Since Einstein’s prediction regarding the existence of gravitational waves was directly verified by the ground-based detector Advanced LIGO, research on gravitational wave detection has garnered increasing attention. To overcome limitations imposed by ground vibrations and interference at arm’s length, a space-based gravitational wave detection initiative was proposed, which focuses on analyzing a large number of waves within the frequency range below 1 Hz. Due to the weak signal intensity, the TMs must move along their geodesic orbit with a residual acceleration less than 10⁻¹⁵ m/s²/Hz^1/2. Consequently, the core payload-inertial sensor was designed to shield against stray force noise while maintaining the high-precision motion of the test mass through a drag-free control system, providing an ultra-stable inertial reference for laser interferometry. To meet these requirements, the inertial sensor integrates a series of unit settings and innovative designs, involving numerous subsystems and technologies. This article provides a comprehensive overview of these critical technologies used in the development of inertial sensors for space gravitational wave detection and discusses future trends and potential applications for these sensors.

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.

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.

Space-based gravitational wave detection imposes extremely high requirements on displacement measurement accuracy, with its core measurement components being laser interferometers and inertial sensors. The laser interferometers detect gravitational wave signals by measuring the distance between two test masses (TMs) housed within the inertial sensors. Spatial alignment errors of the TMs relative to the laser interferometers can severely degrade the interferometric performance, primarily by significantly amplifying tilt-to-length (TTL) coupling noise and reducing interferometric efficiency. This paper presents a systematic analysis of the coupling mechanisms between TM alignment errors and TTL coupling noise. We first establish a comprehensive TTL noise model that accounts for alignment errors, then verify and analyze it through optical simulations. This research ultimately clarifies the coupling mechanisms of TM alignment errors in the context of space-borne gravitational wave missions and determines the allowable alignment tolerance specifications required to meet the gravitational wave detection sensitivity requirements. This work provides critical theoretical foundations and design guidance for the ground alignment procedures and on-orbit performance prediction of future space-based gravitational wave detection missions.

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.