Ptychography is a powerful computational imaging technique that reconstructs both the complex object function and the illumination probe from overlapping diffraction patterns. While it provides high-resolution, aberration-corrected imaging, its reliance on stepwise mechanical scanning limits acquisition speed. In this work, we propose a fly-scan ptychographic approach that enables continuous sample translation along arbitrary trajectories, significantly reducing measurement time. To account for motion-induced decoherence, we incorporate an object mode decomposition model combined with automatic differentiation for accurate trajectory correction. This method enables diffraction-limited reconstructions without the need for high-speed tracking, allowing fast and precise measurements using standard ptychographic setups.

Ptychography is a computational imaging technique that enables the reconstruction of the amplitude and phase of an object and an illumination field using a series of recorded diffraction patterns [1]. Compared to conventional imaging techniques, ptychographic measurements offer more comprehensive information about the reconstructed object without requiring high-quality lenses, while also accommodating correction of experimental imperfections such as distance inaccuracies, angular misalignments, and other experimental errors. However, as ptychography is not a single-shot measurement technique, it is time-consuming, with a significant part of the measurement time attributed to the scanning process. Such mechanical scanning is inherently slow due to the acceleration limitations of the sample stage and the time required for stabilization [2].

We present a maximum-likelihood estimation (MLE) framework tailored to event-driven detectors to perform computational image reconstruction and phase retrieval. Using Poissonian photon statistics, we built an event-based loss function that maximizes the probability of having the set of events and non-events given the initial parameters. Our loss function can be utilized in both optical and electron ptychography. We demonstrate experimental reconstructions using data acquired with a Timepix3 detector.