Subgradient-projection-based stable phase-retrieval algorithm for X-ray ptychography.

X-ray ptychography is a lensless imaging technique that visualizes the nano-structure of a thick specimen which cannot be observed with an electron microscope. It reconstructs a complex-valued refractive index of the specimen from observed diffraction patterns. This reconstruction problem is called phase retrieval (PR). For further improvement in the imaging capability, including expansion of the depth of field, various PR algorithms have been proposed. Since a high-quality PR method is built upon a base PR algorithm such as ePIE, developing a well performing base PR algorithm is important. This paper proposes an improved iterative algorithm named CRISP. It exploits subgradient projection which allows adaptive step size and can be expected to avoid yielding a poor image. The proposed algorithm was compared with ePIE, which is a simple and fast-convergence algorithm, and its modified algorithm, rPIE. The experiments confirmed that the proposed method improved the reconstruction performance for both simulation and real data.

Morphology of Copper Nanofoams for Radiation Hydrodynamics and Fusion Applications Investigated by 3D Ptychotomography.

The performance of metal and polymer foams used in inertial confinement fusion (ICF), inertial fusion energy (IFE), and high-energy-density (HED) experiments is currently limited by our understanding of their nanostructure and its variation in bulk material. We utilized an X-ray-free electron laser (XFEL) together with lensless X-ray imaging techniques to probe the 3D morphology of copper foams at nanoscale resolution (28 nm). The observed morphology of the thin shells is more varied than expected from previous characterizations, with a large number of them distorted, merged, or open, and a targeted mass density 14% less than calculated. This nanoscale information can be used to directly inform and improve foam modeling and fabrication methods to create a tailored material response for HED experiments.

Imaging Negative Charge around Single Vanadium Dopant Atoms in Monolayer Tungsten Diselenide Using 4D Scanning Transmission Electron Microscopy.

There has been extensive activity exploring the doping of semiconducting two-dimensional (2D) transition metal dichalcogenides in order to tune their electronic and magnetic properties. The outcome of doping depends on various factors, including the intrinsic properties of the host material, the nature of the dopants used, their spatial distribution, as well as their interactions with other types of defects. A thorough atomic-level analysis is essential to fully understand these mechanisms. In this work, the vanadium-doped WSe2 monolayer grown by molecular beam epitaxy is investigated using four-dimensional scanning transmission electron microscopy (4D-STEM). Through center-of-mass-based reconstruction, atomic-scale maps are produced, allowing the visualization of both the electric field and the electrostatic potential around individual V atoms. To provide quantitative insights, these results are successfully compared to multislice image simulations based on ab initio calculations, accounting for lens aberrations. Finally, a negative charge around the V dopants is detected as a drop in the electrostatic potential, unambiguously demonstrating that 4D-STEM can be used to detect and to accurately analyze single-dopant charge states in semiconducting 2D materials.

Near-field electron ptychography using full-field structured illumination.

A new configuration for near-field ptychography using a full-field illumination with a structured electron beam is proposed. A structured electron beam illuminating the entire field of view is scanned over the specimen, and a series of in-line holograms formed in the near-field region below the specimen are collected. The structured beam is generated by a conductive film with random openings, which ensures high stability and coherence of the beam. Observation in the near-field region reduces the beam concentration that occurs in the far-field region, which contributes to accurate recording of the beam intensity with a finite dynamic range of the detectors. The use of full-field illumination prevents the accumulation of errors caused by concatenating the local structures, which is the method used in conventional reconstruction. Since all holograms are obtained from the entire field of view, they have uniform multiplicity in terms of specimen information within the field of view. This contributes to robust and efficient reconstruction for a large field of view. The proposed method was tested using both simulated and experimental holograms. For the simulated holograms, the reconstruction of the specimen transmission function was achieved with an error less than 1/3485 of the wavelength. The method was further validated using experimental holograms obtained from MgO particles. The reconstructed phase transmission function of the specimen was consistent with the specimen structure and was equivalent to a mean inner potential of V on the MgO particle, which is in close agreement with previously reported values.

Simultaneous Multifocal Plane Fourier Ptychographic Microscopy Utilizing a Standard RGB Camera.

Fourier ptychographic microscopy (FPM) is a computational imaging technology that can acquire high-resolution large-area images for applications ranging from biology to microelectronics. In this study, we utilize multifocal plane imaging to enhance the existing FPM technology. Using an RGB light emitting diode (LED) array to illuminate the sample, raw images are captured using a color camera. Then, exploiting the basic optical principle of wavelength-dependent focal length variation, three focal plane images are extracted from the raw image through simple R, G, and B channel separation. Herein, a single aspherical lens with a numerical aperture (NA) of 0.15 was used as the objective lens, and the illumination NA used for FPM image reconstruction was 0.08. Therefore, simultaneous multifocal plane FPM with a synthetic NA of 0.23 was achieved. The multifocal imaging performance of the enhanced FPM system was then evaluated by inspecting a transparent organic light-emitting diode (OLED) sample. The FPM system was able to simultaneously inspect the individual OLED pixels as well as the surface of the encapsulating glass substrate by separating R, G, and B channel images from the raw image, which was taken in one shot.

Enhanced tissue slide imaging in the complex domain via cross-explainable GAN for Fourier ptychographic microscopy.

Achieving microscopy with large space-bandwidth products plays a key role in diagnostic imaging and is widely significant in the overall field of clinical practice. Among quantitative microscopy techniques, Fourier Ptychography (FP) provides a wide field of view and high-resolution images, suitable to the histopathological field, but onerous in computational terms. Artificial intelligence can be a solution in this sense. In particular, this research delves into the application of Generative Adversarial Networks (GAN) for the dual-channel complex FP image enhancement of human kidney samples. The study underscores the GANs' efficacy in promoting biological architectures in FP domain, thereby still guaranteeing high resolution and visibility of detailed microscopic structures. We demonstrate successful GAN-based enhanced reconstruction through two strategies: cross-explainability and expert survey. The cross-explainability is evaluated through the comparison of explanation maps for both real and imaginary components underlining its robustness. This comparison further shows that their interplay is pivotal for accurate reconstruction without hallucinations. Secondly, the enhanced reconstruction accuracy and effectiveness in a clinical workflow are confirmed through a two-step survey conducted with nephrologists.

Multi-scale structural characterization of ceramic-based photonic glasses for structural colors.

Structural colors arise from selective light interaction with (nano)structures, which give them advantages over pigmented colors such as resistance to fading and possibility to be fabricated out of traditional low-cost and non-toxic materials. Since the color arises from the photonic (nano)structures, different structural features can impact their photonic response and thus, their color. Therefore, the detailed characterization of their structural features is crucial for further improvement of structural colors. In this work, we present a detailed multi-scale structural characterization of ceramic-based photonic glasses by using a combination of high-resolution ptychographic X-ray computed tomography and small angle X-ray scattering. Our results uncover the structure-processing-properties' relationships of such nanoparticles-based photonic glasses and point out to the need of a review of the structural features used in simulation models concomitantly with the need for further investigations by experimentalists, where we point out exactly which structural features need to be improved.

X-Ray Multibeam Ptychography at up to 20 keV: Nano-Lithography Enhances X-Ray Nano-Imaging.

Hard X-rays are needed for non-destructive nano-imaging of solid matter. Synchrotron radiation facilities (SRF) provide the highest-quality images with single-digit nm resolution using advanced techniques such as X-ray ptychography. However, the resolution or field of view is ultimately constrained by the available coherent flux. To address this, the beam's incoherent fraction can be exploited using multiple parallel beams in an X-ray multibeam ptychography (MBP) approach. This expands the domain of X-ray ptychography to larger samples or more rapid measurements. Both qualities favor the study of complex composite or functional samples, such as catalysts, energy materials, or electronic devices. The challenge of performing ptychography at high energy and with many parallel beams must be overcome to extract the full advantages for extended samples while minimizing beam attenuation. Here, that challenge is overcome by creating a lens array using cutting-edge laser printing technology and applying it to perform scanning with MBP with up to 12 beams and at photon energies of 13 and 20 keV. This exceeds the measurement limits of conventional hard X-ray ptychography without compromising image quality for various samples: Siemens star test pattern, Ni/Al2O3 catalyst, microchip, and gold nano-crystal clusters.

A Methodology for Robust Multislice Ptychography.

While multislice electron ptychography can provide thermal vibration limited resolution and structural information in 3D, it relies on properly selecting many intertwined acquisition and computational parameters. Here, we outline a methodology for selecting acquisition parameters to enable robust ptychographic reconstructions. We develop two physically informed metrics, areal oversampling and Ronchigram magnification, to describe the selection of these parameters in multislice ptychography. Through simulations, we comprehensively evaluate the validity of these two metrics over a broad range of conditions and show that they accurately guide reconstruction success. Further, we validate these conclusions with experimental ptychographic data and demonstrate close agreement between trends in simulated and experimental data. Using these metrics, we achieve experimental multislice reconstructions at a scan step of 2.1Å/px, enabling large field-of-view, data-efficient reconstructions. These experimental design principles enable the routine and robust use of multislice ptychography for 3D characterization of materials at the atomic scale.

High-speed 4-dimensional scanning transmission electron microscopy using compressive sensing techniques.

Here we show that compressive sensing allows 4-dimensional (4-D) STEM data to be obtained and accurately reconstructed with both high-speed and reduced electron fluence. The methodology needed to achieve these results compared to conventional 4-D approaches requires only that a random subset of probe locations is acquired from the typical regular scanning grid, which immediately generates both higher speed and the lower fluence experimentally. We also consider downsampling of the detector, showing that oversampling is inherent within convergent beam electron diffraction (CBED) patterns and that detector downsampling does not reduce precision but allows faster experimental data acquisition. Analysis of an experimental atomic resolution yttrium silicide dataset shows that it is possible to recover over 25 dB peak signal-to-noise ratio in the recovered phase using 0.3% of the total data. Lay abstract: Four-dimensional scanning transmission electron microscopy (4-D STEM) is a powerful technique for characterizing complex nanoscale structures. In this method, a convergent beam electron diffraction pattern (CBED) is acquired at each probe location during the scan of the sample. This means that a 2-dimensional signal is acquired at each 2-D probe location, equating to a 4-D dataset. Despite the recent development of fast direct electron detectors, some capable of 100kHz frame rates, the limiting factor for 4-D STEM is acquisition times in the majority of cases, where cameras will typically operate on the order of 2kHz. This means that a raster scan containing 256^2 probe locations can take on the order of 30s, approximately 100-1000 times longer than a conventional STEM imaging technique using monolithic radial detectors. As a result, 4-D STEM acquisitions can be subject to adverse effects such as drift, beam damage, and sample contamination. Recent advances in computational imaging techniques for STEM have allowed for faster acquisition speeds by way of acquiring only a random subset of probe locations from the field of view. By doing this, the acquisition time is significantly reduced, in some cases by a factor of 10-100 times. The acquired data is then processed to fill-in or inpaint the missing data, taking advantage of the inherently low-complex signals which can be linearly combined to recover the information. In this work, similar methods are demonstrated for the acquisition of 4-D STEM data, where only a random subset of CBED patterns are acquired over the raster scan. We simulate the compressive sensing acquisition method for 4-D STEM and present our findings for a variety of analysis techniques such as ptychography and differential phase contrast. Our results show that acquisition times can be significantly reduced on the order of 100-300 times, therefore improving existing frame rates, as well as further reducing the electron fluence beyond just using a faster camera.

Multimodal 2D and 3D microscopic mapping of growth cartilage by computational imaging techniques - a short review including new research.

Being able to image the microstructure of growth cartilage is important for understanding the onset and progression of diseases such as osteochondrosis and osteoarthritis, as well as for developing new treatments and implants. Studies of cartilage using conventional optical brightfield microscopy rely heavily on histological staining, where the added chemicals provide tissue-specific colours. Other microscopy contrast mechanisms include polarization, phase- and scattering contrast, enabling non-stained or 'label-free' imaging that significantly simplifies the sample preparation, thereby also reducing the risk of artefacts. Traditional high-performance microscopes tend to be both bulky and expensive.Computational imagingdenotes a range of techniques where computers with dedicated algorithms are used as an integral part of the image formation process. Computational imaging offers many advantages like 3D measurements, aberration correction and quantitative phase contrast, often combined with comparably cheap and compact hardware. X-ray microscopy is also progressing rapidly, in certain ways trailing the development of optical microscopy. In this study, we first briefly review the structures of growth cartilage and relevant microscopy characterization techniques, with an emphasis on Fourier ptychographic microscopy (FPM) and advanced x-ray microscopies. We next demonstrate with our own results computational imaging through FPM and compare the images with hematoxylin eosin and saffron (HES)-stained histology. Zernike phase contrast, and the nonlinear optical microscopy techniques of second harmonic generation (SHG) and two-photon excitation fluorescence (TPEF) are explored. Furthermore, X-ray attenuation-, phase- and diffraction-contrast computed tomography (CT) images of the very same sample are presented for comparisons. Future perspectives on the links to artificial intelligence, dynamic studies andin vivopossibilities conclude the article.

First X-ray spectral ptychography and resonant ptychographic computed tomography experiments at the SWING beamline from Synchrotron SOLEIL.

X-ray ptychography and ptychographic computed tomography have seen a rapid rise since the advent of fourth-generation synchrotrons with a high degree of coherent radiation. In addition to quantitative multiscale structural analysis, ptychography with spectral capabilities has been developed, allowing for spatial-localized multiscale structural and spectral information of samples. The SWING beamline of Synchrotron SOLEIL has recently developed a nanoprobe setup where the endstation's first spectral and resonant ptychographic measurements have been successfully conducted. A metallic nickel wire sample was measured using 2D spectral ptychography in XANES mode and resonant ptychographic tomography. From the 2D spectral ptychography measurements, the spectra of the components of the sample's complex-valued refractive index, δ and ß, were extracted, integrated along the sample thickness. By performing resonance ptychographic tomography at two photon energies, 3D maps of the refractive index decrement, δ, were obtained at the Ni K-edge energy and another energy above the edge. These maps allowed the detection of impurities in the Ni wire. The significance of accounting for the atomic scattering factor is demonstrated in the calculation of electron density near a resonance through the use of the δ values. These results indicate that at the SWING beamline it is possible to conduct state-of-the-art spectral and resonant ptychography experiments using the nanoprobe setup.

Aberration Correction for Large-Angle Illumination Scanning Transmission Electron Microscopy by Using Iterative Electron Ptychography Algorithms.

Modern aberration correctors in the scanning transmission electron microscope (STEM) have dramatically improved the attainable spatial resolution and enabled atomical structure and spectroscopic analysis even at low acceleration voltages (≤80 kV). For a large-angle illumination, achieving successful aberration correction to high angles is challenging with an aberration corrector, which limits further improvements in applications such as super-resolution, three-dimensional atomic depth resolution, or atomic surface morphology analyses. Electron ptychography based on four-dimensional STEM can provide a postprocessing strategy to overcome the current technological limitations. In this work, we have demonstrated that aberration correction for large-angle illumination is feasible by pushing the capabilities of regularized ptychographic iterative engine algorithms to reconstruct 4D data sets acquired using a relatively low-efficiency complementary metal oxide semiconductor camera. We report super resolution (0.71 Å) with large-angle illumination (50-60 mrad) and under 60 kV accelerating voltage.

An Efficient Electron Ptychography Method for Retrieving the Object Spectrum from Only a Few Iterations.

We present an efficient approach for electron ptychography based on a mathematical relationship that differs from that underlying the established algorithms of the ptychography iterative engine or the noniterative algorithms like the Wigner-distribution-deconvolution or the single-side-band method. Three variables are handled in this method-the transfer function of the objective lens, the object spectrum, and the diffraction wave whose phase is unknown. In the case of an aberration-corrected electron microscope, one is able to obtain a well-estimated transfer function of the lens. After reducing the number of three variables down to two, we construct an iterative loop between the object spectrum and the diffraction wave, which retrieves the object spectrum within a small number of iterations. We tested this object spectrum retrieval method on both a calculated and an experimental 4D-STEM datasets. By applying this method, we explore the influence of sampling, dose, and the size of illumination aperture on the reconstructed phase images.

ProSPyX: software for post-processing images of X-ray ptychography with spectral capabilities.

X-ray ptychography is a coherent diffraction imaging technique based on acquiring multiple diffraction patterns obtained through the illumination of the sample at different partially overlapping probe positions. The diffraction patterns collected are used to retrieve the complex transmittivity function of the sample and the probe using a phase retrieval algorithm. Absorption or phase contrast images of the sample as well as the real and imaginary parts of the probe function can be obtained. Furthermore, X-ray ptychography can also provide spectral information of the sample from absorption or phase shift images by capturing multiple ptychographic projections at varying energies around the resonant energy of the element of interest. However, post-processing of the images is required to extract the spectra. To facilitate this, ProSPyX, a Python package that offers the analysis tools and a graphical user interface required to process spectral ptychography datasets, is presented. Using the PyQt5 Python open-source module for development and design, the software facilitates extraction of absorption and phase spectral information from spectral ptychographic datasets. It also saves the spectra in file formats compatible with other X-ray absorption spectroscopy data analysis software tools, streamlining integration into existing spectroscopic data analysis pipelines. To illustrate its capabilities, ProSPyX was applied to process the spectral ptychography dataset recently acquired on a nickel wire at the SWING beamline of the SOLEIL synchrotron.

Live Iterative Ptychography.

We demonstrate live-updating ptychographic reconstruction with the extended ptychographical iterative engine, an iterative ptychography method, during ongoing data acquisition. The reconstruction starts with a small subset of the total data, and as the acquisition proceeds the data used for reconstruction are extended. This creates a live-updating view of object and illumination that allows monitoring the ongoing experiment and adjusting parameters with quick turn around. This is particularly advantageous for long-running acquisitions. We show that such a gradual reconstruction yields interpretable results already with a small subset of the data. We show simulated live processing with various scan patterns, parallelized reconstruction, and real-world live processing at the hard X-ray ptychographic nanoanalytical microscope PtyNAMi at the PETRA III beamline.

Ptychographic Nanoscale Imaging of the Magnetoelectric Coupling in Freestanding BiFeO3.

Understanding the magnetic and ferroelectric ordering of magnetoelectric multiferroic materials at the nanoscale necessitates a versatile imaging method with high spatial resolution. Here, soft X-ray ptychography is employed to simultaneously image the ferroelectric and antiferromagnetic domains in an 80 nm thin freestanding film of the room-temperature multiferroic BiFeO3 (BFO). The antiferromagnetic spin cycloid of period 64 nm is resolved by reconstructing the corresponding resonant elastic X-ray scattering in real space and visualized together with mosaic-like ferroelectric domains in a linear dichroic contrast image at the Fe L3 edge. The measurements reveal a near perfect coupling between the antiferromagnetic and ferroelectric ordering by which the propagation direction of the spin cycloid is locked orthogonally to the ferroelectric polarization. In addition, the study evinces both a preference for in-plane propagation of the spin cycloid and changes of the ferroelectric polarization by 71° between multiferroic domains in the epitaxial strain-free, freestanding BFO film. The results provide a direct visualization of the strong magnetoelectric coupling in BFO and of its fine multiferroic domain structure, emphasizing the potential of ptychographic imaging for the study of multiferroics and non-collinear magnetic materials with soft X-rays.

Fast nanoscale imaging of strain in a multi-segment heterostructured nanowire with 2D Bragg ptychography.

Developing semiconductor devices requires a fast and reliable source of strain information with high spatial resolution and strain sensitivity. This work investigates the strain in an axially heterostructured 180 nm-diameter GaInP nanowire with InP segments of varying lengths down to 9 nm, simultaneously probing both materials. Scanning X-ray diffraction (XRD) is compared with Bragg projection ptychography (BPP), a fast single-projection method. BPP offers a sufficient spatial resolution to reveal fine details within the largest segments, unlike scanning XRD. The spatial resolution affects the quantitative accuracy of the strain maps, where BPP shows much-improved agreement with an elastic 3D finite element model compared with scanning XRD. The sensitivity of BPP to small deviations from the Bragg condition is systematically investigated. The experimental confirmation of the model suggests that the large lattice mismatch of 1.52% is accommodated without defects.

Recovery of spatial frequencies in coherent diffraction imaging in the presence of a central obscuration.

Coherent diffraction imaging (CDI) and its scanning version, ptychography, are lensless imaging approaches used to iteratively retrieve a sample's complex scattering amplitude from its measured diffraction patterns. These imaging methods are most useful in extreme ultraviolet (EUV) and X-ray regions of the electromagnetic spectrum, where efficient imaging optics are difficult to manufacture. CDI relies on high signal-to-noise ratio diffraction data to recover the phase, but increasing the flux can cause saturation effects on the detector. A conventional solution to this problem is to place a beam stop in front of the detector. The pixel masking method is a common solution to the problem of missing frequencies due to a beam stop. This paper describes the information redundancy in the recorded data set and expands on how the reconstruction algorithm can exploit this redundancy to estimate the missing frequencies. Thereafter, we modify the size of the beam stop in experimental and simulation data to assess the impact of the missing frequencies, investigate the extent to which the lost portion of the diffraction spectrum can be recovered, and quantify the effect of the beam stop on the image quality. The experimental findings and simulations conducted for EUV imaging demonstrate that when using a beam stop, the numerical aperture of the condenser is a crucial factor in the recovery of lost frequencies. Our thorough investigation of the reconstructed images provides information on the overall quality of reconstruction and highlights the vulnerable frequencies if the beam stop size is larger than the extent of the illumination NA. The outcome of this study can be applied to other sources of frequency loss, and it will contribute to the improvement of experiments and reconstruction algorithms in CDI.

Phase offset method of ptychographic contrast reversal correction.

The contrast transfer function of direct ptychography methods such as the single side band (SSB) method are single signed, yet these methods still sometimes exhibit contrast reversals, most often where the projected potentials are strong. In thicker samples central focusing often provides the best ptychographic contrast as this leads to defocus variations within the sample canceling out. However focusing away from the entrance surface is often undesirable as this degrades the annular dark field (ADF) signal. Here we discuss how phase wrap asymptotes in the frequency response of SSB ptychography give rise to contrast reversals, without the need for dynamical scattering, and how these can be counteracted by manipulating the phases such that the asymptotes are either shifted to higher frequencies or damped via amplitude modulation. This is what enables post collection defocus correction of contrast reversals. However, the phase offset method of counteracting contrast reversals we introduce here is generally found to be superior to post collection application of defocus, with greater reliability and generally stronger contrast. Importantly, the phase offset method also works for thin and thick samples where central focusing does not. Finally, the independence of the method from focus is useful for optical sectioning involving ptychography, improving interpretability by better disentangling the effects of strong potentials and focus.