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DOE OSTI2024

Improved Three-Dimensional Reconstructions in Electron Ptychography through Defocus Series Measurements

A detailed analysis of ptychography for three-dimensional (3D) phase reconstructions of thick specimens is performed. Here, we introduce multi-focus ptychography, which incorporates a 4D-STEM defocus series to enhance the quality of 3D reconstructions along the beam direction through a higher overdetermination ratio. This method is compared with established multi-slice ptychography techniques, such as conventional ptychography, regularized ptychography, and multi-mode ptychography. Additionally, we contrast multi-focus ptychography with an alternative method that uses virtual optical sectioning through a reconstructed scattering matrix (S-matrix), which offers more precise 3D structure information compared to conventional ptychography. Our findings from multiple 3D reconstructions based on simulated and experimental data demonstrate that multi-focus ptychography surpasses other techniques, particularly in accurately reconstructing the surfaces and interface regions of thick specimens.

3D reconstruction↗

DOE OSTI2025

Ptychography at all wavelengths

Ptychography is a computational imaging technique that operates across multiple wavelength regimes, from electron (picometres) to X-ray (~0.1 nm), extreme ultraviolet (~10 nm) and visible light (micrometres). By reconstructing both amplitude and phase from diffraction patterns, ptychography enables high-resolution, quantitative imaging without conventional limitations imposed by lens-based optics. Ptychography has enabled advances across a range of scales: achieving deep-sub-angstrom resolution with electron microscopy, becoming an indispensable tool at X-ray synchrotron facilities worldwide and overcoming the trade-offs between resolution and field-of-view in optical imaging. This Primer provides a unified treatment of ptychography across these wavelength regimes. First, we discuss theoretical foundations, reconstruction algorithms, experimental considerations and wavelength-specific challenges. We then give examples of raw and processed data from various configurations and wavelengths. Next, we highlight key applications of ptychography in life sciences, materials science and industry. We also discuss data standards, open-source software implementations and best practices for ensuring reproducibility across different wavelength regimes. Finally, we consider limitations and future opportunities for ptychography. Together with accompanying datasets and code implementations, this Primer aims to serve newcomers and experienced practitioners in the field, facilitating broader adoption of ptychography across different disciplines.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Super-Resolution Ptychography with Small Segmented Detectors

To overcome the spatial resolution limit set by aperture-limited diffraction in traditional scanning transmission electron microscopy, microscopists have developed ptychography enabled by iterative phase retrieval algorithms and high-dynamic-range pixel array detectors. Current detector designs are limited by the data rate off chip, so a high-pixel-count detector has a proportionally lower frame rate than the few-segment detectors used for differential phase contrast (DPC) imaging. This slower acquisition speed leads to heightened vulnerability to scan noise, drift, and potential sample damage. This creates opportunities for repurposing fast segmented detectors for ptychography by trading a reduction in reciprocal space pixels for an increase in real space pixels. Here, we explore a strategy of oversampling in real space and instead apply detector pixel upsampling during the reconstruction process. Further, we demonstrate the viability of achieving super-resolution ptychography on thin objects using only 2 × 2 detector pixels, surpassing the resolution of integrated DPC (iDPC) imaging. With optimization using simulated datasets and experiments on MoTe 2 /WSe 2 bilayer moiré superlattices, we achieved super-resolution ptychography reconstructions under rapid acquisition conditions (37.5 pA, 1 μs dwell time), yielding over 50% improvements in contrast and information limit compared to annular dark field and iDPC imaging on the same detectors.

2D materials↗

DOE OSTI2024

Predicting ptychography probe positions using single-shot phase retrieval neural network

Ptychography is a powerful imaging technique that is used in a variety of fields, including materials science, biology, and nanotechnology. However, the accuracy of the reconstructed ptychography image is highly dependent on the accuracy of the recorded probe positions which often contain errors. These errors are typically corrected jointly with phase retrieval through numerical optimization approaches. When the error accumulates along the scan path or when the error magnitude is large, these approaches may not converge with satisfactory result. We propose a fundamentally new approach for ptychography probe position prediction for data with large position errors, where a neural network is used to make single-shot phase retrieval on individual diffraction patterns, yielding the object image at each scan point. The pairwise offsets among these images are then found using a robust image registration method, and the results are combined to yield the complete scan path by constructing and solving a linear equation. We show that our method can achieve good position prediction accuracy for data with large and accumulating errors on the order of 10 2 pixels, a magnitude that often makes optimization-based algorithms fail to converge. For ptychography instruments without sophisticated position control equipment such as interferometers, our method is of significant practical potential.

47 OTHER INSTRUMENTATION↗

DOE OSTI2025

Efficient near-field ptychography reconstruction using the Hessian operator

X-ray ptychography is a powerful and robust coherent imaging method providing access to the complex object and probe (illumination). Ptychography reconstruction is typically performed using first-order methods due to their computational efficiency. Higher-order methods, while potentially more accurate, are often prohibitively expensive in terms of computation. In this study, we present a mathematical framework for reconstruction using second-order information derived from an efficient computation of the bilinear Hessian and Hessian operator. The formulation is provided for Gaussian-based models, enabling the simultaneous reconstruction of the object, probe, and object positions. Synthetic data tests, along with experimental near-field ptychography data processing, demonstrate a ten-fold reduction in computation time compared to first-order methods. The derived formulas for computing the Hessians, along with the strategies for incorporating them into optimization schemes, are well-structured and easily adaptable to various ptychography problem formulations.

Carlsson, Marcus [Lund Univ. (Sweden)] (ORCID:0000↗

DOE OSTI2024

Uncovering the three-dimensional structure of upconverting core–shell nanoparticles with multislice electron ptychography

In photon upconverting core–shell nanoparticles, structure strongly dictates performance. Typical imaging in scanning transmission electron microscopy has sufficient resolution to probe the atomic structure of these nanoparticles, but contrast, dose, and projection limitations make conventional methods insufficient for fully characterizing these structures. Phase retrieval techniques provide a promising alternative imaging mode, and, in particular, multislice electron ptychography can recover depth-dependent information. Here, we study beam-sensitive photon upconverting core–shell nanoparticles with a multislice ptychography approach using a low electron dose to avoid damage. Large strain fields arise in these heterostructures due to the mismatch in lattice parameter between the core and the shell. We reconstruct both a nanoparticle that appears defect-free and one that has a large break in the side and map the distribution of strain in 3D by computing distortion fields from high-resolution potential images of each slice. In the defect-free nanoparticle, we observe twisting of the shell, while in the broken nanoparticle, we measure the 3D position of the crack, the core, and dislocations. These results highlight the advantage of multislice electron ptychography to recover 3D information from a single scan, even under strict electron dose requirements from beam-sensitive samples.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2026

Relaxing Direct Ptychography Sampling Requirements via Parallax Imaging Insights

Direct ptychography enables the retrieval of information encoded in the phase of an electron wave passing through a thin sample by deconvolving the interference effects of a converged probe with known aberrations. Under the weak phase object approximation, this permits the optimal transfer of information using noniterative techniques. However, the achievable resolution of the technique is traditionally limited by the probe step size—setting stringent Nyquist sampling requirements. At the same time, parallax imaging has emerged as a dose-efficient phase technique which relaxes sampling requirements and enables scan-upsampling. Here, we formulate parallax imaging as a quadratic approximation to part of the direct ptychography kernel and use this insight to enable upsampling in direct ptychography. We validate our analytical results numerically using simulated and experimental reconstructions.

direct ptychography, parallax imaging, scan Nyquis↗

DOE OSTI2024

Efficient boundary-guided scanning for high-resolution X-ray ptychography

In the realm of X-ray ptychography experiments, a considerable amount of ptychography scans are typically performed within a field of view encompassing the target sample. While it is crucial to obtain overlapping scans in small increments over the region of interest for achieving high-resolution sample reconstruction, a significant number of these scans often redundantly measure the empty background within the wide field of view. To address this inefficiency, an innovative algorithm is proposed that introduces automatic guidance for data acquisition. The algorithm first directs the scan point to actively search for the object of interest within the field of view. Subsequently, it intelligently scans along the perimeter of the sample, strategically acquiring measurements exclusively within the boundary of the region of interest. By employing this approach, a reduction in the number of measurements required to obtain high-resolution reconstruction images is demonstrated, as compared with conventional raster scanning methods. Furthermore, the automatic guidance provided by the algorithm offers the added advantage of saving valuable time during the reconstruction process. Through practical implementation on real experiments, these findings showcase the efficacy of the proposed algorithm in enhancing the efficiency and accuracy of X-ray ptychography experiments. This novel approach holds immense potential for advancing sample analysis and imaging techniques in various scientific disciplines.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2025

X-ray near-field multi-slice ptychography for in-situ imaging

Abstract In-situ imaging of chemical reactions can provide valuable insight into nanoparticle growth and structural evolution. Hard X-ray imaging is an excellent tool for this purpose, as it combines high spatial resolution with high penetration depth, allowing for realistic reaction environments. While far-field ptychography is a well-established method at synchrotron radiation sources, its near-field analog has received less attention. In this work we show that near-field multi-slice ptychography is a competitive method for high-resolution in-situ imaging by studying the formation of gold nanocages via galvanic replacement. Our work extends near-field X-ray ptychography to sub-50 nm spatial resolution by using multilayer Laue lenses. These high numerical aperture optics enable to distinguish sample layers that are separated by less than 100 µm by multi-slicing techniques.

Science & Technology - Other Topics↗

DOE OSTI2025

Fabrication and characterization of boron-terminated tetravacancies in monolayer hBN using STEM, EELS and electron ptychography

Tetravacancies in monolayer hexagonal boron nitride (hBN) with consistent edge termination (boron or nitrogen) form triangular nanopores with electrostatic potentials that can be leveraged for applications such as selective ion transport and neuromorphic computing. In order to quantitatively predict the properties of these structures, an atomic-level understanding of their local electronic and chemical environments is required. Moreover, robust methods for their precision manufacture are needed. Here we use electron irradiation in a scanning transmission electron microscope (STEM) at a high dose rate to drive the formation of boron-terminated tetravacancies in monolayer hBN. Characterization of the defects is achieved using aberration-corrected STEM, monochromated electron energy-loss spectroscopy (EELS), and electron ptychography. Z-contrast in STEM and chemical fingerprinting by core-loss EELS enable identification of the edge terminations, while electron ptychography gives insight into structural relaxation of the tetravacancies and provides evidence of enhanced electron density around the defect perimeters indicative of bonding effects.

2D hBN↗

DOE OSTI2023

Projected Multi-Agent Consensus Equilibrium (PMACE) With Application to Ptychography

Multi-Agent Consensus Equilibrium (MACE) formulates an inverse imaging problem as a balance among multiple update agents such as data-fitting terms and denoisers. However, each such agent operates on a separate copy of the full image, leading to redundant memory use and slow convergence when each agent affects only a small subset of the full image. In this article, we extend MACE to Projected Multi-Agent Consensus Equilibrium (PMACE), in which each agent updates only a projected component of the full image, thus greatly reducing memory use for some applications. We describe PMACE in terms of an equilibrium problem and an equivalent fixed-point problem and show that in most cases the PMACE equilibrium is not the solution of an optimization problem. To demonstrate the value of PMACE, we apply it to the problem of ptychography, in which a sample is reconstructed from the diffraction patterns resulting from coherent X-ray illumination at multiple overlapping spots. In our PMACE formulation, each spot corresponds to a separate data-fitting agent, with the final solution found as an equilibrium among all the agents. In conclusion, our results demonstrate that the PMACE reconstruction algorithm generates more accurate reconstructions at a lower computational cost than existing ptychography algorithms when the spots are sparsely sampled.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Accelerating iterative ptychography with an integrated neural network

Electron ptychography is a powerful and versatile tool for high-resolution and dose-efficient imaging. Iterative reconstruction algorithms are powerful but also computationally expensive due to their relative complexity and the many hyperparameters that must be optimised. Gradient descent-based iterative ptychography is a popular method, but it may converge slowly when reconstructing low spatial frequencies. Here, in this work, we present a method for accelerating a gradient descent-based iterative reconstruction algorithm by training a neural network (NN) that is applied in the reconstruction loop. The NN works in Fourier space and selectively boosts low spatial frequencies, thus enabling faster convergence in a manner similar to accelerated gradient descent algorithms. We discuss the difficulties that arise when incorporating a NN into an iterative reconstruction algorithm and show how they can be overcome with iterative training. We apply our method to simulated and experimental data of gold nanoparticles on amorphous carbon and show that we can significantly speed up ptychographic reconstruction of the nanoparticles.

4DSTEM↗

DOE OSTI2024

Achieving sub-0.5-angstrom–resolution ptychography in an uncorrected electron microscope

Subangstrom resolution has long been limited to aberration-corrected electron microscopy, where it is a powerful tool for understanding the atomic structure and properties of matter. Here, we demonstrate electron ptychography in an uncorrected scanning transmission electron microscope (STEM) with deep subangstrom spatial resolution down to 0.44 angstroms, exceeding the conventional resolution of aberration-corrected tools and rivaling their highest ptychographic resolutions. Our approach, which we demonstrate on twisted two-dimensional materials in a widely available commercial microscope, far surpasses prior ptychographic resolutions (1 to 5 angstroms) of uncorrected STEMs. We further show how geometric aberrations can create optimized, structured beams for dose-efficient electron ptychography. Our results demonstrate that expensive aberration correctors are no longer required for deep subangstrom resolution.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Soft X-ray reflection ptychography

Scanning transmission X-ray microscopy and ptychography have become mature tools for high-resolution, element-specific imaging of nanoscale structures. However, transmission geometries impose stringent constraints on sample thickness and preparation, thereby limiting investigations of extended or bulk specimens, especially in the soft X-ray region. Here, we demonstrate reflection-geometry soft X-ray ptychography as a robust imaging mode. Instrumental feasibility and spatial resolution are established using a lithographically defined Siemens star and barcode test pattern on a multilayer substrate. We empirically demonstrate a full-pitch spatial resolution of ca. 45 nm from Fourier ring correlation analysis of the reconstructed object. The results highlight the potential of the reflection geometry for nondestructive X-ray studies of materials without the need for transmissive samples.

Guenzing, Damian [Lawrence Berkeley National Labor↗

DOE OSTI2026

Atomic-Scale Imaging of Lithium Vacancies in a Battery Cathode by Multislice Electron Ptychography

Atomic-resolution imaging of battery materials is critical for identification of local defects and structural variations, which are tied to battery performance. However, since battery materials are, by design, optimized to allow ion motion in response to an applied electric field, they are also very sensitive to radiation damage by an electron beam. Image resolution is therefore severely constrained by the dose applied. Here, we show that multislice electron ptychography (MEP) can provide sub-ångström lateral resolution images of both light and heavy elements of a Li-ion battery cathode, along with nanometer-scale depth information and greater dose efficiency than conventional electron microscopy methods. Using the depth-sectioning capability of MEP, we have been able to obtain direct visualizations of Li vacancy clusters, atom column by atom column, in Li x Ni 0.33 Mn 0.33 Co 0.33 O 2 (NMC111) cathodes. This capability to track Li distributions will be valuable in understanding, informing, and optimizing electrode material design for ion storage and transfer.

batteries↗

DOE OSTI2026

Direct Determination of 3C/4H Silicon Carbide Heterophase Interfaces by Electron Ptychography

Silicon carbide is a technologically relevant material that can exist in various structural polymorphs, each with its own electronic properties. Through the controlled growth of abrupt interfaces between the polymorphs, systems with emergent properties arise from differences in local bonding and stacking sequences. Determining the structure of these interfaces provides important insights into predicting and ultimately controlling their properties. Here, in this study, we use multislice electron ptychography (MEP) to qualitatively and quantitatively analyze interfaces between 3C and 4H silicon carbide in three dimensions. Two distinct interfaces are investigated: a coherent interface between $(1\bar{1}1)$ (3C) and $(0001)$ (4H) , and an incoherent interface between $(1\bar{1}2)$ (3C) and $(1\bar{1}00)$ (4H) . At the coherent interface, MEP enables direct quantification of a sharp boundary with an inclined step, whereas at the incoherent interface, local atomic displacements are determined along dislocation cores. By quantifying the spatial distribution and atomic-scale structure of these interfaces in three dimensions, this study provides insight into the complexity of silicon carbide heteropolytype interfaces, paving the way for theoretical modeling and the development of design rules to achieve desired properties.

heterophase interface↗

DOE OSTI2026

Learning neural representations for X-ray ptychography reconstruction with unknown probes

X-ray ptychography provides exceptional nanoscale resolution and is widely applied in materials science, biology, and nanotechnology. However, its full potential is constrained by the critical challenge of accurately reconstructing images when the illuminating probe is unknown. Conventional iterative methods and deep learning approaches are often suboptimal, particularly under the low-signal conditions inherent to low-dose and high-speed experiments. These limitations compromise reconstruction fidelity and restrict the broader adoption of the technique. In this work, we introduce the Ptychographic Implicit Neural Representation (PtyINR), a self-supervised framework that simultaneously addresses the object- and probe-recovery problem. By parameterizing both as continuous neural representations, PtyINR performs end-to-end reconstruction directly from raw diffraction patterns without requiring any pre-characterization of the probe. Extensive evaluations demonstrate that PtyINR achieves superior reconstruction quality on both simulated and experimental data, with remarkable robustness under challenging low-signal conditions. Furthermore, PtyINR offers a generalizable, physics-informed framework for addressing probe-dependent inverse problems, making it applicable to a wide range of computational microscopy problems.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Electron ptychography reveals a ferroelectricity dominated by anion displacements

Sodium niobate, a lead-free ferroic material, hosts delicately balanced, competing order parameters, including ferroelectric states that can be stabilized by epitaxial strain. Here we show that the resulting macroscopic ferroelectricity exhibits an unconventional microscopic structure using multislice electron ptychography. This technique overcomes multiple scattering artefacts limiting conventional electron microscopy, enabling both lateral spatial resolution beyond the diffraction limit and recovery of three-dimensional structural information. These imaging capabilities allow us to separate the ferroelectric interior of the sample from the relaxed surface structure and identify the soft phonon mode and related structural distortions with picometre precision. Unlike conventional ferroelectric perovskites, we find that the polar distortion in this material involves minimal distortions of the cation sublattices and is instead dominated by anion displacements relative to the niobium sublattice. We establish limits on film thickness for interfacial octahedral rotation engineering and directly visualize a random octahedral rotation pattern, arising from the flat dispersion of the associated phonon mode.

ferroelectrics and multiferroics↗