Residual neural-field ptychography for dose-efficient electron, X-ray, and optical nanoscopy

Abstract: Ptychography spans from sub-angstrom to meter scales yet suffers from convergence instability and excessive data redundancy. Here we introduce self-correcting residual neural fields as a dose-efficient framework for electron, X-ray, and optical ptychography. Unlike approaches that split complex fields, our complex-valued architecture employs holomorphic phasor activation e^iωz to preserve intrinsic phase-amplitude coupling. We reformulate reconstruction as residual learning, where the network learns only corrections to physical priors rather than complete wavefields. By embedding the physical model as a differentiable layer within the network, we enable end-to-end automatic differentiation where experimental parameters are jointly corrected alongside the neural fields. We validate our scheme across conventional, near-field, coded, and Fourier ptychography and achieve record-breaking lensless resolution of 244-nm linewidth with visible light. Extending to electron wavelengths, we reveal synaptic connectivity in brain sections with superior performance over conventional approaches. Our framework provides a solution for high-throughput, dose-efficient nanoscopy across the electromagnetic spectrum.