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.

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.