分块主镜共相位误差的全口径同步检测方法研究

The detection for the cophasing error of segmented primary mirror is divided into three stages with different methods, which makes detection system complex. To solve this problem, this project proposes a novel detection method which could detect piston and tip-tilt at same time for all of segments in full aperture of the segmented primary mirror. According to the Fourier transform principle, the relationship between the intensity distribution and the piston error is transformed and descripted in the spatial frequency domain. And then the tip-tilt and piston errors can be detected synchronously by analyzing OTF. Meanwhile, the dynamic range of the piston error detection is not limited by 2Pi uncertainty, and optical array element is not needed during the piston error detection. Based on Monte Carlo inversion method, the project puts forward an optimization algorithm to realize a non-redundant arrangement of the positions of the pupil’s sparse holes. It makes OTF, which is used to detect phasing errors, distribute non-redundantly. Consequently, the synchronous detection of co-phasing errors of all segments in full aperture is achieved. By the research on synchronous detection method of co-phasing errors, the method to suppress the residual tip-tilt error influence on the piston error detection, synchronous detection method of co-phasing errors of all segments in full aperture, and the establishment of corresponding system and the experimental verification of the synchronous co-phasing error detection for segmented primary mirror in full aperture, the project explores a new detection method which could detect co-phasing error at same time for all of segments in full aperture for the high resolution segmented telescopes, and it has a great value in the science and application.

针对分块主镜共相位误差检测需用不同方法分步、分阶段实现的问题，项目提出一种新型的共相位误差全口径同步检测方法。该方法利用傅里叶分析，将空域中的光强分布与共相位误差的关系转换为频域中的描述，借助频域指标实现tip-tilt和piston误差的同步检测，并有效突破了2Pi不定性对piston误差检测范围的困扰，也使检测不再需要光学阵列元件的介入；基于蒙特卡罗反演法，提出离散孔非冗余排布优化算法，使用于各子镜共相位误差检测的信息在频域中分开，实现了全口径共相位误差的同步检测。项目通过对共相位误差的同步检测方法、抑制残余tip-tilt误差对piston误差检测影响的方法、全口径共相位误差的同步检测方法的研究、及构建实验系统进行实验验证，探索出一种全新的分块主镜共相位误差的全口径同步检测方法，为高分辨率拼接主镜望远镜的共相位误差检测提供新途径，研究具有重要的学术及应用价值。

分块主镜共相位误差（tip-tilt和piston误差）检测是大型望远镜及强激光武器系统的关键技术之一。误差检测的大跨度（100微米）、高精度（λ/40 RMS）使检测需采用多种方法分步、分阶段实现，使系统复杂、实时性差。本项目研究了测量范围大且精度高的共相位误差全口径同步检测方法，只需设置一个具有离散孔结构的光阑，解决了上述问题。. 在共相位误差检测系统的入瞳处设置带有离散孔结构的光阑，并置于分块镜的共轭面；依据傅里叶光学原理，将混叠于空间域指标PSF中的各分块镜的共相位误差有效分开，建立了空间频域指标光学调制传递函数（MTF）与piston误差、及相位传递函数（PTF）与tip-tilt误差的理论模型；依据MTF-piston关系可对piston实现纳米级高精度检测、测量范围可达光源的相干长度，突破了2Pi不定性的困扰且无需光学阵列元件；依据PTF-tip-tilt关系，实现了piston与tip-tilt的解耦、可对tip-tilt进行高精度检测，规避了质心探测法的测量不确定性且无需反复偏转分块镜。至此，实现了piston和tip-tilt误差的同步检测且无需分粗测和精测两阶段完成。依据建立的OTF理论模型分析得到：以tip-tilt误差存在时的MTF旁瓣中心幅值对实际的MTF旁瓣进行归一化，可消除残余tip-tilt误差对piston测量的影响。依据建立的MTF理论模型，研究提出了离散孔非冗余排布方法，依此设计光阑实现了全口径内的共相位误差的并行检测，避免了移动部件的使用，提高了检测效率及系统稳定性。建立仿真及实验系统分析了影响因素、对方法的正确可行性进行了验证，结果表明：piston检测范围200微米、精度0.024λRMS，tip-tilt检测精度为1.89nmRMS。本研究为大型望远镜、高能激光武器的共相位误差检测提供了新途径，具有重要的学术价值和应用价值。