# Hybrid deep learning-based phase diversity method for wavefront reconstruction

arXiv: https://arxiv.org/abs/2606.25855 · HTML: https://mlsanity.com/paper/2606.25855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 54 references that are in the map.
- First posted on arXiv 24 Jun 2026.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Self-optimizing adaptive optics control with Reinforcement Learning for high-contrast imaging](https://mlsanity.com/paper/2108.11332/) (2021)

## Abstract (arXiv)

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.