Phase Retrieval for Antennas via Angular Spectrum Propagation and Adaptive Gradient Optimization

Phase information is essential for accurate antenna characterization, yet it is considerably more difficult to obtain than amplitude, often requiring costly and complex measurement setups. Existing Gerchberg-Saxton (GS) type algorithms either require dual conjugate planes—often unattainable for near-field data or tend to converge to local minima when adapted to electromagnetic problems. In this work we propose a variational angular-spectrum Gerchberg-Saxton (VAS-GS) framework that retrieves phase from two measured near-field amplitude planes via spectral extrapolation. The method formulates angular-spectrum propagation as an adjoint operator, derives a closed-form gradient, and employs an AdaBelief-driven alternating optimization that iteratively updates forward and backward planes. Phase retrieval simulations on a 0.3 GHz dipole antenna show fast decay of both error and gradient, outperforming classical GS, hybrid input-output (HIO), and Fienup methods, and yielding far-field radiation patterns that coincide with analytical solutions. These results demonstrate that VAS-GS offers a fast and accurate route to phase retrieval, enabling high-fidelity antenna analyses.