Circular Phase Representation and Geometry-Aware Optimization for Ptychographic Image Reconstruction

2026-04-29

AI Summary

This work addresses the limitations of conventional iterative phase retrieval methods, which are computationally expensive, and existing deep learning approaches that treat phase as a Euclidean scalar, thereby neglecting its inherent 2π periodicity and introducing wrapping artifacts and geometric inconsistencies. To overcome these issues, the authors propose a novel deep learning framework for ptychographic reconstruction that, for the first time, represents phase via cosine-sine coordinates on the unit circle and incorporates a differentiable geodesic loss to preserve the intrinsic geometry of phase and avoid branch-cut discontinuities. Combined with a saturation-aware dual-gain input scheme, a parallel encoder, a three-branch decoder, and a composite loss function, the method consistently outperforms current deep learning techniques on both synthetic and experimental data, achieving markedly improved mid-to-high-frequency phase fidelity, significantly faster reconstruction speeds than iterative solvers, and strong physical consistency.

Abstract

Traditional iterative reconstruction methods are accurate but computationally expensive, limiting their use in high-throughput and real-time ptychography. Recent deep learning approaches improve speed, but often predict phase as a Euclidean scalar despite its $2π$ periodicity, which can introduce wrapping artifacts, discontinuities at $\pmπ$, and a mismatch between the loss and the underlying signal geometry. We present a deep learning framework for ptychographic reconstruction that models phase on the unit circle using cosine and sine components. Phase error is optimized with a differentiable geodesic loss, which avoids branch-cut discontinuities and provides bounded gradients. The network further incorporates saturation-aware dual-gain input scaling, parallel encoder branches, and three decoders for amplitude, cosine, and sine prediction, together with a composite loss that promotes circular consistency and structural fidelity. Experiments on synthetic and experimental datasets show consistent improvements in both amplitude and phase reconstruction over existing deep learning methods. Frequency-domain analysis further shows better preservation of mid- and high-frequency phase content. The proposed method also provides substantial speedup over iterative solvers while maintaining physically consistent reconstructions.

Problem

• phase periodicity
• wrapping artifacts
• geometric mismatch
• ptychographic reconstruction
• phase discontinuities

Innovation

• circular phase representation
• geometry-aware optimization
• geodesic loss
• ptychographic reconstruction
• deep learning