Circular Phase Representation and Geometry-Aware Optimization for Ptychographic Image Reconstruction
For ptychography practitioners, this work addresses the mismatch between Euclidean phase representation and the underlying circular geometry, improving reconstruction quality and speed.
The paper presents a deep learning framework for ptychographic image reconstruction that models phase on the unit circle using cosine and sine components, with a differentiable geodesic loss to avoid wrapping artifacts. The method achieves consistent improvements in amplitude and phase reconstruction over existing deep learning methods and provides substantial speedup over iterative solvers.
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.