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.

Taking the LISA system as a reference, the phase noise of the inter-satellite transmission needs to be less than 1 pm. Research has shown that the defocus and the astigmatism are the main aberrations affecting jitter noise at a distance of 2.5×10⁹ m. There is a deviation between the phase stationary point and the origin position. To minimize the phase noise, the telescope angle needs to be adjusted. The gravitational wave detection at the phase stationary point can effectively reduce the phase noise and the requirements of the telescope exit pupil wavefront RMS. The large defocus and small coma can make the phase stationary point close to the optical axis and increase the received laser power.

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。

在空间引力波探测的超长臂干涉测量过程中，杂散光问题长期以来受到广泛关注。一方面，本地干涉仪发出的激光通过望远镜时会产生后向相干杂散光。另一方面，在轨情况下，来自空间的环境辐射入射到航天器还会产生前向非相干杂散光。一直以来，前向非相干杂散光受到的关注较少，然而却是空间引力波望远镜设计必须要考虑的因素。因此，本文对空间引力波探测望远镜在轨情况下产生的杂散光进行测量与抑制。首先，根据太极计划三星卫星编队的轨道数据对全年太阳角进行计算，对1064 nm波段附近的太阳辐射进行评估，推导了遮光罩投影函数，最终给出遮光罩设计指标。然后，对望远镜进行光学与机械建模，并对关键光学元件进行散射测量。最后，根据入射太阳光能量对到达望远镜出瞳的杂散光进行计算。结果表明：当入射光与光轴夹角为60°时，出瞳处的杂散辐射可达到3.9×10⁻¹² W，对应点源透射比为8.7×10⁻⁹，满足空间引力波探测超低杂散光的需求。