Fourier ptychography (FP) is a powerful light-based synthetic aperture imaging technique that allows one to reconstruct a high-resolution, wide field-of-view image by computationally integrating a diverse collection of low-resolution, far-field measurements. Typically, FP measurement diversity is introduced by changing the angle of the illumination or the position of the camera; either approach results in sampling different portions of the target's spatial frequency content, but both approaches introduce substantial costs and complexity to the acquisition process. In this work, we introduce Inverse Synthetic Aperture Fourier Ptychography, a novel approach to FP that foregoes changing the illumination angle or camera position and instead generates measurement diversity through target motion. Critically, we also introduce a novel learning-based method for estimating k-space coordinates from dual plane intensity measurements, thereby enabling synthetic aperture imaging without knowing the rotation of the target. We experimentally validate our method in simulation and on a tabletop optical system.

Ptychography is a scanning coherent diffractive imaging technique that enables imaging nanometer-scale features in extended samples. One main challenge is that widely used iterative image reconstruction methods often require significant amount of overlap between adjacent scan locations, leading to large data volumes and prolonged acquisition times. To address this key limitation, this paper proposes a Bayesian inversion method for ptychography that performs effectively even with less overlap between neighboring scan locations. Furthermore, the proposed method can quantify the inherent uncertainty on the ptychographic object, which is created by the ill-posed nature of the ptychographic inverse problem. At a high level, the proposed method first utilizes a deep generative model to learn the prior distribution of the object and then generates samples from the posterior distribution of the object by using a Markov Chain Monte Carlo algorithm. Our results from simulated ptychography experiments show that the proposed framework can consistently outperform a widely used iterative reconstruction algorithm in cases of reduced overlap. Moreover, the proposed framework can provide uncertainty estimates that closely correlate with the true error, which is not available in practice. The project website is available here.

Ptychography is a coherent diffraction imaging method that uses phase retrieval techniques to reconstruct complex-valued images. It achieves this by sequentially illuminating overlapping regions of a sample with a coherent beam and recording the diffraction pattern. Although this addresses traditional imaging system challenges, it is computationally intensive and highly sensitive to noise, especially with reduced illumination overlap. Data-driven regularisation techniques have been applied in phase retrieval to improve reconstruction quality. In particular, plug-and-play (PnP) offers flexibility by integrating data-driven denoisers as implicit priors. In this work, we propose a half-quadratic splitting framework for using PnP and other data-driven priors for ptychography. We evaluate our method both on natural images and real test objects to validate its effectiveness for ptychographic image reconstruction.

Ptychography is an advanced computational imaging technique in X-ray and electron microscopy. It has been widely adopted across scientific research fields, including physics, chemistry, biology, and materials science, as well as in industrial applications such as semiconductor characterization. In practice, obtaining high-quality ptychographic images requires simultaneous optimization of numerous experimental and algorithmic parameters. Traditionally, parameter selection often relies on trial and error, leading to low-throughput workflows and potential human bias. In this work, we develop the "Ptychographic Experiment and Analysis Robot" (PEAR), a framework that leverages large language models (LLMs) to automate data analysis in ptychography. To ensure high robustness and accuracy, PEAR employs multiple LLM agents for tasks including knowledge retrieval, code generation, parameter recommendation, and image reasoning. Our study demonstrates that PEAR's multi-agent design significantly improves the workflow success rate, even with smaller open-weight models such as LLaMA 3.1 8B. PEAR also supports various automation levels and is designed to work with customized local knowledge bases, ensuring flexibility and adaptability across different research environments.

Three-dimensional atomic resolution imaging using transmission electron microscopes is a unique capability that requires challenging experiments. Linear electron tomography methods are limited by the missing wedge effect, requiring a high tilt range. Multislice ptychography can achieve deep sub-{\AA}ngstrom resolution in the transverse direction, but the depth resolution is limited to 2 to 3 nanometers. In this paper, we propose and demonstrate an end-to-end approach to reconstructing the electrostatic potential volume of the sample directly from the 4D-STEM datasets. End-to-end multi-slice ptychographic tomography recovers several slices at each tomography tilt angle and compensates for the missing wedge effect. The algorithm is initially tested in simulation with a Pt@$\mathrm{Al_2O_3}$ core-shell nanoparticle, where both heavy and light atoms are recovered in 3D from an unaligned 4D-STEM tilt series with a restricted tilt range of 90 degrees. We also demonstrate the algorithm experimentally, recovering a Te nanoparticle with sub-{\AA}ngstrom resolution.

Noninvasive X-ray imaging of nanoscale three-dimensional objects, e.g. integrated circuits (ICs), generally requires two types of scanning: ptychographic, which is translational and returns estimates of complex electromagnetic field through ICs; and tomographic scanning, which collects complex field projections from multiple angles. Here, we present Attentional Ptycho-Tomography (APT), an approach trained to provide accurate reconstructions of ICs despite incomplete measurements, using a dramatically reduced amount of angular scanning. Training process includes regularizing priors based on typical IC patterns and the physics of X-ray propagation. We demonstrate that APT with 12-time reduced angles achieves fidelity comparable to the gold standard with the original set of angles. With the same set of reduced angles, APT also outperforms baseline reconstruction methods. In our experiments, APT achieves 108-time aggregate reduction in data acquisition and computation without compromising quality. We expect our physics-assisted machine learning framework could also be applied to other branches of nanoscale imaging.

Coherent microscopy techniques provide an unparalleled multi-scale view of materials across scientific and technological fields, from structural materials to quantum devices, from integrated circuits to biological cells. Driven by the construction of brighter sources and high-rate detectors, coherent X-ray microscopy methods like ptychography are poised to revolutionize nanoscale materials characterization. However, associated significant increases in data and compute needs mean that conventional approaches no longer suffice for recovering sample images in real-time from high-speed coherent imaging experiments. Here, we demonstrate a workflow that leverages artificial intelligence at the edge and high-performance computing to enable real-time inversion on X-ray ptychography data streamed directly from a detector at up to 2 kHz. The proposed AI-enabled workflow eliminates the sampling constraints imposed by traditional ptychography, allowing low dose imaging using orders of magnitude less data than required by traditional methods.

Ptychography is a well-studied phase imaging method that makes non-invasive imaging possible at a nanometer scale. It has developed into a mainstream technique with various applications across a range of areas such as material science or the defense industry. One major drawback of ptychography is the long data acquisition time due to the high overlap requirement between adjacent illumination areas to achieve a reasonable reconstruction. Traditional approaches with reduced overlap between scanning areas result in reconstructions with artifacts. In this paper, we propose complementing sparsely acquired or undersampled data with data sampled from a deep generative network to satisfy the oversampling requirement in ptychography. Because the deep generative network is pre-trained and its output can be computed as we collect data, the experimental data and the time to acquire the data can be reduced. We validate the method by presenting the reconstruction quality compared to the previously proposed and traditional approaches and comment on the strengths and drawbacks of the proposed approach.

Abstract: Over the past couple of years, ptychography has become increasingly computationally intensive with larger detectors running at higher speeds. Today, it is routine to run Ptychography experiments which produce Gb/s data. This trend will continue, and traditional iterative reconstruction algorithms will struggle to keep pace with the speed of data generation even when GPU-accelerated and running on HPC resources. Recently, machine learning (ML) methods have proven to be successful – speeding up image reconstruction by orders of magnitude and allowing for advanced algorithms to improve image quality. Nevertheless, challenges and caveats exist with respect to the reliability of results predicted by ML methods.

Ptychography, as an essential tool for high-resolution and nondestructive material characterization, presents a challenging large-scale nonlinear and non-convex inverse problem; however, its intrinsic photon statistics create clear opportunities for statistical-based deep learning approaches to tackle these challenges, which has been underexplored. In this work, we explore normalizing flows to obtain a surrogate for the high-dimensional posterior, which also enables the characterization of the uncertainty associated with the reconstruction: an extremely desirable capability when judging the reconstruction quality in the absence of ground truth, spotting spurious artifacts and guiding future experiments using the returned uncertainty patterns. We demonstrate the performance of the proposed method on a synthetic sample with added noise and in various physical experimental settings.