Training networks without wavefront label for pixel-based wavefront sensing

Traditional image-based wavefront sensing often faces challenges in efficiency and stagnation. Deep learning methods, when properly trained, offer superior robustness and performance. However, obtaining sufficient real labeled data remains a significant challenge. Existing self-supervised methods based on Zernike coefficients struggle to resolve high-frequency phase components. To solve this problem, this paper proposes a pixel-based self-supervised learning method for deep learning wavefront sensing. This method predicts the wavefront aberration in pixel dimensions and preserves more high-frequency information while ensuring phase continuity by adding phase constraints. Experiments show that the network can accurately predict the wavefront aberration on a real dataset, with a root mean square error of 0.017 lambda. resulting in a higher detection accuracy compared with the method of predicting the aberration with Zernike coefficients. This work contributes to the application of deep learning to high-precision image-based wavefront sensing in practical conditions.