Co-phase errors simultaneous detection for optical sparse aperture systems via deep learning

Since the sparse structure of the optical sparse aperture systems, co-phasing is crucial for achieving high resolution. In practice, tip-tilt errors affect the piston error, necessitating step-by-step detection, reducing efficiency, and most existing methods focus on detecting single-type co-phase error. In this Letter, we propose a novel, to the best of our knowledge, piston and tip-tilt errors simultaneous detection method using both the object-independent feature map (FM) related to optical transfer function (OTF) and deep learning. Firstly, we theoretically derived the relationship between the OTF and co-phase errors, demonstrating that tip-tilt errors detection is unaffected by piston error, while obtaining piston error requires prior error separation. Secondly, we employ a separation network to obtain a separated FM containing only piston error from the original FM, thereby eliminating interference from tip-tilt errors and enabling accurate detection. Finally, by integrating the original and separated FMs as inputs to our proposed detection network, piston and tip-tilt errors can be detected simultaneously. Once trained, the networks require only a single original FM input. Simulations demonstrate that our proposed method achieves high detection accuracy and robust performance.