The Shack-Hartmann wavefront sensor produces incorrect wavefront measurements when some sub-spots are weak and missing. In this paper, a method is proposed to predict the centroids of these sub-spots for the Shack-Hartmann wavefront sensor based on the deep neural network. Using the centroid information of present sub-spots, the method is able to predict the absent sub-spots’ positions. The feasibility and effectiveness of this method are verified by a large number of numerical simulations. The method is applied to wavefront measurement of light with non-uniform near-field intensity. The simulation results show that the proposed method is of great help to improve the measurement accuracy and the Strehl ratio of the focal spot. For wavefronts outside of the training sample, the proposed method shows good generalization and adaptability. In addition, the experiment results demonstrate that the proposed method can predict the missing sub-spots’ centroid displacements accurately even though a large proportion of sub-spot is lost randomly.

Aiming at the problem that it is difficult for the conventional Shack–Hartmann wavefront sensor to achieve high-precision wavefront reconstruction with low spatial sampling, a kind of Shack–Hartmann wavefront sensing technology based on four-quadrant binary phase modulation is proposed in this paper. By introducing four-quadrant binary phase modulation into each subaperture, the technology is able to use an optimization algorithm to reconstruct wavefronts with high precision. The feasibility and effectiveness of this method are verified at extreme low spatial frequency by a series of numerical simulations, which show that the proposed method can reliably reconstruct wavefronts with high accuracy with rather low spatial sampling. In addition, the experiment demonstrates that with a 2 × 2 microlens array, the four-quadrant binary phase-modulated Shack–Hartmann wavefront sensor is able to achieve approximately 54% reduction in wavefront reconstitution error over the conventional Shack–Hartmann wavefront sensor.