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.

Overview: The space gravitational wave detection telescope is one of the core payloads of the gravitational wave detection satellite, simultaneously expanding and contracting the transmitted beam. Optical path stability is one of the core indices for the telescope, closely related to its structural stability. To meet the ultra-high path stability and structural stability requirements posed by the gravitational wave detection mission, it is essential to study the structural deformation measurement of the telescope. Currently, there are still several shortcomings in the research of multi-degree-of-freedom deformation measurement methods for gravitational wave detection telescopes, such as inaccurate selection of measurement points, inability to decouple multi-degree-of-freedom coupling, and unclear identification of error sources in multi-degree-of-freedom measurement. This paper deeply investigates the high-precision measurement of structural deformation of space-borne telescopes designed for space gravitational wave detection. It preliminarily establishes a framework and method system for measuring the structural deformation of space-borne telescopes, theoretically describing the measurement principle of the method. The feasibility of this method applied to space gravitational wave detection is verified through simulation analysis and error decomposition. The paper focuses on resolving the issue of decoupling multiple degrees of freedom, establishing a mathematical model using analytical methods, and conducting preliminary validation using Zemax. Finally, noise analysis of the measurement system is carried out, with experimental testing of the main noise components in the measurement system, validating the correctness of the theoretical noise model proposed in this paper. The experimental results show that near 1 Hz, the displacement noise background of the single-link interferometer is 100 pm/Hz^1/2. At 1 mHz in the low-frequency range, the displacement noise background reaches 10 nm/Hz^1/2. The noise level of the measurement system below 1 mHz is mainly limited by environmental temperature noise, while above 10 mHz, it is primarily constrained by laser frequency noise, phase acquisition background noise, and vibration noise. During the development phase of the space gravitational wave detection telescope, the research on this measurement method is expected to fulfill the telescope's multi-degree-of-freedom deformation measurement needs. It also provides data feedback for telescope design and offers guidance for the study of the telescope's optical path stability.

The empirical findings from this study confirm the superiority of reinforcement learning in formulating effective stray light suppression measures for space gravitational wave detection telescope systems. The approach not only achieves superior suppression outcomes but also introduces an efficient, flexible, and innovative solution to the challenges of stray light in space gravitational wave detection and other high-precision optical systems.

Overview: Space gravitational wave detection missions typically consist of three identical satellites, with two laser links between the satellites at an angle of sixty degrees forming a Michelson interferometer. The arm length changes are measured using high-precision inter-satellite laser interferometry. As a key component of the inter-satellite laser interferometry system, the telescope system needs to have picometer-level optical path stability, a wavefront error of λ/30, and stray light less than 10^?10 of the transmitted power. To meet the requirements of space gravitational wave detection for the telescope system, an optical and mechanical integrated analysis and optimization method is proposed to design and optimize the primary mirror and its supporting structure. The off-axis parabolic primary mirror adopts the side three-point support method, and the influence of the support point position on the mirror surface shape and the rigid body displacement under gravity conditions has been studied. Optimization of the size of the triangular lightweighting holes on the primary mirror has been performed, and density-based topology optimization has been used to optimize the support backplate while ensuring that the first-order mode of the primary mirror component remains essentially unchanged. The flexural matrix of the primary mirror component supported by a parallel bipod linkage structure was derived based on spinor theory, and an evaluation function for the support structure was established. The size parameter range of flexible support was preliminarily determined by Matlab analysis. A optical-mechanical integrated simulation platform is set up to optimize the parameters of the support structure using a weighted sum method to convert the multi-objective optimization problem into a single-objective optimization problem. The results showed that the first-order frequency of the primary mirror component system was 392.43 Hz. Under gravity and temperature loads, the deformation of the primary mirror surface was better than λ/60, the translational rigid body displacement was better than 2.5 μm, and the rotational rigid body displacement was better than 0.5 μrad, all of which met the design specifications. Under space thermal disturbance of 10 μK/Hz^1/2, the size stability of the primary mirror component, represented by the displacement of the central point of the mirror, was at a level of 10 pm/Hz^1/2.

大口径空间光学望远镜是实现高分辨率遥感与高灵敏度探测的重要科学仪器。传统的整体式望远镜口径超过4 m将难以突破现有运载器整流罩有效包络的限制，采用分块式的技术手段可以在满足运载能力的前提下实现口径最大化，是解决当前望远镜高分辨率与高信息收集能力的最优选择。文章先从部署形式上对分块式空间望远镜的国内外研究现状进行了梳理，归纳出分块望远镜在技术实现路线上的技术类型和特点，分别对高精度机构展开技术、机器人智能装配技术、波前检测与调控技术以及超轻可调分块镜技术进行了技术内涵及实现技术途径分析，最后面向未来远景目标，对分块式空间望远镜的技术发展作了展望。

为了更好地实现多镜面大视场主动光学望远镜波前像差抑制、提升望远镜探测能力极限，本文基于望远镜视场边缘内置的错位型曲率传感器进行波前感知，并利用功率谱对波前感知结果进行分析，进而基于波前像差的空间频率特征进行调控。首先，基于复光场理论分析了非瞳面对系统波前调控的影响机理。其次，分析了本方法在多镜面大视场主动光学望远镜调控过程中的精度特性。再次，利用桌面实验对多镜面大视场主动光学望远镜调控的可行性进行了验证。最终，波前重建结果与理论波前相关性高于0.85。利用功率谱对各个视场的空间频率特性进行了分析，与单纯使用均方根对多镜面影响敏感度进行分析的方法相比，灵敏度提升了20%。

为了更好地对大口径分段望远镜进行集成检测与稳定性保持基准构建，本文提出一种大口径环形分段光学系统基准构建方法。首先，采用局部光瞳投射的方式实现光瞳对准映射；其次，利用微透镜阵列构建系统共焦空间基准；之后，基于环带整体调控模式，采用共焦与曲率半径联合分析，实现曲率半径与系统对准的共同调节；最后，利用白光干涉所形成的条纹包络进行粗共相探测，并利用通道光谱方法实现粗共相与精共相间的精度衔接，空间共焦基准定位精度优于125 μm，共相基准覆盖范围优于20 μm，精度优于0.5 μm，光谱基准不确定度优于5%。实现了不同时空特征扰动的分层次、多模态抑制，利用以上共基准原位测量新方法有效提升了光学系统原位计量检测精度并缩短了溯源链长度，增加了检测效率与准确度。

太阳望远镜内部因太阳辐射作用使镜面升温，镜面上方产生局部大气湍流，导致镜面视宁度不佳，从而造成像质的严重衰减。文中基于温度梯度和气体流动导致固体-流场的耦合作用，提出镜面视宁度效应的形成机制，建立湍流大气光学产生镜面视宁度效应的理论，利用1 550 mm大口径双曲面镜的实验数据推导并验证镜面视宁度的实验模型，并对太阳望远镜主镜温控目标进行确定。在自然对流和强迫对流两种条件下，不同环境风速时镜面温差改变对镜面视宁度的影响。结果表明：镜面温差和环境风速与镜面视宁度相关性很强，增加主动通风可以降低镜面视宁度。温差是4 ℃条件下，自然对流时镜面视宁度为 1.43″；温差是 3 ℃条件下，0.2 m/s 强迫对流时镜面视宁度为 0.44″，1 m/s 强迫对流时镜面视宁度为 0.27″。根据镜面视宁度效应容差标准，在0.2 m/s强迫对流条件下，镜面-空气温差应控制在0.2 K以下；在1.0 m/s强迫对流条件下，镜面-空气温差应控制在1 K以下。此研究成果旨在揭示空气湍流的形成机理与传播规律及其对望远镜像质退化影响规律，为提升大口径太阳望远镜工作分辨率奠定基础。