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: 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.

太极计划是中国科学院提出的空间引力波探测任务，其利用激光差分干涉的方法探测卫星间由引力波引起的pm级位移波动。为消除卫星间因时钟不同步而产生的测量误差，拟采用边带倍频时钟噪声传递方法进行星间时钟噪声测量与消除。本文讨论太极计划星间时钟噪声传递的需求、原理、方法，并设计实验进行原理验证。通过搭建电子学实验测试两个系统时钟噪声的极限值，确定实验相关参数，进一步通过光学实验验证边带倍频传递方案的原理。实验结果表明，本文提出的时钟噪声消除方案及相关参数合理可行，满足太极计划的应用需求。在0.05 Hz~1 Hz频段，星间时钟噪声的抑制效果优于2π×10⁻⁵ rad/Hz^1/2，满足太极探路者的噪声需求。本文研究为未来太极计划的时钟噪声传递方案与参数设计奠定实验和理论基础。

太极计划是中国探测空间引力波的一项重点任务。望远镜作为空间引力波探测中的重要组成部分，它的性能会直接影响引力波探测的精度。现有的典型空间引力波望远镜结构中次镜灵敏度高，难以满足更大口径的空间引力波望远镜对制造装调公差的要求，特别是在轨稳定性公差要求。为解决以上问题，首先，提出了一种中间像面设置于三四镜之间的新型空间引力波望远镜光学系统结构，以降低次镜灵敏度；结合高斯光学理论方法，从理论上分析并计算新型望远镜结构的初始参数。其次，通过优化设计，获得入瞳直径为400 mm，放大倍率为80倍，科学视场为±8 μrad，波前误差RMS值优于0.0063λ的望远镜光学系统。最后，建立了望远镜系统的灵敏度评价公差分配表，对比分析了现有望远镜结构与新型望远镜结构的公差情况。结果显示：相较于现有望远镜结构，新型望远镜结构的灵敏度降低了30.4%，具有低灵敏度优势，为空间引力波望远镜的设计提供了一种优选方案。

在空间引力波探测太极计划中，激光干涉测距系统是获取引力波信号的直接手段，为了消除激光频率不稳定性对其的影响，需利用时间延迟干涉技术降低噪声的干扰。时间延迟干涉是一种数据后处理方法，要实现该技术的数据构型，需对卫星臂长实现精确的绝对距离测量。本文从太极计划的需求分析出发，分别从信源编码设计、延迟环设计以及数据处理算法等方面介绍测距系统的设计方案。在信源编码中，文章通过分析m序列、gold序列、Weil码三种伪随机码的自、互相关性优劣以及长度选取上的灵活性，最终选择了Weil码并筛选出其自相关性最优的移位-截取组合，将其作为测距系统所用的伪随机码。同时，基于该测距系统，搭建了一套地面电子学验证实验装置，以模拟信号传输的物理过程并验证系统性能。实验主体装置采用一块基于Xilinx公司K7芯片的自研FPGA板卡用以模拟卫星通信测距过程以及实现锁相环、延迟环等功能。实验将24.4 kbps的16位信息码与1.5625 Mbps的1024位Weil码进行BPSK调制，采样频率为50 MHz，通过10~60 m的射频同轴电缆进行传输后，使用质心法对采集数据进行优化，随后测定该距离。实验结果表明：在60 m范围内，测距精度优于1.6 m。实验证明了测距系统原理及设计的可行性，为下一步的光学系统验证奠定了技术基础。

探测低频引力波需要脱离地缘噪声干扰，在空间搭建激光干涉引力波探测装置。太极、LISA、天琴等空间引力波探测任务，计划在几十万到几百万公里量级的臂长上实现皮米级的位移测量精度，以满足引力波探测的要求。在探测任务中，考虑轨道季节性变化和星间激光传输时间等因素，发射光束需要一个超前角度，确保远端望远镜能够接收到光束，从而完成星间激光干涉。针对发射光束需要超前角度的需求，设计并研制了一款用于激光干涉链路中提供超前角度的光束指向机构，即超前瞄准机构。该机构基于将偏转轴配置在反射镜面上的设计理念，采用柔性铰链和杠杆配合的结构形式，利用压电陶瓷自闭环进行驱动控制，实现光束一维高精度偏转。对该机构进行仿真分析，验证其力学特性以及偏转范围。对所研制的机构进行了一系列实验测试，结果表明，该机构偏转范围可达到 $ 709.4 $ μrad，偏转精度可达到 $ {\text{0}}{\text{.44 }} $ μrad，机构偏转引起的光程差优于 ${\text{10}}\;{{{\text{pm}}}/{\sqrt {{\text{Hz}}} }}\;$ (1~10 Hz)。从而验证了该机构设计的可行性，为实现光束超稳高精度偏转提供一定的参考。