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.

Integrating deformable mirrors within the optical train of an adaptive telescope was one of the major innovations in astronomical observation technology, distinguished by its high optical throughput, reduced optical surfaces, and the incorporation of the deformable mirror. Typically, voice-coil actuators are used, which require additional position sensors, internal control electronics, and cooling systems, leading to a very complex structure. Piezoelectric deformable secondary mirror technologies were proposed to overcome these problems. Recently, a high-order piezoelectric deformable secondary mirror has been developed and installed on the 1.8-m telescope at Lijiang Observatory in China to make it an adaptive telescope. The system consists of a 241-actuator piezoelectric deformable secondary mirror, a 192-sub-aperture Shack-Hartmann wavefront sensor, and a multi-core-based real-time controller. The actuator spacing of the PDSM measures 19.3 mm, equivalent to approximately 12.6 cm when mapped onto the primary mirror, significantly less than the voice-coil-based adaptive telescopes such as LBT, Magellan and VLT. As a result, stellar images with Strehl ratios above 0.49 in the R band have been obtained. To our knowledge, these are the highest R band images captured by an adaptive telescope with deformable secondary mirrors. Here, we report the system description and on-sky performance of this adaptive telescope.