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All sourcesNASA NTRSDOE OSTI
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 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 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 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 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 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↗
DOE OSTI2026

Evaluating multi-slice ptychography tomography for X-ray imaging

X-ray ptychography typically relies on single-slice reconstruction approaches that assume minimal beam propagation through the specimen. However, this approximation breaks down for thick samples or when using high numerical aperture optics, leading to reconstruction artifacts due to multiple scattering. Multi-slice ptychographic tomography (MSPT) addresses this limitation by explicitly modeling beam propagation through the specimen while reducing angular sampling requirements for tomography, but its performance depends critically on reconstruction parameters and experimental conditions. Here, we systematically evaluate MSPT using numerical simulations and experimental X-ray datasets to understand how factors such as object thickness, optical parameters, and initialization strategies affect reconstruction accuracy. We demonstrate that informed object initialization significantly improves depth resolution and enables accurate projection extension, reducing the angular sampling requirements for tomographic reconstruction. Experimental demonstration confirms that MSPT produces reconstructions with reduced artifacts, establishing it as a robust approach for nanoscale imaging at modern synchrotron facilities.

Luktuke, Amey [Argonne National Laboratory (ANL), ↗
NASA NTRSDate not supplied

Portable Flow Device Using Fourier Ptychography Microscopy and Deep Learning for Detection of Biosignatures

A proof-of-concept, compact, portable Fourier Ptychographic Microscope (FPM) to perform wide field-of-view, high spatial resolution imaging (<1 μm) for biosignature motility in liquid samples, is presented. The FPM has the potential to be developed as a space-based payload for future landers destined to the Ocean Worlds. A portable FPM using an existing Fourier ptychography (FP) algorithm adapted for reconstruction is demonstrated. A NVIDIA Jetson Nano board and camera combined with FP, is used to computationally reconstruct sub-micron resolution images. Additionally, deep learning was employed to perform inferencing prediction which enables the on-edge FPM device.

Fourier↗
DOE OSTI2026

Fidelity-preserving enhancement of ptychography with foundational text-to-image models

Ptychographic phase retrieval enables high-resolution imaging of complex samples but often suffers from artifacts such as grid pathology and multislice crosstalk, which degrade reconstructed images. We propose a plug-and-play (PnP) framework that integrates physics model-based phase retrieval with text-guided image editing using foundational diffusion models. By employing the alternating direction method of multipliers, our approach ensures consensus between data fidelity and artifact removal subproblems, maintaining physical consistency while enhancing image quality. Artifact removal is achieved using a text-guided diffusion image editing method (LEDITS++) with a pre-trained foundational diffusion model, allowing users to specify artifacts for removal in natural language. Demonstrations on simulated and experimental datasets show significant improvements in artifact suppression and structural fidelity, validated by metrics such as peak signal-to-noise ratio and diffraction pattern consistency. This work highlights the combination of text-guided generative models and model-based phase retrieval algorithms as a transferable and fidelity-preserving method for high-quality diffraction imaging.

image editing↗