Tilt-to-length (TTL) coupling noise arises from angular misalignments of interfering beams in optical path length (OPL) measurements and significantly impacts the accuracy of interferometry measurement systems. This paper focuses on geometric TTL coupling in a test mass (TM) interferometer and examines how an imaging system influences TTL noise suppression. First, the analytical expression of the geometric TTL coupling in a TM interferometer with alignment errors is derived and confirmed through numerical simulation. Subsequently, an imaging system is incorporated into the geometric model and the corresponding analytical expressions are obtained under two common conjugate relationships. Nevertheless, the TTL coupling remains beyond the requirement of TM interferometer, as the residual TTL coupled with alignment errors persists even with the imaging system. Therefore, an optimal position of the imaging system capable of eliminating the second-order term of the TTL coupling is determined. Meanwhile, the first-order term can be mitigated through in-orbit calibrations. These findings offer valuable guidance for the design and adjustment of imaging systems in space-borne gravitational wave detection missions, which require high-precision laser interferometry.

In space-based gravitational wave detection, establishing ultra-long-distance and ultra-high-precision laser links between satellites is achieved through the laser acquisition and tracking system. The laser spot centroid positioning method, which offers low computational complexity and strong adaptability to beam shape, is currently the core measurement method during the laser acquisition phase. However, due to various interference factors encountered in practical tests, this algorithm often falls short of meeting the extremely high requirements. To address this challenge, this paper first defines the specific performance criteria for the centroid positioning method based on the needs of laser acquisition in gravitational wave detection. It then comprehensively analyzes how detector noise, window truncation effects, and beam wavefront aberrations impact the accuracy of angular measurements. Using derived analytical expressions, an improved centroiding algorithm is proposed to mitigate the effects of detector noise and wavefront aberrations simultaneously. Numerical simulations are conducted to design the specific parameters for the algorithm and the system, resulting in the ability to achieve an angular measurement accuracy of 60 nrad at the telescope front end.

The predecessor of China Optics was China Optics and Applied Optics Digest, which was founded in 1985. At that time, it was the only retrieval journal in the field of optics in China. At the end of 2008, China Optics and Applied Optics Digest was renamed 《中国光学》的前身是1985年创办的《中国光学与应用光学文摘》，当时是国内光学领域唯一的检索刊物。2008年底《中国光学与应用光学文摘》转型更名为《中国光学与应用光学》期刊，刊载内容突破了文摘的限制，正式成为学术刊物。

For the Taiji program or other LISA-like space-based gravitational wave (GW) detection missions, establishing laser links is a prerequisite for entering the normal science mode. There has been a lack of in-depth research on inter-satellite link acquisition under weak light and low-speed conditions. In this paper, we comprehensively analyze the impact of key parameters, including scan speed, track width, acquisition camera integration time, and jitter, on the acquisition process. By introducing laser spot location error under weak light conditions, we derive an analytical expression for the acquisition failure probability. Focusing on variations in scan speed and track width and carefully selecting the appropriate acquisition camera integration time, we then simulate the actual acquisition process to closely replicate real conditions. Analytical results of the acquisition failure probability align closely with the simulation results. Under the Taiji program’s parameter settings, the scan speed is set to 3.31 $\mathsf{\mu }$$\mathrm{rad}/\mathrm{s}$, the track width to $0.87$ $\mathsf{\mu }$$\mathrm{rad}$, and the integration time to $800\mathrm{ms}$. These parameters are optimized to minimize the mean acquisition time over multiple scans, resulting in a single link acquisition time of $223.77\mathrm{s}$. The analytical model can be used for the parameter design of inter-satellite laser link acquisition under weak light conditions.

In space-based gravitational-wave detection, the noise budget assigned to the point-ahead angle mechanism (PAAM) is at the picometer level within the 0.1 mHz–1 Hz. However, environmental disturbances severely restrict the effective bandwidth of PAAM-dependent parasitic displacement in differential wavefront sensing (DWS), rendering conventional approaches inadequate for low-frequency observability. This paper proposes a model-based evaluation method via frequency-domain extrapolation. The low-signal-to-noise-ratio optical path difference (OPD) in the environmental-additive-noise-dominated small-deflection regime is inferred by exploiting the transfer function and the Fourier transform. Experiments confirm strong agreement between predicted and measured displacement spectra. The method achieves parasitic displacement sensitivity better than 1pm/√Hz×NSF( f ) across the band without sole reliance on extreme thermal control. This approach provides a practical strategy for improving low-frequency precision interferometric metrology in space-based gravitational-wave detection and related applications.

Space-based gravitational wave detection missions impose extremely stringent requirements on the measurement precision of the laser interferometer, where tilt-to-length coupling noise emerges as a critical factor degrading performance. This paper focuses on geometric tilt-to-length noise in the test mass interferometer, conducting both theoretical modeling and experimental validation. First, based on the principles of geometrical optics, an analytical expression is derived for the optical path length difference variation induced by test mass angular jitter, clarifying the coupling mechanisms of the various system parameters to the tilt-to-length coupling. Numerical simulations demonstrate an excellent agreement between the theoretical model and simulation results. To further validate the theoretical model, an experimental system combining laser heterodyne interferometry and differential wavefront sensing technique is designed and constructed, with a fast steering mirror employed to simulate test mass angular jitter, enabling precise measurement of both the optical path and angular variations. By varying the lateral displacement $d_{\mathrm{lat}}$ of the fast steering mirror, the experimental data exhibit strong consistency with the theoretical prediction of the first-order tilt-to-length coupling coefficient, with a linear fitting error as low as 1.5%. Moreover, the independence of the second-order and zero-order terms relative to $d_{\mathrm{lat}}$ also aligns with the theoretical expectation. Thus, the first experimental verification of the geometric tilt-to-length coupling model is presented in this paper.