Misalignment calculation for on-axis four-mirror segmented aperture optical systems based on neural networks

With the growing demand for high-resolution astronomical observations, large-aperture optical telescopes have become essential tools in modern astronomy. The use of segmented mirrors has been proven to be an effective solution for achieving large apertures. However, these telescopes face complex mirror alignment issues during deployment, where relative positional and phase errors among the segments directly affect the imaging performance. In the disordered state, the mirror segments are misaligned in position and phase, severely impacting imaging quality. In the confocal state, although the focal points are aligned, rotational or curvature errors may still exist. The ideal co-phase state requires that the mirror segments align precisely in both focal length and phase. However, achieving perfect co-phase alignment in practical applications is highly challenging, especially for complex large-aperture optical systems. Artificial neural networks (ANNs), with their powerful learning abilities and excellent generalization performance, can effectively predict and correct highly nonlinear, strongly coupled error data, providing a possible solution for achieving perfect co-phase alignment in such systems. Therefore, the paper further proposes and analyzes a hybrid deployment strategy combining ANNs with numerical optimization methods to improve the precision and efficiency of mirror segment alignment.