Deep learning wavefront sensing method for Shack-Hartmann sensors with sparse sub-apertures

In this letter, we proposed a deep learning wavefront sensing approach for the Shack-Hartmann sensors (SHWFS) to predict the wavefront from sub-aperture images without centroid calculation directly. This method can accurately reconstruct high spatial frequency wavefronts with fewer sub-apertures, breaking the limitation of d/r 0  ≈ 1 (d is the diameter of sub-apertures and r 0 is the atmospheric coherent length) when using SHWFS to detect atmospheric turbulence. Also, we used transfer learning to accelerate the training process, reducing training time by 98.4% compared to deep learning-based methods. Numerical simulations were employed to validate our approach, and the mean residual wavefront root-mean-square (RMS) is 0.08λ. The proposed method provides a new direction to detect atmospheric turbulence using SHWFS.