基于结构函数的大口径光学红外望远镜中频误差分配方法研究

Mid-spatial frequency errors cause scattering in the optical systems and reduce the image contrast. Therefore, the mid-spatial frequency errors have attracted more and more attention for the pursuit of high resolution imaging. Due to the development of the fabrication, testing and statistic, controlling and reducing the mid-spatial frequency errors become a research hotspot in recent years. The traditional peak and valley value (PV) as well as root mean square value (RMS) are difficult to characterize mid-spatial frequencies completely. The SlopeRMS and power spectral density function (PSD) method have large local distortions. As a statistical moment method, structure function (SF) can characterize not only the processing errors of optical components, but also the errors induced by atmospheric turbulence ,vibration and theraml. It also can be used to construct the mid-spatial frequency error calibration model in the telescope system. Therefore, with the help of SF, characterization of each error of the mid-spatial frequencies, and exploring a new method to allocate the errors based on SF are proposed and followed. Overall, this work can enhance scientific targets in optical system decomposition ability and accumulate the key technologies for the development of the large aperture optical infrared telescope.

中频误差会造成光学系统视场内的散射，降低图像的对比度。因此，对高分辨率成像的需求使得介乎于高低频之间的中频误差愈来愈受到重视。而随着大口径光学元件加工、检测以及误差统计方法的发展，控制和减小中频误差成为可能，也成为最近几年的研究热点。但对于中频误差，传统的峰谷值（PV）以及均方根值（RMS）难以表征完全，而后期提出的斜率均方根（SlopeRMS）以及功率谱密度函数（PSD）等方法具有较大的局部失真，也不能完整的对其表述。结构函数（SF）却能够解决这一问题，其作为一种统计矩，不仅可以表征光学元器件加工误差，也可以表征大气湍流、振动、温度等因素引起的误差，因此能够用来构建望远镜体系下的中频误差模型。综上，借助结构函数，表征各个误差项中的中频误差，明晰各种误差的结构函数特征，探索基于结构函数的中频误差分配方法，提升光学系统科学目标的分解能力，为掌握超大口径光学红外望远镜的研制积累关键性的技术。

中频误差对光学系统高分辨率成像、激光通信系统/引力波探测望远镜后向散射的影响较大，如何评价和抑制中频误差已成为该领域的研究热点。不同于传统采用像差评价方法，本项目从中频误差统计特性出发，通过研究中频误差的特性，提出基于结构函数/标准化点源敏感性函数的中频误差分配方法，为大口径光学红外望远镜误差分配提供新思路。具体为，针对合成孔径望远镜，基于“Brownian Bridge”过程结合标准化点源敏感性函数建立误差模型；针对大口径拼接望远镜，使用稀疏采样和曲率传感技术，控制误差；而针对抑制背向散射的需求，将结构函数和Wigner函数应用于中高频面形误差表征中，建立表面误差与散射光的关系，为超高杂散光抑制提供原理支撑。本课题的工作对提高光学系统性能具有重要的理论研究价值和应用价值。