Perception of misalignment states for sky survey telescopes with the digital twin and the deep neural networks

Sky survey telescopes play a critical role in modern astronomy, but misalignment of their optical elements can introduce significant variations in point spread functions, leading to reduced data quality. To address this, we need a method to obtain misalignment states, aiding in the reconstruction of accurate point spread functions for data processing methods or facilitating adjustments of optical components for improved image quality. Since sky survey telescopes consist of many optical elements, they result in a vast array of potential misalignment states, some of which are intricately coupled, posing detection challenges. However, by continuously adjusting the misalignment states of optical elements, we can disentangle coupled states. Based on this principle, we propose a deep neural network to extract misalignment states from continuously varying point spread functions in different field of views. To ensure sufficient and diverse training data, we recommend employing a digital twin to obtain data for neural network training. Additionally, we introduce the state graph to store misalignment data and explore complex relationships between misalignment states and corresponding point spread functions, guiding the generation of training data from experiments. Once trained, the neural network estimates misalignment states from observation data, regardless of the impacts caused by atmospheric turbulence, noise, and limited spatial sampling rates in the detector. The method proposed in this paper could be used to provide prior information for the active optic system and the optical system alignment.