At present, the majority of sparse-aperture telescopes (SATs) are unable to observe moving targets. In this paper, we describe the construction of and present the results obtained using a Fizeau directly-imaging sparse-aperture telescope (FDISAT) that permits pointing and the tracking of moving targets. The telescope comprises three sub-apertures, each of which is equipped with a Risley prism system that permits a maximum tracking range of 5° and has independent boresight adjustment capability. On targets in various positions, experiments with pointing and tracking are conducted. The maximum root-mean-square error (RMSE) of pointing in the sub-apertures was found to be 8.22 arcsec. When considering a target moving at 0.01°/s for approximately 320 s, the maximum RMSE of tracking in the sub-apertures was found to be 4.23 arcsec. The images obtained from the focal plane detector exhibit clear interference fringes while tracking. The experimental results demonstrate that the system can effectively track moving targets, providing a method for SAT observation of moving targets.

Differential phase shift keying (DPSK) modulation and multi-aperture receiving are effective means for suppressing flickering, deviation, and fragmentation of the light spot by atmospheric turbulence. What is challenging in coherent beam combination of such an array receiver system is to detect and compensate for phase deviation of sub-apertures. In this paper, a method of phase alignment of an array optical telescope system using balanced detection was proposed and demonstrated. The improved Mach Zehnder Interferometer (MZI) can demodulate the digital signal and recover the phase difference at the same time. It also brings a 3 dB gain to the receiver and improves the detection sensitivity of the system. Adequate simulations with OptiSystem and MATLAB were carried out to show that the power value remains near the ideal state of 2.75 mW, and the bit error rate is less than 10⁻⁹ after phase compensation, which indicates the effectiveness and accuracy of the proposed method. Furthermore, taking the communication interruption difference of ninety degrees as an example, the system bit error rate was reduced from 1 to 10⁻³⁵, and communication was established again.

The power spectral density estimation algorithms, logarithmic frequency axis for power spectral density (LPSD), and the LISA-LPSD algorithm are widely utilized in the implementation of system evaluations for space-based gravitational-wave-detection projects, particularly in the low-frequency band ranging from 0.1 mHz to 1 Hz. However, existing adaptive sine multi-taper algorithms suffer from low resolution and high computational complexity in obtaining the optimal cone number across the entire frequency domain, which has hindered its application in this field. These algorithms often face challenges related to inadequate resolution when dealing with low-frequency signals, as well as the issue of high computational demands. In response to these challenges, this paper introduces an advanced adaptive sine multi-taper algorithm designed to optimize the determination of the cone number. By balancing the relationship between bias and variance, this approach facilitates gradient processing of the cone number specifically tailored for low-frequency signals. Comparative evaluations against the LPSD algorithm, the original adaptive sine multi-taper algorithm, and the LISA-LPSD algorithm reveal that the proposed method demonstrates superior spectral resolution and reduced algorithmic complexity. This improvement offers a more effective solution for the system evaluation of low-frequency gravitational-wave-detection projects.

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.

Laser pointing jitter noise can significantly impact heterodyne interferometric ranging in space gravitational wave detection. Existing differential wavefront sensing (DWS)-based laser pointing control systems fail to achieve the required accuracy due to inadequate disturbance suppression resulting from sensor performance degradation and actuator nonlinearity. In this study, a DWS-based high-precision dual closed-loop control for the point-ahead angle mechanism (PAAM) is proposed. A laser heterodyne interferometry experimental platform is constructed, and a high-precision DWS phase-to-angle conversion coefficient calibration method is presented. Experimental verification of both single closed-loop and dual closed-loop architectures is conducted. Experimental measurements demonstrate that the dual closed-loop control system achieves a pointing jitter noise of less than 5nrad/Hz^1/2 within the 1 mHz to 1 Hz frequency band, an 87.18% reduction compared to the single closed-loop system, representing a breakthrough at low frequencies. This system verifies the necessity of the PAAM dual closed-loop pointing control strategy based on differential wavefront sensing in a heterodyne interferometer optical system. It overcomes the ultra-low-frequency pointing control bottleneck and provides a feasible technical path that meets the noise budget for space gravitational wave detection missions.

Tilt-to-length (TTL) coupling is a critical noise source in high-precision interferometric measurements, particularly in systems involving angular actuation and beam steering. This paper proposes a nonlinear cyclic modulation method to identify lateral misalignment and suppress the associated TTL coupling. By applying controlled sinusoidal angular excitation and evaluating the complex modulus ratio between the optical path difference (OPD) and the beam angle at the modulation frequency, the TTL noise induced by the point-ahead angle mechanism (PAAM) is separated and quantified in the frequency domain. Experimental results demonstrate that lateral offset correction reduces TTL noise by 94%, corresponding to a suppression factor of 15.5 and enabling pointing control better than 21 µm/rad. Meanwhile, the parasitic displacement noise of the PAAM is reduced from 10 pm/Hz^1/2 to below 4 pm/Hz^1/2. These results validate the effectiveness of the proposed modulation-based identification framework and demonstrate its applicability to precision interferometric systems.