Hard-x-ray lensless imaging of extended objects

Prospects for coherent X-ray diffraction imaging at fourth-generation synchrotron sources

Coherent X-ray diffraction imaging is a lens-less microscopy technique that emerged with the advent of third-generation synchrotrons, modern detectors and computers. It can image isolated micrometre-sized objects with a spatial resolution of a few nanometres. The method is based on the inversion of the speckle pattern in the far field produced by the scattering from the object under coherent illumination. The retrieval of the missing phase is performed using an iterative algorithm that numerically phases the amplitudes from the intensities of speckles measured with sufficient oversampling. Two- and three-dimensional imaging is obtained by simple inverse Fourier transform. This lens-less imaging technique has been applied to various specimens for their structural characterization on the nanoscale. Here, we review the theoretical and experimental elements of the technique, its achievements, and its limitations at third-generation synchrotrons. We also discuss the new opportunities offered by modern fourth-generation synchrotrons and outline the developments necessary to maximize the potential of the technique.

Diatom Lensless Imaging Using Laser Scattering and Deep Learning

We present a novel approach for imaging diatoms using lensless imaging and deep learning. We used a laser beam to scatter off samples of diatomaceous earth (diatoms) and then recorded and transformed the scattered light into microscopy images of the diatoms. The predicted microscopy images gave an average SSIM of 0.98 and an average RMSE of 3.26 as compared to the experimental data. We also demonstrate the capability of determining the velocity and angle of movement of the diatoms from their scattering patterns as they were translated through the laser beam. This work shows the potential for imaging and identifying the movement of diatoms and other microsized organisms in situ within the marine environment. Implementing such a method for real-time image acquisition and analysis could enhance environmental management, including improving the early detection of harmful algal blooms.

Sampling requirements in near-field ptychography

Ptychography is a robust lensless form of microscopy routinely used for applications spanning life and physical sciences. The most common ptychography setup consists in using a detector to record diffraction patterns in the far-field. A near-field version has been more recently introduced, and its potential is yet to be fully exploited. In this work, the sampling requirements for near-field ptychography are analysed. Starting from the characterisation available in literature, the formalism of the fractional Fourier transform is used to generalise analytically the sampling conditions. The results harmonise the far- and near-field regimes and widen the applications of the technique with respect to the current knowledge. This study is supported by simulations and provides clear guidelines on how to optimise the setup and acquisition strategies for near-field ptychography experiments. The results are key to drive the translation of the technique towards low brilliance sources.

High-Fidelity Computational Microscopy via Feature-Domain Phase Retrieval

Computational microscopy enhances the space-bandwidth product and corrects aberrations for high-fidelity imaging by reconstructing complex optical wavefronts. Phase retrieval, a core technique in computational microscopy, faces challenges maintaining consistency between physical and real-world imaging formation, as physical models idealize real phenomena. The discrepancy between ideal and actual imaging formation limits the application of computational microscopy especially in non-ideal situations. Here, the feature-domain consistency for achieving high-fidelity computational microscopy is introduced. Feature-domain consistency tells that certain features, such as edges, textures, or patterns of an image, remain invariant in different image transformations, degradations, or representations. Leveraging the feature-domain consistency, Feature-Domain Phase Retrieval (FD-PR) is proposed, a framework applicable to various computational microscopy. Instead of working directly with images' pixel values, FD-PR uses image features to guide the reconstruction of optical wavefronts and takes advantage of invariance components of images against mismatches of physical models. Experimental studies, across diverse phase retrieval microscopic tasks, including coded/Fourier ptychography, inline holography, and aberration correction, demonstrate that FD-PR improves resolution by a factor of 1.5 and reduces noise levels by a factor of 2. The proposed framework can immediately benefit a wide range of computational microscopies, such as X-ray ptychography, diffraction tomography, and wavefront shaping.

Computational microscopy with coherent diffractive imaging and ptychography

Microscopy and crystallography are two essential experimental methodologies for advancing modern science. They complement one another, with microscopy typically relying on lenses to image the local structures of samples, and crystallography using diffraction to determine the global atomic structure of crystals. Over the past two decades, computational microscopy, encompassing coherent diffractive imaging (CDI) and ptychography, has advanced rapidly, unifying microscopy and crystallography to overcome their limitations. Here, I review the innovative developments in CDI and ptychography, which achieve exceptional imaging capabilities across nine orders of magnitude in length scales, from resolving atomic structures in materials at sub-ångstrom resolution to quantitative phase imaging of centimetre-sized tissues, using the same principle and similar computational algorithms. These methods have been applied to determine the 3D atomic structures of crystal defects and amorphous materials, visualize oxygen vacancies in high-temperature superconductors and capture ultrafast dynamics. They have also been used for nanoscale imaging of magnetic, quantum and energy materials, nanomaterials, integrated circuits and biological specimens. By harnessing fourth-generation synchrotron radiation, X-ray-free electron lasers, high-harmonic generation, electron microscopes, optical microscopes, cutting-edge detectors and deep learning, CDI and ptychography are poised to make even greater contributions to multidisciplinary sciences in the years to come.

Three-Dimensional Nanoscale Imaging of SiO2 Nanofiller in Styrene-Butadiene Rubber with High-Resolution and High-Sensitivity Ptychographic X-ray Computed Tomography

SiO2 aggregates in styrene-butadiene rubber (SBR) were observed using ptychographic X-ray computed tomography (PXCT). The rubber composites were illuminated with X-rays focused by total reflection focusing mirrors, and the ptychographic diffraction patterns were collected using a CITIUS detector in the range of -75° to +75° angle of incidence. The projection images of the rubber composites were reconstructed with a two-dimensional resolution of 76 nm, and no significant structural changes were observed during the PXCT measurements. A three-dimensional image of the rubber composite was reconstructed with an isotropic resolution of 98 nm. Segmentation of SiO2 from the SBR, based on a histogram analysis of the phase shift, revealed a fragmented network structure of interconnected SiO2 aggregates.

Computational microscopy beyond perfect lenses

We demonstrate that in situ coherent diffractive imaging (CDI), which leverages the coherent interference between strong and weak beams to illuminate static and dynamic structures, can serve as a highly dose-efficient imaging method. At low doses, in situ CDI can achieve higher resolution than perfect lenses with the point spread function as a delta function. Both our numerical simulations and experimental results demonstrate that combining in situ CDI with ptychography can reduce the required dose by up to two orders of magnitude compared with ptychography alone. We anticipate that computational microscopy based on in situ CDI can be applied across various imaging modalities using photons and electrons for low-dose imaging of radiation-sensitive materials and biological samples.

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.

Wavelength-multiplexed multi-mode EUV reflection ptychography based on automatic differentiation

Ptychographic extreme ultraviolet (EUV) diffractive imaging has emerged as a promising candidate for the next generationmetrology solutions in the semiconductor industry, as it can image wafer samples in reflection geometry at the nanoscale. This technique has surged attention recently, owing to the significant progress in high-harmonic generation (HHG) EUV sources and advancements in both hardware and software for computation. In this study, a novel algorithm is introduced and tested, which enables wavelength-multiplexed reconstruction that enhances the measurement throughput and introduces data diversity, allowing the accurate characterisation of sample structures. To tackle the inherent instabilities of the HHG source, a modal approach was adopted, which represents the cross-density function of the illumination by a series of mutually incoherent and independent spatial modes. The proposed algorithm was implemented on a mainstream machine learning platform, which leverages automatic differentiation to manage the drastic growth in model complexity and expedites the computation using GPU acceleration. By optimising over 200 million parameters, we demonstrate the algorithm's capacity to accommodate experimental uncertainties and achieve a resolution approaching the diffraction limit in reflection geometry. The reconstruction of wafer samples with 20-nm high patterned gold structures on a silicon substrate highlights our ability to handle complex physical interrelations involving a multitude of parameters. These results establish ptychography as an efficient and accurate metrology tool.

Meta Shack-Hartmann wavefront sensor with large sampling density and large angular field of view: phase imaging of complex objects

Shack-Hartmann wavefront sensors measure the local slopes of an incoming wavefront based on the displacement of focal spots created by a lenslet array, serving as key components for adaptive optics for astronomical and biomedical imaging. Traditionally, the challenges in increasing the density and the curvature of the lenslet have limited the use of such wavefront sensors in characterizing slowly varying wavefront structures. Here, we develop a metasurface-enhanced Shack-Hartmann wavefront sensor (meta SHWFS) to break this limit, considering the interplay between the lenslet parameters and the performance of SHWFS. We experimentally validate the meta SHWFS with a sampling density of 5963 per mm2 and a maximum acceptance angle of 8° which outperforms the traditional SFWFS by an order of magnitude. Furthermore, to the best of our knowledge, we demonstrate the first use of a wavefront sensing scheme in single-shot phase imaging of highly complex patterns, including biological tissue patterns. The proposed approach opens up new opportunities in incorporating exceptional light manipulation capabilities of the metasurface platform in complex wavefront characterization.

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 β, 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.

Nanoscale imaging of Fe-rich inclusions in single-crystal zircon using X-ray ptycho-tomography

We apply X-ray ptycho-tomography to perform high-resolution, non-destructive, three-dimensional (3D) imaging of Fe-rich inclusions in paleomagnetically relevant materials (zircon single crystals from the Bishop Tuff ignimbrite). Correlative imaging using quantum diamond magnetic microscopy combined with X-ray fluorescence mapping was used to locate regions containing potential ferromagnetic remanence carriers. Ptycho-tomographic reconstructions with voxel sizes 85 nm and 21 nm were achievable across a field-of-view > 80 µm; voxel sizes as small as 5 nm were achievable over a limited field-of-view using local ptycho-tomography. Fe-rich inclusions 300 nm in size were clearly resolved. We estimate that particles as small as 100 nm-approaching single-domain threshold for magnetite-could be resolvable using this "dual-mode" methodology. Fe-rich inclusions (likely magnetite) are closely associated with apatite inclusions that have no visible connection to the exterior surface of the zircon (e.g., via intersecting cracks). There is no evidence of radiation damage, alteration, recrystallisation or deformation in the host zircon or apatite that could provide alternative pathways for Fe infiltration, indicating that magnetite and apatite grew separately as primary phases in the magma, that magnetite adhered to the surfaces of the apatite, and that the magnetite-coated apatite was then encapsulated as primary inclusions within the growing zircon. Rarer examples of Fe-rich inclusions entirely encapsulated by zircon are also observed. These observations support the presence of primary inclusions in relatively young and pristine zircon crystals. Combining magnetic and tomography results we deduce the presence of magnetic carriers that are in the optimal size range for carrying strong and stable paleomagnetic signals but that remain below the detection limits of even the highest-resolution X-ray tomography reconstructions. We recommend the use of focused ion beam nanotomography and/or correlative transmission electron microscopy to directly confirm the presence of primary magnetite in the sub 300 nm range as a necessary step in targeted paleomagnetic workflows.

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.

In Situ and Operando X-ray Scattering Methods in Electrochemistry and Electrocatalysis

Electrochemical and electrocatalytic processes are of key importance for the transition to a sustainable energy supply as well as for a wide variety of other technologically relevant fields. Further development of these processes requires in-depth understanding of the atomic, nano, and micro scale structure of the materials and interfaces in electrochemical devices under reaction conditions. We here provide a comprehensive review of in situ and operando studies by X-ray scattering methods, which are powerful and highly versatile tools to provide such understanding. We discuss the application of X-ray scattering to a wide variety of electrochemical systems, ranging from metal and oxide single crystals to nanoparticles and even full devices. We show how structural data on bulk phases, electrode-electrolyte interfaces, and nanoscale morphology can be obtained and describe recent developments that provide highly local information and insight into the composition and electronic structure. These X-ray scattering studies yield insights into the structure in the double layer potential range as well as into the structural evolution during electrocatalytic processes and phase formation reactions, such as nucleation and growth during electrodeposition and dissolution, the formation of passive films, corrosion processes, and the electrochemical intercalation into battery materials.

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.

Rotational position error correction in ptychography

Accurate determination of scan positions is essential for achieving high-quality reconstructions in ptychographic imaging. This study presents and demonstrates a method for determining the rotation angle of the scan pattern relative to the detector pixel array using diffraction data. The method is based on the Fourier-Mellin transform and cross-correlation calculation. It can correct rotation errors up to 60 deg. High-quality reconstructions were obtained for visible light and electron microscopy datasets, and intricate structures of samples can be revealed. We believe that this refinement method for rotary position errors can be valuable for improving the performance of ptychographic four-dimensional scanning transmission electron microscopy.

Direct observation of single-atom defects in monolayer two-dimensional materials by using electron ptychography at 200 kV acceleration voltage

Electron ptychography has emerged as a popular technology for high-resolution imaging by combining the high coherence of electron sources with the ultra-fast scanning electron coil. However, the limitations of conventional pixelated detectors, including poor dynamic range and slow data readout speeds, have posed restrictions in the past on conducting electron ptychography experiments. We used the Gatan STELA pixelated detector to capture sequential diffraction data of monolayer two-dimensional (2D) materials for ptychographic reconstruction. By using the pixelated detector and electron ptychography, we demonstrate the observation of the radiation damage at atomic resolution in Transition Metal Dichalcogenides (TMDs).

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.

Solving complex nanostructures with ptychographic atomic electron tomography

Transmission electron microscopy (TEM) is essential for determining atomic scale structures in structural biology and materials science. In structural biology, three-dimensional structures of proteins are routinely determined from thousands of identical particles using phase-contrast TEM. In materials science, three-dimensional atomic structures of complex nanomaterials have been determined using atomic electron tomography (AET). However, neither of these methods can determine the three-dimensional atomic structure of heterogeneous nanomaterials containing light elements. Here, we perform ptychographic electron tomography from 34.5 million diffraction patterns to reconstruct an atomic resolution tilt series of a double wall-carbon nanotube (DW-CNT) encapsulating a complex ZrTe sandwich structure. Class averaging the resulting tilt series images and subpixel localization of the atomic peaks reveals a Zr11Te50 structure containing a previously unobserved ZrTe2 phase in the core. The experimental realization of atomic resolution ptychographic electron tomography will allow for the structural determination of a wide range of beam-sensitive nanomaterials containing light elements.

High-resolution and high-sensitivity X-ray ptychographic coherent diffraction imaging using the CITIUS detector

Ptychographic coherent diffraction imaging (PCDI) is a synchrotron X-ray microscopy technique that provides high spatial resolution and a wide field of view. To improve the performance of PCDI, the performance of the synchrotron radiation source and imaging detector should be improved. In this study, ptychographic diffraction pattern measurements using the CITIUS high-speed X-ray image detector and the corresponding image reconstruction are reported. X-rays with an energy of 6.5 keV were focused by total reflection focusing mirrors, and a flux of ∼2.6 × 1010 photons s-1 was obtained at the sample plane. Diffraction intensity data were collected at up to ∼250 Mcounts s-1 pixel-1 without saturation of the detector. Measurements of tantalum test charts and silica particles and the reconstruction of phase images were performed. A resolution of ∼10 nm and a phase sensitivity of ∼0.01 rad were obtained. The CITIUS detector can be applied to the PCDI observation of various samples using low-emittance synchrotron radiation sources and to the stability evaluation of light sources.

Broadband ptychography using curved wavefront illumination

We examine the interplay between spectral bandwidth and illumination curvature in ptychography. By tailoring the divergence of the illumination, broader spectral bandwidths can be tolerated without requiring algorithmic modifications to the forward model. In particular, a strong wavefront curvature transitions a far-field diffraction geometry to an effectively near-field one, which is less affected by temporal coherence effects. The relaxed temporal coherence requirements allow for leveraging wider spectral bandwidths and larger illumination spots. Our findings open up new avenues towards utilizing pink and broadband beams for increased flux and throughput at both synchrotron facilities and lab-scale beamlines.

X-ray ptychographic and fluorescence microscopy using virtual single-pixel imaging based deconvolution with accurate probe images

Simultaneous measurement of X-ray ptychography and fluorescence microscopy allows high-resolution and high-sensitivity observations of the microstructure and trace-element distribution of a sample. In this paper, we propose a method for improving scanning fluorescence X-ray microscopy (SFXM) images, in which the SFXM image is deconvolved via virtual single-pixel imaging using different probe images for each scanning point obtained by X-ray ptychographic reconstruction. Numerical simulations confirmed that this method can increase the spatial resolution while suppressing artifacts caused by probe imprecision, e.g., probe position errors and wavefront changes. The method also worked well in synchrotron radiation experiments to increase the spatial resolution and was applied to the observation of S element maps of ZnS particles.

Characterisation of engineered defects in extreme ultraviolet mirror substrates using lab-scale extreme ultraviolet reflection ptychography

Ptychography is a lensless imaging technique that is aberration-free and capable of imaging both the amplitude and the phase of radiation reflected or transmitted from an object using iterative algorithms. Working with extreme ultraviolet (EUV) light, ptychography can provide better resolution than conventional optical microscopy and deeper penetration than scanning electron microscope. As a compact lab-scale EUV light sources, high harmonic generation meets the high coherence requirement of ptychography and gives more flexibilities in both budget and experimental time compared to synchrotrons. The ability to measure phase makes reflection-mode ptychography a good choice for characterising both the surface topography and the internal structural changes in EUV multilayer mirrors. This paper describes the use of reflection-mode ptychography with a lab-scale high harmonic generation based EUV light source to perform quantitative measurement of the amplitude and phase reflection from EUV multilayer mirrors with engineered substrate defects. Using EUV light at 29.6nm from a tabletop high harmonic generation light source, a lateral resolution down to ∼88nm and a phase resolution of 0.08rad (equivalent to topographic height variation of 0.27nm) are achieved. The effect of surface distortion and roughness on EUV reflectivity is compared to topographic properties of the mirror defects measured using both atomic force microscopy and scanning transmission electron microscopy. Modelling of reflection properties from multilayer mirrors is used to predict the potential of a combination of on-resonance, actinic ptychographic imaging at 13.5nm and atomic force microscopy for characterising the changes in multilayered structures.

In Situ and Emerging Transmission Electron Microscopy for Catalysis Research

Catalysts are the primary facilitator in many dynamic processes. Therefore, a thorough understanding of these processes has vast implications for a myriad of energy systems. The scanning/transmission electron microscope (S/TEM) is a powerful tool not only for atomic-scale characterization but also in situ catalytic experimentation. Techniques such as liquid and gas phase electron microscopy allow the observation of catalysts in an environment conducive to catalytic reactions. Correlated algorithms can greatly improve microscopy data processing and expand multidimensional data handling. Furthermore, new techniques including 4D-STEM, atomic electron tomography, cryogenic electron microscopy, and monochromated electron energy loss spectroscopy (EELS) push the boundaries of our comprehension of catalyst behavior. In this review, we discuss the existing and emergent techniques for observing catalysts using S/TEM. Challenges and opportunities highlighted aim to inspire and accelerate the use of electron microscopy to further investigate the complex interplay of catalytic systems.

Cryogenic electron ptychographic single particle analysis with wide bandwidth information transfer

Advances in cryogenic transmission electron microscopy have revolutionised the determination of many macromolecular structures at atomic or near-atomic resolution. This method is based on conventional defocused phase contrast imaging. However, it has limitations of weaker contrast for small biological molecules embedded in vitreous ice, in comparison with cryo-ptychography, which shows increased contrast. Here we report a single-particle analysis based on the use of ptychographic reconstruction data, demonstrating that three dimensional reconstructions with a wide information transfer bandwidth can be recovered by Fourier domain synthesis. Our work suggests future applications in otherwise challenging single particle analyses, including small macromolecules and heterogeneous or flexible particles. In addition structure determination in situ within cells without the requirement for protein purification and expression may be possible.

PtyLab.m/py/jl: a cross-platform, open-source inverse modeling toolbox for conventional and Fourier ptychography

Conventional (CP) and Fourier (FP) ptychography have emerged as versatile quantitative phase imaging techniques. While the main application cases for each technique are different, namely lens-less short wavelength imaging for CP and lens-based visible light imaging for FP, both methods share a common algorithmic ground. CP and FP have in part independently evolved to include experimentally robust forward models and inversion techniques. This separation has resulted in a plethora of algorithmic extensions, some of which have not crossed the boundary from one modality to the other. Here, we present an open source, cross-platform software, called PtyLab, enabling both CP and FP data analysis in a unified framework. With this framework, we aim to facilitate and accelerate cross-pollination between the two techniques. Moreover, the availability in Matlab, Python, and Julia will set a low barrier to enter each field.

Accurate real space iterative reconstruction (RESIRE) algorithm for tomography

Tomography has made a revolutionary impact on the physical, biological and medical sciences. The mathematical foundation of tomography is to reconstruct a three-dimensional (3D) object from a set of two-dimensional (2D) projections. As the number of projections that can be measured from a sample is usually limited by the tolerable radiation dose and/or the geometric constraint on the tilt range, a main challenge in tomography is to achieve the best possible 3D reconstruction from a limited number of projections with noise. Over the years, a number of tomographic reconstruction methods have been developed including direct inversion, real-space, and Fourier-based iterative algorithms. Here, we report the development of a real-space iterative reconstruction (RESIRE) algorithm for accurate tomographic reconstruction. RESIRE iterates between the update of a reconstructed 3D object and the measured projections using a forward and back projection step. The forward projection step is implemented by the Fourier slice theorem or the Radon transform, and the back projection step by a linear transformation. Our numerical and experimental results demonstrate that RESIRE performs more accurate 3D reconstructions than other existing tomographic algorithms, when there are a limited number of projections with noise. Furthermore, RESIRE can be used to reconstruct the 3D structure of extended objects as demonstrated by the determination of the 3D atomic structure of an amorphous Ta thin film. We expect that RESIRE can be widely employed in the tomography applications in different fields. Finally, to make the method accessible to the general user community, the MATLAB source code of RESIRE and all the simulated and experimental data are available at  https://zenodo.org/record/7273314 .

Ptychographic measurements of varying size and shape along zeolite channels

Sub-angstrom resolution imaging of porous materials like zeolites is important to reveal their structure-property relationships involved in ion exchange, molecule adsorption and separation, and catalysis. Using multislice electron ptychography, we successfully measured the atomic structure of zeolite at sub-angstrom lateral resolution for 100-nanometer-thick samples. Both lateral and depth deformations of the straight channels are mapped, showing the three-dimensional structural inhomogeneity and flexibility. Since most zeolites in industrial applications are usually tens to hundreds of nanometers thick, the sub-angstrom resolution imaging and accurate measurements of depth-dependent local structures with electron ptychography at low-dose condition will find wide applications in porous materials close to their industrially relevant conditions.

Three-dimensional topological magnetic monopoles and their interactions in a ferromagnetic meta-lattice

Topological magnetic monopoles (TMMs), also known as hedgehogs or Bloch points, are three-dimensional (3D) non-local spin textures that are robust to thermal and quantum fluctuations due to the topology protection^1-4. Although TMMs have been observed in skyrmion lattices^1,5, spinor Bose-Einstein condensates^6,7, chiral magnets⁸, vortex rings^2,9 and vortex cores¹⁰, it has been difficult to directly measure the 3D magnetization vector field of TMMs and probe their interactions at the nanoscale. Here we report the creation of 138 stable TMMs at the specific sites of a ferromagnetic meta-lattice at room temperature. We further develop soft X-ray vector ptycho-tomography to determine the magnetization vector and emergent magnetic field of the TMMs with a 3D spatial resolution of 10 nm. This spatial resolution is comparable to the magnetic exchange length of transition metals¹¹, enabling us to probe monopole-monopole interactions. We find that the TMM and anti-TMM pairs are separated by 18.3 ± 1.6 nm, while the TMM and TMM, and anti-TMM and anti-TMM pairs are stabilized at comparatively longer distances of 36.1 ± 2.4 nm and 43.1 ± 2.0 nm, respectively. We also observe virtual TMMs created by magnetic voids in the meta-lattice. This work demonstrates that ferromagnetic meta-lattices could be used as a platform to create and investigate the interactions and dynamics of TMMs. Furthermore, we expect that soft X-ray vector ptycho-tomography can be broadly applied to quantitatively image 3D vector fields in magnetic and anisotropic materials at the nanoscale.

Optical ptychography for biomedical imaging: recent progress and future directions [Invited]

Ptychography is an enabling microscopy technique for both fundamental and applied sciences. In the past decade, it has become an indispensable imaging tool in most X-ray synchrotrons and national laboratories worldwide. However, ptychography's limited resolution and throughput in the visible light regime have prevented its wide adoption in biomedical research. Recent developments in this technique have resolved these issues and offer turnkey solutions for high-throughput optical imaging with minimum hardware modifications. The demonstrated imaging throughput is now greater than that of a high-end whole slide scanner. In this review, we discuss the basic principle of ptychography and summarize the main milestones of its development. Different ptychographic implementations are categorized into four groups based on their lensless/lens-based configurations and coded-illumination/coded-detection operations. We also highlight the related biomedical applications, including digital pathology, drug screening, urinalysis, blood analysis, cytometric analysis, rare cell screening, cell culture monitoring, cell and tissue imaging in 2D and 3D, polarimetric analysis, among others. Ptychography for high-throughput optical imaging, currently in its early stages, will continue to improve in performance and expand in its applications. We conclude this review article by pointing out several directions for its future development.

Multimodal imaging of cubic Cu2O@Au nanocage formation via galvanic replacement using X-ray ptychography and nano diffraction

Being able to observe the formation of multi-material nanostructures in situ, simultaneously from a morphological and crystallographic perspective, is a challenging task. Yet, this is essential for the fabrication of nanomaterials with well-controlled composition exposing the most active crystallographic surfaces, as required for highly active catalysts in energy applications. To demonstrate how X-ray ptychography can be combined with scanning nanoprobe diffraction to realize multimodal imaging, we study growing Cu₂O nanocubes and their transformation into Au nanocages. During the growth of nanocubes at a temperature of 138 °C, we measure the crystal structure of an individual nanoparticle and determine the presence of (100) crystallographic facets at its surface. We subsequently visualize the transformation of Cu₂O into Au nanocages by galvanic replacement. The nanocubes interior homogeneously dissolves while smaller Au particles grow on their surface and later coalesce to form porous nanocages. We finally determine the amount of radiation damage making use of the quantitative phase images. We find that both the total surface dose as well as the dose rate imparted by the X-ray beam trigger additional deposition of Au onto the nanocages. Our multimodal approach can benefit in-solution imaging of multi-material nanostructures in many related fields.

Deep-Learning Electron Diffractive Imaging

We report the development of deep-learning coherent electron diffractive imaging at subangstrom resolution using convolutional neural networks (CNNs) trained with only simulated data. We experimentally demonstrate this method by applying the trained CNNs to recover the phase images from electron diffraction patterns of twisted hexagonal boron nitride, monolayer graphene, and a gold nanoparticle with comparable quality to those reconstructed by a conventional ptychographic algorithm. Fourier ring correlation between the CNN and ptychographic images indicates the achievement of a resolution in the range of 0.70 and 0.55 Å. We further develop CNNs to recover the probe function from the experimental data. The ability to replace iterative algorithms with CNNs and perform real-time atomic imaging from coherent diffraction patterns is expected to find applications in the physical and biological sciences.

Abrasive slurry jet machining system using polyurethane@silica core-shell particles for internal surfaces of axisymmetric x-ray mirrors

Abrasive machining has been used for inner surface processing of various hollow components. In this study, we applied an in-air fluid jet as a precision machining method for the inner surface of an axisymmetric x-ray mirror whose inner diameter was less than 10 mm. We employed an abrasive with a polyurethane@silica core-shell structure, which has a low density of about 1.2 g/cm³ and a relatively large particle size of about 15 µm. By using this abrasive, a practical removal rate and a smooth machined surface were simultaneously obtained. We performed figure corrections for an axisymmetric mirror and improved the circumferential figure accuracy to a sub-10 nm root mean square level. To evaluate the machining performance in the longitudinal direction of the ellipsoidal surface, we also performed periodic figure fabrication on the inner surface of a 114 mm-long nickel ellipsoidal mirror. X-ray ptychography, an optical phase retrieval method, was also employed as a three-dimensional figure measurement technique of the mirror. The wavefield of the x-ray beam focused by the processed ellipsoidal mirror was observed with the ptychographic system at SPring-8, a synchrotron radiation facility. The retrieval calculations for the wavefront error confirmed that a sinusoidal waveform with a period of 12 mm was fabricated on the mirror surface. These experimental results suggest that a nanoscale figure fabrication cycle for the inner surface consisting of jet machining and wavefront measurement has been successfully constructed. We expect this technique to be utilized in the fabrication of error-free optical mirrors and various parts having hollow shapes.

Differential phase contrast for quantitative imaging and spectro-microscopy at a nanoprobe beamline

The interaction of a focused X-ray beam with a sample in a scanning probe experiment can provide a variety of information about the interaction volume. In many scanning probe experiments X-ray fluorescence (XRF) is supplemented with measurements of the transmitted or scattered intensity using a pixelated detector. The automated extraction of different signals from an area pixelated detector is described, in particular the methodology for extracting differential phase contrast (DPC) is demonstrated and different processing methods are compared across a range of samples. The phase shift of the transmitted X-ray beam by the sample, extracted from DPC, is also compared with ptychography measurements to provide a qualitative and quantitative comparison. While ptychography produces a superior image, DPC can offer a simple, flexible method for phase contrast imaging which can provide fast results and feedback during an experiment; furthermore, for many science problems, such as registration of XRF in a lighter matrix, DPC can provide sufficient information to meet the experimental aims. As the DPC technique is a quantitative measurement, it can be expanded to spectroscopic studies and a demonstration of DPC for spectro-microscopy measurements is presented. Where ptychography can separate the absorption and phase shifts by the sample, quantitative interpretation of a DPC image or spectro-microscopy signal can only be performed directly when absorption is negligible or where the absorption contribution is known and the contributions can be fitted.

4D-STEM Ptychography for Electron-Beam-Sensitive Materials

Recent advances in high-speed pixelated electron detectors have substantially facilitated the implementation of four-dimensional scanning transmission electron microscopy (4D-STEM). A critical application of 4D-STEM is electron ptychography, which reveals the atomic structure of a specimen by reconstructing its transmission function from redundant convergent-beam electron diffraction patterns. Although 4D-STEM ptychography offers many advantages over conventional imaging modes, this emerging technique has not been fully applied to materials highly sensitive to electron beams. In this Outlook, we introduce the fundamentals of 4D-STEM ptychography, focusing on data collection and processing methods, and present the current applications of 4D-STEM ptychography in various materials. Next, we discuss the potential advantages of imaging electron-beam-sensitive materials using 4D-STEM ptychography and explore its feasibility by performing simulations and experiments on a zeolite material. The preliminary results demonstrate that, at the low electron dose required to preserve the zeolite structure, 4D-STEM ptychography can reliably provide higher resolution and greater tolerance to the specimen thickness and probe defocus as compared to existing imaging techniques. In the final section, we discuss the challenges and possible strategies to further reduce the electron dose for 4D-STEM ptychography. If successful, it will be a game-changer for imaging extremely sensitive materials, such as metal-organic frameworks, hybrid halide perovskites, and supramolecular crystals.

Single-shot measurement of the near-field and focal spot profiles of a 351 nm laser beam for SGII-upgraded facility with multiple-focal-plane constraint coherent modulation imaging

Inertial confinement fusion (ICF) places an urgent demand for precise measurement of 351 nm (3ω) laser beam parameters when performing physical experiments on high-power laser facilities. The near-field and focal spot distributions are the utmost important parameters to characterize the quality of the laser beam. Coherent modulation imaging (CMI) is a promising technique for online laser beam measurement, however, it fails to reconstruct the near-field and focal spot profiles when it is used to measure the beam quality of a 351 nm laser beam for SGII-upgrade facility. To solve this problem, a novel CMI reconstruction algorithm is proposed in this work, and the performance of the algorithm in 3ω laser beam measurement can be obviously improved. By adopting multiple-virtual-focal-plane constraint in the proposed algorithm, the near-field and focal spot profiles of the 3ω laser beam can be successfully reconstructed. Experiments have been conducted on SGII-upgrade facility to verify the feasibility of the proposed method.

A modern look at a medieval bilayer metal leaf: nanotomography of Zwischgold

Many European sculptures and altarpieces from the Middle Ages were decorated with Zwischgold, a bilayer metal leaf with an ultra-thin gold face backed by silver. Zwischgold corrodes quickly when exposed to air, causing the surface of the artefact to darken and lose gloss. The conservation of such Zwischgold applied artefacts has been an obstinate problem. We have acquired quantitative, 3D nanoscale images of Zwischgold samples from 15^th century artefacts and modern materials using ptychographic X-ray computed tomography (PXCT), a recently developed coherent diffractive imaging technique, to investigate the leaf structure and chemical state of Zwischgold. The measurements clearly demonstrate decreasing density (increasing porosity) of the leaf materials and their corrosion products, as well as delamination of the leaves from their substrate. Each of these effects speak to typically observed issues in the conservation of such Zwischgold applied artefacts. Further, a rare variant of Zwischgold that contains extremely thin multiple gold layers and an overlapping phenomenon of Zwischgold with other metal leaves are observed through PXCT. As supportive data, scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM) coupled with energy dispersive X-ray analysis (EDX) were performed on the medieval samples.

Imaging Cu2O nanocube hollowing in solution by quantitative in situ X-ray ptychography

Understanding morphological changes of nanoparticles in solution is essential to tailor the functionality of devices used in energy generation and storage. However, we lack experimental methods that can visualize these processes in solution, or in electrolyte, and provide three-dimensional information. Here, we show how X-ray ptychography enables in situ nano-imaging of the formation and hollowing of nanoparticles in solution at 155 °C. We simultaneously image the growth of about 100 nanocubes with a spatial resolution of 66 nm. The quantitative phase images give access to the third dimension, allowing to additionally study particle thickness. We reveal that the substrate hinders their out-of-plane growth, thus the nanocubes are in fact nanocuboids. Moreover, we observe that the reduction of Cu2O to Cu triggers the hollowing of the nanocuboids. We critically assess the interaction of X-rays with the liquid sample. Our method enables detailed in-solution imaging for a wide range of reaction conditions.

Temporal and spectral multiplexing for EUV multibeam ptychography with a high harmonic light source

We demonstrate temporally multiplexed multibeam ptychography implemented for the first time in the EUV, by using a high harmonic based light source. This allows for simultaneous imaging of different sample areas, or of the same area at different times or incidence angles. Furthermore, we show that this technique is compatible with wavelength multiplexing for multibeam spectroscopic imaging, taking full advantage of the temporal and spectral characteristics of high harmonic light sources. This technique enables increased data throughput using a simple experimental implementation and with high photon efficiency.

Three-dimensional electron ptychography of organic-inorganic hybrid nanostructures

Three dimensional scaffolded DNA origami with inorganic nanoparticles has been used to create tailored multidimensional nanostructures. However, the image contrast of DNA is poorer than those of the heavy nanoparticles in conventional transmission electron microscopy at high defocus so that the biological and non-biological components in 3D scaffolds cannot be simultaneously resolved using tomography of samples in a native state. We demonstrate the use of electron ptychography to recover high contrast phase information from all components in a DNA origami scaffold without staining. We further quantitatively evaluate the enhancement of contrast in comparison with conventional transmission electron microscopy. In addition, We show that for ptychography post-reconstruction focusing simplifies the workflow and reduces electron dose and beam damage.

The authors demonstrate electron ptychographic computed tomography by simultaneously recording high contrast data from both the organic- and inorganic components in a 3D DNA-origami framework hybrid nanostructure.

Fast scanning in x-ray microscopy: the effects of offset in the central stop position

Scanning of lightweight circular diffractive optics, separate from central stops and apertures, is emerging as an approach to exploit advances in synchrotron x-ray sources. We consider the effects in a scanning microscope of offsets between the optic and its central stop and find that scan ranges of up to about half the diameter of the optic are possible with only about a 10% increase in the focal spot width. For large scanning ranges, we present criteria for the working distance between the last aperture and the specimen to be imaged.

Method for restoration of X-ray absorption fine structure in sparse spectroscopic ptychography

The spectroscopic ptychography method, a technique combining X-ray ptychography imaging and X-ray absorption spectroscopy, is one of the most promising and powerful tools for studying the chemical states and morphological structures of bulk materials at high resolutions. However, this technique still requires long measurement periods because of insufficient coherent X-ray intensity. Although the improvements in hardware represent a critical solution, breakthroughs in software for experiments and analyses are also required. This paper proposes a novel method for restoring the spectrum structures from spectroscopic ptychography measurements with reduced energy points, by utilizing the Kramers–Kronig relationship. First, a numerical simulation is performed of the spectrum restoration for the extended X-ray absorption fine structure (EXAFS) oscillation from the thinned theoretical absorption and phase spectra. Then, this algorithm is extended by binning the noise removal to handle actual experimental spectral data. Spectrum restoration for the experimental EXAFS data obtained from spectroscopic ptychography measurements is also successfully demonstrated. The proposed restoration will help shorten the time required for spectroscopic ptychography single measurements and increase the throughput of the entire experiment under limited time resources.

Morphological variations to a ptychographic algorithm

Ptychography is a technique widely used in microscopy for achieving high-resolution imaging. This method relies on computational processing of images gathered from diffraction patterns produced by several partial illuminations of a sample. We numerically studied the effect of using different shapes for illuminating the aforementioned sample: convex shapes, such as circles and regular polygons, and unconnected shapes that resemble a QR code. Our results suggest that the use of unconnected shapes seems to outperform convex shapes in terms of convergence and, in some cases, accuracy.

Imaging mesoscopic antiferromagnetic spin textures in the dilute limit from single-geometry resonant coherent x-ray diffraction

The detection and manipulation of antiferromagnetic domains and topological antiferromagnetic textures are of central interest to solid-state physics. A fundamental step is identifying tools to probe the mesoscopic texture of an antiferromagnetic order parameter. In this work, we demonstrate that Bragg coherent diffractive imaging can be extended to study the mesoscopic texture of an antiferromagnetic order parameter using resonant magnetic x-ray scattering. We study the onset of the antiferromagnet transition in PrNiO₃, focusing on a temperature regime in which the antiferromagnetic domains are dilute in the beam spot and the coherent diffraction pattern modulating the antiferromagnetic peak is greatly simplified. We demonstrate that it is possible to extract the arrangements and sizes of these domains from single diffraction patterns and show that the approach could be extended to a time-structured light source to study the motion of dilute domains or the motion of topological defects in an antiferromagnetic spin texture.

High-resolution ptychographic imaging enabled by high-speed multi-pass scanning

As a coherent diffraction imaging technique, ptychography provides high-spatial resolution beyond Rayleigh's criterion of the focusing optics, but it is also sensitively affected by the decoherence coming from the spatial and temporal variations in the experiment. Here we show that high-speed ptychographic data acquisition with short exposure can effectively reduce the impact from experimental variations. To reach a cumulative dose required for a given resolution, we further demonstrate that a continuous multi-pass scan via high-speed ptychography can achieve high-resolution imaging. This low-dose scan strategy is shown to be more dose-efficient, and has potential for radiation-sensitive sample studies and time-resolved imaging.

Sample Preparation and Warping Accuracy for Correlative Multimodal Imaging in the Mouse Olfactory Bulb Using 2-Photon, Synchrotron X-Ray and Volume Electron Microscopy

Integrating physiology with structural insights of the same neuronal circuit provides a unique approach to understanding how the mammalian brain computes information. However, combining the techniques that provide both streams of data represents an experimental challenge. When studying glomerular column circuits in the mouse olfactory bulb, this approach involves e.g., recording the neuronal activity with in vivo 2-photon (2P) calcium imaging, retrieving the circuit structure with synchrotron X-ray computed tomography with propagation-based phase contrast (SXRT) and/or serial block-face scanning electron microscopy (SBEM) and correlating these datasets. Sample preparation and dataset correlation are two key bottlenecks in this correlative workflow. Here, we first quantify the occurrence of different artefacts when staining tissue slices with heavy metals to generate X-ray or electron contrast. We report improvements in the staining procedure, ultimately achieving perfect staining in ∼67% of the 0.6 mm thick olfactory bulb slices that were previously imaged in vivo with 2P. Secondly, we characterise the accuracy of the spatial correlation between functional and structural datasets. We demonstrate that direct, single-cell precise correlation between in vivo 2P and SXRT tissue volumes is possible and as reliable as correlating between 2P and SBEM. Altogether, these results pave the way for experiments that require retrieving physiology, circuit structure and synaptic signatures in targeted regions. These correlative function-structure studies will bring a more complete understanding of mammalian olfactory processing across spatial scales and time.

Coherent Diffractive Imaging with Diffractive Optics

We present a novel approach to x-ray microscopy based on a multilayer zone plate which is positioned behind a sample similar to an objective lens. However, unlike transmission x-ray microscopy, we do not content ourselves with a sharp intensity image; instead, we incorporate the multilayer zone plate transfer function directly in an iterative phase retrieval scheme to exploit the large diffraction angles of the small layers. The presence of multiple diffraction orders, which is conventionally a nuisance, now comes as an advantage for the reconstruction and photon efficiency. In a first experiment, we achieve sub-10-nm resolution and a quantitative phase contrast.

Functional and multiscale 3D structural investigation of brain tissue through correlative in vivo physiology, synchrotron microtomography and volume electron microscopy

Understanding the function of biological tissues requires a coordinated study of physiology and structure, exploring volumes that contain complete functional units at a detail that resolves the relevant features. Here, we introduce an approach to address this challenge: Mouse brain tissue sections containing a region where function was recorded using in vivo 2-photon calcium imaging were stained, dehydrated, resin-embedded and imaged with synchrotron X-ray computed tomography with propagation-based phase contrast (SXRT). SXRT provided context at subcellular detail, and could be followed by targeted acquisition of multiple volumes using serial block-face electron microscopy (SBEM). In the olfactory bulb, combining SXRT and SBEM enabled disambiguation of in vivo-assigned regions of interest. In the hippocampus, we found that superficial pyramidal neurons in CA1a displayed a larger density of spine apparati than deeper ones. Altogether, this approach can enable a functional and structural investigation of subcellular features in the context of cells and tissues.

Two-dimensional wavefront characterization of adaptable corrective optics and Kirkpatrick-Baez mirror system using ptychography

Aberrations introduced during fabrication degrade the performance of X-ray optics and their ability to achieve diffraction limited focusing. Corrective optics can counteract these errors by introducing wavefront perturbations prior to the optic which cancel out the distortions. Here we demonstrate two-dimensional wavefront correction of an aberrated Kirkpatrick-Baez mirror pair using adaptable refractive structures. The resulting two-dimensional wavefront is measured using hard X-ray ptychography to recover the complex probe wavefield with high spatial resolution and model the optical performance under coherent conditions. The optical performance including the beam caustic, focal profile and wavefront error is examined before and after correction with both mirrors found to be diffraction limited after correcting. The results will be applicable to a wide variety of high numerical aperture X-ray optics aiming to achieve diffraction limited focussing using low emittance sources.