Optical mirror misalignments, which are caused by assembly mistakes and changes in the surrounding environment (such as gravity, temperature, and atmosphere), degrade the system’s imaging performance. Therefore, active misalignment correction is essential for ensuring the image quality of the off-axis telescope. In this paper, a novel misalignment correction method without wavefront sensors is proposed. The point spread functions (PSFs) of the system are analytically related to the optical mirror misalignments. On this basis, a fully connected neural network (FCNN) is used to establish the mapping relationship between the misalignments and the discrete orthogonal unbiased finite impulse response (UFIR) moment features, which can effectively characterize changes of intensity and geometric of the spot image. The simulation and experimental results in this paper justify the effectiveness and practicality of the proposed method. This approach offers a low-cost and straightforward technical method for achieving high imaging quality throughout the alignment and observation phases. This approach can prevent the accumulation of errors caused by wavefront detection and the high delay of multiple iterations.

Optical system misalignment aberrations caused by various factors such as environmental conditions and mechanical jitter of optical components can lead to a decline in the imaging quality of the system. The non-rotational symmetry structure and the coupling effect of different degrees of freedom of off-axis reflective telescopes make them more sensitive to misalignment aberrations. Moreover, when the Z -axis of the secondary mirror in an off-axis system has eccentricity errors, using a defocused PSF to solve the misalignment will result in a decrease in the accuracy of the lateral misalignment solution. Therefore, this paper proposes a misalignment error detection technology based on the wavelet transform and the Gabor filter and establishes a nonlinear mapping relationship between the wavelet transform-Gabor filter hybrid features of defocused PSF images and the misalignment of the secondary mirror through ShuffleNetV2. Using the hybrid features extracted by the biorthogonal wavelet transform and the Gabor filter as the input of the neural network can reduce the difficulty of decoupling the aberration features of defocused PSF images, thereby improving the accuracy of solving the misalignment of the secondary mirror. The algorithm was verified through an actual off-axis two-mirror afocal system, proving its feasibility and effectiveness.

Off-axis reflective telescopes are prone to component misalignment due to external environmental factors and mechanical vibrations. This misalignment introduces low-order aberrations, which severely degrade imaging quality. Thus, active misalignment correction is crucial for maintaining the imaging performance of off-axis reflective telescopes. Current computer-aided alignment technologies for optical systems mostly rely on wavefront sensors to acquire aberrations at multiple fixed fields of view (FOVs) or even the full FOV. This significantly increases system complexity and hinders practical engineering applications. To address this issue, this study first conducts sensitivity analysis of misaligned degrees of freedom (DOFs) using a mode truncation algorithm based on singular value decomposition (SVD). A compensation strategy is proposed to avoid the aberration coupling effect. Furthermore, two novel misalignment aberration compensation methods for off-axis reflective telescopes are presented. These methods require only a single focal spot image and eliminate the need for aberration detection and iterative calculations. One method directly solves component misalignment errors using a convolutional neural network (CNN) based on the system’s point spread function (PSF). To further improve compensation performance, an improved method fusing spot images and Zernike coefficients is proposed. In practical misalignment correction, both methods input a single acquired focal spot image into a well-trained model to obtain the misalignment compensation amount. Simulation experiments demonstrate that the improved method, which uses Zernike polynomial coefficients as an intermediate feature bridge, effectively establishes the mapping relationship between spot images and misalignment amounts. It achieves higher solution accuracy and better aberration compensation effect compared to the direct CNN method. This verifies the necessity of extracting Zernike polynomial coefficient features from spot images. Comparative experiments with the traditional sensitivity matrix method show that the two proposed methods outperform the sensitivity matrix method in aberration compensation accuracy over a large misalignment range. Comprehensive simulation results confirm the feasibility and effectiveness of the proposed methods. They overcome the limitations of existing methods, such as complex structure, high cost, and low efficiency, to a certain extent.

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.

Off-axis telescopes in operational states are susceptible to environmental variations and mechanical vibrations, which deviate the secondary mirror (SM) from its nominal positions and induce misalignment aberrations. Existing compensation techniques for SM misalignment-induced aberrations of off-axis telescopes typically rely on fixed multi-field points wavefront sensing data or spot images to solve for misalignment restoration solutions. These methods suffer from limitations such as poor environmental adaptability, inflexible field-of-view configuration, and high computational costs for achieving high-precision misalignment restoration solutions. To address this, this paper proposes an aberration compensation technique based on feature extraction and optimization from arbitrary single field point spot images. It utilizes unbiased finite impulse response (UFIR) moments to extract spot image features and combines them with the differential evolution (DE) nonlinear optimization algorithm to find equivalent misalignments, thereby achieving system aberration compensation. Simulation verifies the feasibility of this method and compares its performance with typical image moment approaches. The influence of atmospheric turbulence on the presented method is also analyzed. Finally, physical experiments are conducted on an experimental platform for further validation. This technique compensates for aberrations using only arbitrary single field point spot images, without requiring multiple field points wavefront or spot data, nor precise determination of actual misalignments. It simplifies the misalignment-induced aberration compensation process and provides a reference for subsequent engineering applications.

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.