Overview: Gravitational waves are spacetime oscillations radiated outward by accelerating mass objects. Significant astronomical events in the universe, such as the merging of massive black holes, emit stronger gravitational waves. Detecting gravitational waves allows for a deeper study of the laws governing celestial bodies and the origins of the universe, making accurate detection crucial. Gravitational wave detection technology utilizes Michelson interferometers to convert the extremely faint spacetime fluctuations caused by gravitational waves into measurable changes in optical path length. Recently, ground-based large Michelson interferometers have achieved direct detection of high-frequency gravitational waves. However, the detection of low-frequency gravitational waves, which is equally important, is not feasible on the ground due to arm length and ground noise issues. This necessitates the construction of ultra-large Michelson interferometers in space for low-frequency gravitational wave detection. Spaceborne gravitational wave detection telescopes play a vital role in collimating bidirectional beams in ultra-long interferometric optical paths in space. The extremely subtle changes in optical path caused by gravitational waves impose high demands for pm-level optical path length stability and below 10^?10 level backscattered light in these telescopes. The ultra-high level index requirements exceed the precision limits of current ground testing techniques for telescopes. To ensure that spaceborne telescopes maintain their ultra-high design performance in the orbital environment, developing testing and evaluation techniques for these key indicators is a crucial prerequisite for the success of the space gravitational wave detection program. This paper provides an overview of the development of spaceborne gravitational wave detection telescopes, both domestically and internationally. It focuses on the current status and some test results of optical path length stability and backscattered light testing of telescopes under development, as well as further testing plans, providing a reference for the testing and evaluation of Chinese space gravitational wave detection space-borne telescopes.

Overview: Since the groundbreaking discovery of gravitational waves, the scientific community has fervently pursued the exploration of low-frequency gravitational waves to glean deeper insights into the cosmos. The inherent limitations of ground-based conditions, however, pose formidable challenges for detectors in capturing gravitational waves below the 1 Hz threshold. Consequently, the imperative has shifted toward the deployment of space-based gravitational wave detectors as the paramount solution for effective low-frequency gravitational wave detection. At the crux of space-based gravitational wave detection lies the pivotal role of spaceborne telescopes. Given the expansive transmission distances spanning magnitudes of 10⁹ m between celestial constellations, the demand for nanoradian-level precision in telescope pointing accuracy becomes non-negotiable. The concomitant necessity for high-precision measurements and calibration emerges as a prerequisite for achieving the exacting standards of pointing accuracy in spaceborne telescopes dedicated to gravitational wave detection. To ameliorate the deleterious effects of pointing deviations on gravitational wave detection, this study strategically optimizes key parameters, including microlens structures, detector selection, and algorithmic frameworks, thereby achieving a breakthrough in high-precision pointing deviation measurements. Leveraging a low-density microlens array with extended sub-aperture focal lengths enhances the spatial scale of the light spot within each sub-aperture. This, coupled with detectors boasting a high signal-to-noise ratio, synergistically elevates the pointing detection accuracy of each discrete lens. Moreover, the paper introduces an innovative, Hartmann principle-based methodology for high-precision pointing deviation measurements, deploying a spatially reused paradigm across multiple sub-apertures. By aggregating measurement results from diverse sub-apertures, the approach effectively mitigates the influence of assorted random errors on measurement accuracy, thereby markedly enhancing the precision of pointing deviation measurements. Illustrating the efficacy of these methodologies, the paper exemplifies their application within the ambit of the "Tianqin Plan" for space-based gravitational wave detection. Employing numerical simulations and factoring in the design parameters of the Hartmann sensor, the study performs a meticulous analysis of pointing deviation measurement accuracy. Comparative analysis between single sub-aperture and sub-aperture correlation reuse technologies reveals a compelling enhancement in measurement accuracy, approximating a sevenfold improvement with the latter. The pointing deviation measurement accuracy achieved through sub-aperture correlation reuse technology is quantified at approximately 18.81 nanoradians. Considering the optical magnification inherent in spaceborne telescopes, estimated at around 30 times, the resultant pointing deviation measurement accuracy reaches an impressive 0.62 nanoradians. This design precision significantly surpasses the stipulated 1 nanoradian accuracy requirement for ground-based gravitational wave pointing deviation measurements. As a prudential measure, the proposed design incorporates a substantial margin to accommodate potential accuracy diminution attributable to external perturbations during empirical testing.

盲解卷积是常用的自适应光学图像事后重建方法之一。为提高盲解卷积对太阳(自适应光学)图像的重建效果，本文提出了基于二阶广义总变分的空变多帧盲解卷积算法。该算法首先利用交替最小化和半二次分裂方法求解本文提出的二阶广义总变分约束的空不变多帧盲解卷积模型；然后针对非等晕大视场太阳图像特性，利用重叠分块与加权拼接实现空变盲解卷积扩展。在一米新真空太阳望远镜(NVST)观测的真实太阳图像上进行的重建实验与分析表明，本文算法在主观视觉效果和客观指标上均具有较好的图像重建效果。

在天文大视场高分辨率成像领域，对地表层自适应光学(Ground-Layer Adaptive Optics, GLAO)系统作出准确的理论评估是系统设计与优化的关键前提。在GLAO技术中，地表层湍流特性与导引星布局是影响系统性能的重要因素。针对不同湍流环境与导引星位置分布，基于空间频谱滤波理论和蒙特卡洛方法对GLAO系统进行理论分析与性能评价工作，从而验证两种方法的正确性与准确性。结果表明，两种模型得到的系统校正规律呈现明显的一致性。在一定条件下，两种方法数值模拟偏差最大不超过4.6%。空间频谱滤波原理将系统简化为线性模型，其计算速度更快，便于发现系统特征规律，但是该方法适用于导引星呈对称布局的系统性能分析，不适用于非对称排布的任意导星布局解析分析。蒙特卡洛方法结合真实系统的物理过程进行实时模拟，其导引星布局可以任意设置，对于系统实际运行状态的预测更加准确。在两种分析方法对比的基础上，进一步针对系统布局给出了初步的优化结果，相关工作对未来GLAO系统的设计与优化具有指导意义。