Accurate broadband wavefront sensing for space telescopes via a compact neural network

Broadband imaging plays a critical role in enabling space telescopes to observe faint celestial targets, but it presents significant challenges for accurate wavefront sensing due to chromatic dispersion and spectral incoherence. Traditional image-based phase retrieval algorithms, while computationally efficient and payload-friendly, often fail to maintain high reconstruction accuracy under broadband illumination. In this study, we explore a deep learning-based solution and adopt a compact convolutional neural network, U-EFFNet, which combines the encoder-decoder structure of U-Net with efficient feature extraction modules from EFFNet. Although not specifically designed for broadband wavefront sensing, U-EFFNet demonstrates strong performance on this task due to its effective balance of local and global feature representation, lightweight structure, and robust generalization. Simulation studies across a wide range of realistic aberrations and noise conditions show that U-EFFNet outperforms classical methods such as the Misell Gerchberg-Saxton (MGS) algorithm and the monochromatic equivalent method, as well as other deep learning models, in terms of comprehensive performance. Experimental validation performed under a broadband imaging spectral range of 400-750 nm further confirms the network's reconstruction accuracy and robustness, suggesting its promise for onboard wavefront sensing in spaceborne optical systems.