Field of view-independent detection of secondary mirror position errors in coaxial reflecting space telescopes using deep learning

The operation of coaxial reflecting space telescopes in orbit is affected by adjustments and space disturbance, causing position errors in the secondary mirror (SM), which reduce resolution and seriously affect imaging quality. Most existing methods for detecting SM position errors rely on wavefronts or images obtained from one or more fixed field of views (FOVs), yet the inherent uncertainty of the FOV can lead to significant errors in detecting SM position errors. To address this problem, this paper, believed to be the first, proposes an FOV-independent SM position error detection method for coaxial reflecting space telescopes based on a pair of symmetric positive and negative defocus point spread functions (PSFs) and the dual-branch convolutional neural network (DB-CNN). First, a nonlinear relationship between the SM position errors and the PSFs at arbitrary FOV is established, using the DB-CNN. Then, the method using a pair of symmetric positive and negative defocus PSFs at arbitrary FOV to obtain the position errors of the SM is proposed, and the simulation results show that, despite the uncertainty of the FOV, the SM position errors can be detected with high precision. This approach enables SM position error correction independent of the FOV, significantly enhancing the imaging quality. Finally, a modified method is proposed to address the problem caused by the primary mirror (PM) figure errors. Simulations prove that the SM position errors can be accurately obtained even in the presence of PM figure errors.