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.

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.

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.

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.

Overview: In order to achieve the measurement of gravitational wave signals in the millihertz frequency band, the space-based gravitational wave detection projects such as LISA, TianQin, and Taiji projects, which are based on laser interference systems, require the hardware noise floor of the interferometers to be lower than the interstellar weak light shot noise limit. This imposes stringent engineering specifications on the optical-mechanical design and the corresponding interferometer payload. This paper approaches the issue from the perspective of detection mode selection and derives the expressions of readout noise and stray light noise in the interference signal under the single detector mode and the balanced mode. Furthermore, a detailed discussion is provided on the weak-light interference process of the scientific interferometer. The results demonstrate that the balanced mode is capable of suppressing the interference phase noise caused by laser power fluctuations and backscattered stray light across multiple orders of magnitude. However, the suppression capability is constrained by the unequal splitting property of the beam combiner. To address this, a relative gain factor is introduced to compensate for the unequal splitting property of the beam combiner. Further analysis reveals that electronic gain compensation can only eliminate the impact of unequal splitting on one of the two noises rather than both simultaneously. Therefore, a balance must be struck in selecting gain compensation between the suppression of laser power fluctuation noise and stray light noise. Even with this consideration, the balanced mode still offers significant noise suppression capabilities at a magnitude difference, thus potentially reducing the engineering requirements for laser power fluctuations and telescope backscattered stray light.

基于离轴四反的方案设计，从同轴反射系统的理论出发，结合高倍率，低波前畸变，以及高杂散光抑制比等特点对天琴望远镜的原理系统进行了优化设计。实现了在捕获±200 μrad视场内系统百倍的压缩倍率，其入瞳直径300 mm，波前误差优于λ/80。提高三四镜之间光线转折角度进行杂散光抑制，在保证高质量波前的条件下，其三镜的偏角优化结果为5.5°，且三镜为平面镜的引入，降低了后期加工装调的难度。为了对原理系统的加工装调以及杂散光抑制能力进行验证，建立了该系统下0.5倍的缩比系统，实现了缩比系统的波前误差优于λ/175。经公差分析，原理系统有90%的累积概率其波前误差优于λ/40，满足引力波望远镜的指标要求。