。第一，研究偏轴光学系统像差场偏移矢量推导方法，实现了沿轴失调和垂轴失调在像差场偏移矢量中的统一解析描述。第二，重点研究偏轴光学系统三阶矢量像差场解析模型，推导其与出瞳波像差Zernike系数间函数关系。第三，针对非光瞳位置自由曲面，初步研究描述自由曲面的各阶Zernike系数在矢量像差场中分解、传递、归类的方法。基于上述研究，构建了偏轴光学系统失调量解算模型，通过模拟装调实验验证了失调解算模型的有效性和解算精度。.阶段性研究进展有望应用于大口径空间天文望远镜地面装调，并为后续针对含自由曲面偏轴光学系统构建完善的高阶矢量像差模型奠定理论基础。