Misalignment-Induced Aberration Compensation for Off-Axis Reflective Telescopes Based on Fusion of Spot Images and Zernike Coefficients

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.