High-speed computational imaging achieved by fly-scan ptychography.

Ptychography is a widely used computational imaging technique capable of reconstructing both the complex object and the illumination field. However, as a scanning-based imaging method, its acquisition speed is inherently limited, and in high-flux regimes, the total measurement time is often dominated by sample positioning and settling overhead rather than exposure time. To overcome this limitation, fly-scan ptychography was introduced, in which the sample is translated continuously during each exposure. This approach maximizes acquisition duty cycle but introduces motion-induced blurring of the diffraction patterns, which is typically addressed using probe-mode or object-mode decomposition. In existing implementations, these methods require precise synchronization between sample motion and detector acquisition, relying on accurate knowledge of the fly-scan trajectory. In this work, we introduce a modified ptychographic forward model that leverages automatic differentiation to simultaneously reconstruct not only the object and probe, but also the fly-scan trajectory directly from the measured data, without requiring precise synchronization or prior knowledge of the sample path. We demonstrate, through both numerical simulations and experimental measurements, accurate fly-scan path retrieval for extended scan lengths, achieving diffraction-limited resolution. We show that trajectory retrieval significantly improves reconstruction quality compared to approaches based on spline-interpolated scan paths. By directly comparing retrieved fly-scan trajectories with independently measured ground-truth paths, we confirm good agreement. This approach eliminates the need for high-speed position tracking and tight hardware synchronization, reducing experimental complexity and cost, and enabling fly-scan operation to be readily implemented in conventional step-scan ptychography setups.