Hybrid deep learning-based phase diversity method for wavefront reconstruction

The efficiency of high-power laser systems is limited by wavefront distortions in the beam, particularly non-common path aberrations, which reduce the peak intensity at the focal plane. Compensating for these aberrations requires the calibration of the adaptive optics system. Conventional calibration methods rely on a time-consuming iterative optimization that is highly sensitive to initial conditions. While deep learning-based models offer high speed, they often demonstrate insufficient accuracy. In this work, we present a hybrid wavefront reconstruction method that combines a convolutional neural network to generate an initial estimate of the wavefront distortions, with the L-BFGS (Limited-memory Broyden-Fletcher-Goldfarb-Shanno) algorithm for its subsequent refinement. In numerical simulations, the method achieved an efficiency of ~ 0.99 in 80% of the cases for a root-mean-square (RMS) of wavefront distortions ranging from 0 to 1.3λ. In a physical experiment, for initial wavefront distortions with RMS values from 0.15 to 0.6λ, the method achieved an efficiency of ~ 0.75. As a result, focusing with a Strehl ratio of 0.96 ± 0.02 was attained within 2 to 4 iterations of the algorithm, confirming the applicability of the method for the fast and accurate calibration of adaptive optics systems under real experimental conditions.