Spatial phase retrieval of vortex beam using convolutional neural network

Abstract Vortex beam (VB) possessing spatially helical phase–front has attracted widespread attention in free-space optical communication, etc. However, the spiral phase of VB is susceptible to atmospheric turbulence, and effective retrieval of the distorted conjugate phase is crucial for its practical applications. Herein, a convolutional neural network (CNN) approach to retrieve the phase distribution of VB is experimentally demonstrated. We adopt a spherical wave to interfere with VB for converting its phase information into intensity changes, and construct a CNN model with excellent image processing capabilities to directly extract phase–front features from the interferogram. Since the interference intensity is correlated with the phase–front, the CNN model can effectively reconstruct the wavefront of conjugate VB carrying different initial phases from a single interferogram. The results show that the CNN-based phase retrieval method has a loss of 0.1418 in the simulation and a loss of 0.2344 for the experimental data, and remains robust even in turbulence environments. This approach can improve the information acquisition capability for recovering the distorted wavefront and reducing the reliance on traditional inverse retrieval algorithms, which may provide a promising tool to retrieve the spatial phase distributions of VBs.