Bessel-beam-based hybrid physics-informed phase retrieval from single-shot measurements

Abstract

We present a deep-learning-based phase-retrieval framework that uses Bessel-beam illumination to extend the recoverable aberration range in wavefront sensing. By exploiting the large effective numerical aperture and extended depth of focus of Bessel beams, the proposed method increases the range of measurable aberrations compared with conventional Gaussian-beam-based approaches while preserving high reconstruction accuracy. A linear grating is used to generate off-axis Bessel-beam orders, providing additional spatial information that enables single-shot phase retrieval from one measured irradiance image. To address the nonlinear inverse mapping from defocused Bessel-beam irradiance patterns to wavefront aberration coefficients, we develop a three-stage hybrid reconstruction pipeline. A convolutional neural network first estimates 25 Zernike coefficients, from Z4 to Z28, providing a coarse initial reconstruction. A physics-informed neural network then refines the estimate by enforcing consistency with a fully differentiable Fresnel propagation model. Finally, gradient-based iterative optimization further improves the solution by minimizing a composite loss that compares predicted and measured intensities in the spatial, spatial-frequency, and gradient domains. In noise-free simulations over 100 test cases with wavefronts spanning up to 7.3λ peak-to-valley, the full pipeline achieved a wavefront reconstruction error of approximately 1.4 nm RMS at λ = 632 nm. These results show that structured Bessel-beam illumination, combined with hybrid data-driven and physics-based inference, enables fast, robust, and accurate wavefront reconstruction. The approach also supports characterization of test optics over a broad range of effective focal lengths without optical reconfiguration, offering a flexible wavefront-sensing strategy for imaging and metrology applications.