Hybrid deep learning-based phase diversity method for wavefront retrieval

The performance 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 non-common path 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 retrieval method that combines a convolutional neural network to generate an initial estimate of the wavefront distortions with the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm for its subsequent refinement. In numerical simulations, this method achieved an efficiency exceeding 0.99 in 80% of the cases for a root-mean-square (RMS) of wavefront distortions up to 1.3λ. The hybrid method was experimentally validated with initial RMS wavefront distortion values ranging from 0.18 to 0.64λ. A Strehl ratio above 0.9 was reached within two correction iterations of the hybrid method in 90% of the series and within four iterations in all cases. The final average Strehl ratio was 0.96 ± 0.01, and the residual measured RMS of wavefront distortions was 0.025 ± 0.005λ.