Optimization of overlap uniformness for ptychography

A high-performance reconstruction method for partially coherent ptychography

Ptychography is now integrated as a tool in mainstream microscopy allowing quantitative and high-resolution imaging capabilities over a wide field of view. However, its ultimate performance is inevitably limited by the available coherent flux when implemented using electrons or laboratory X-ray sources. We present a universal reconstruction algorithm with high tolerance to low coherence for both far-field and near-field ptychography. The approach is practical for partial temporal and spatial coherence and requires no prior knowledge of the source properties. Our initial visible-light and electron data show that the method can dramatically improve the reconstruction quality and accelerate the convergence rate of the reconstruction. The approach also integrates well into existing ptychographic engines. It can also improve mixed-state and numerical monochromatisation methods, requiring a smaller number of coherent modes or lower dimensionality of Krylov subspace while providing more stable and faster convergence. We propose that this approach could have significant impact on ptychography of weakly scattering samples.

Dynamic sparse x-ray nanotomography reveals ionomer hydration mechanism in polymer electrolyte fuel-cell catalyst

Tomographic imaging of time-evolving samples is a challenging yet important task for various research fields. At the nanoscale, current approaches face limitations of measurement speed or resolution due to lengthy acquisitions. We developed a dynamic nanotomography technique based on sparse dynamic imaging and 4D tomography modeling. We demonstrated the technique, using ptychographic x-ray computed tomography as its imaging modality, on resolving the in situ hydration process of polymer electrolyte fuel cell (PEFC) catalyst. The technique provides a 40-time increase in temporal resolution compared to conventional approaches, yielding 28 nm half-period spatial and 12 min temporal resolution. The results allow a quantitative characterization of the water intake process inside PEFC catalysts with nanoscale resolution, which is crucial for understanding their electrochemical mechanisms and optimizing their performance. Our technique enables high-speed operando nanotomography studies and paves the way for wider application of dynamic tomography at the nanoscale.

Ptychographic phase retrieval via a deep-learning-assisted iterative algorithm

Ptychography is a powerful computational imaging technique with microscopic imaging capability and adaptability to various specimens. To obtain an imaging result, it requires a phase-retrieval algorithm whose performance directly determines the imaging quality. Recently, deep neural network (DNN)-based phase retrieval has been proposed to improve the imaging quality from the ordinary model-based iterative algorithms. However, the DNN-based methods have some limitations because of the sensitivity to changes in experimental conditions and the difficulty of collecting enough measured specimen images for training the DNN. To overcome these limitations, a ptychographic phase-retrieval algorithm that combines model-based and DNN-based approaches is proposed. This method exploits a DNN-based denoiser to assist an iterative algorithm like ePIE in finding better reconstruction images. This combination of DNN and iterative algorithms allows the measurement model to be explicitly incorporated into the DNN-based approach, improving its robustness to changes in experimental conditions. Furthermore, to circumvent the difficulty of collecting the training data, it is proposed that the DNN-based denoiser be trained without using actual measured specimen images but using a formula-driven supervised approach that systemically generates synthetic images. In experiments using simulation based on a hard X-ray ptychographic measurement system, the imaging capability of the proposed method was evaluated by comparing it with ePIE and rPIE. These results demonstrated that the proposed method was able to reconstruct higher-spatial-resolution images with half the number of iterations required by ePIE and rPIE, even for data with low illumination intensity. Also, the proposed method was shown to be robust to its hyperparameters. In addition, the proposed method was applied to ptychographic datasets of a Simens star chart and ink toner particles measured at SPring-8 BL24XU, which confirmed that it can successfully reconstruct images from measurement scans with a lower overlap ratio of the illumination regions than is required by ePIE and rPIE.

Block Copolymer-Directed Single-Diamond Hybrid Structures Derived from X-ray Nanotomography

Block copolymers are recognized as a valuable platform for creating nanostructured materials. Morphologies formed by block copolymer self-assembly can be transferred into a wide range of inorganic materials, enabling applications including energy storage and metamaterials. However, imaging of the underlying, often complex, nanostructures in large volumes has remained a challenge, limiting progress in materials development. Taking advantage of recent advances in X-ray nanotomography, we noninvasively imaged exceptionally large volumes of nanostructured hybrid materials at high resolution, revealing a single-diamond morphology in a triblock terpolymer-gold composite network. This morphology, which is ubiquitous in nature, has so far remained elusive in block copolymer-derived materials, despite its potential to create materials with large photonic bandgaps. The discovery was made possible by the precise analysis of distortions in a large volume of the self-assembled diamond network, which are difficult to unambiguously assess using traditional characterization tools. We anticipate that high-resolution X-ray nanotomography, which allows imaging of much larger sample volumes than electron-based tomography, will become a powerful tool for the quantitative analysis of complex nanostructures and that structures such as the triblock terpolymer-directed single diamond will enable the generation of advanced multicomponent composites with hitherto unknown property profiles.

Computational optical sectioning via near-field multi-slice ptychography

We introduce a method for the computational sectioning of optically thick samples based on a combination of near-field and multi-slice ptychography. The method enables a large field-of-view 3D phase imaging of samples that is an order of magnitude thicker than the depth of field of bright-field microscopy. An axial resolution for these thick samples is maintained in the presence of multiple scattering, revealing a complex structure beyond the depth of the field limit. In this Letter, we describe the new, to the best of our knowledge, approach and demonstrate its effectiveness using a range of samples with diverse thicknesses and optical properties.

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.

High-performance 4-nm-resolution X-ray tomography using burst ptychography

Advances in science, medicine and engineering rely on breakthroughs in imaging, particularly for obtaining multiscale, three-dimensional information from functional systems such as integrated circuits or mammalian brains. Achieving this goal often requires combining electron- and photon-based approaches. Whereas electron microscopy provides nanometre resolution through serial, destructive imaging of surface layers1, ptychographic X-ray computed tomography2 offers non-destructive imaging and has recently achieved resolutions down to seven nanometres for a small volume3. Here we implement burst ptychography, which overcomes experimental instabilities and enables much higher performance, with 4-nanometre resolution at a 170-times faster acquisition rate, namely, 14,000 resolution elements per second. Another key innovation is tomographic back-propagation reconstruction4, allowing us to image samples up to ten times larger than the conventional depth of field. By combining the two innovations, we successfully imaged a state-of-the-art (seven-nanometre node) commercial integrated circuit, featuring nanostructures made of low- and high-density materials such as silicon and metals, which offer good radiation stability and contrast at the selected X-ray wavelength. These capabilities enabled a detailed study of the chip's design and manufacturing, down to the level of individual transistors. We anticipate that the combination of nanometre resolution and higher X-ray flux at next-generation X-ray sources will have a revolutionary impact in fields ranging from electronics to electrochemistry and neuroscience.

Ptychographic lensless coherent endomicroscopy through a flexible fiber bundle

Conventional fiber-bundle-based endoscopes allow minimally invasive imaging through flexible multi-core fiber (MCF) bundles by placing a miniature lens at the distal tip and using each core as an imaging pixel. In recent years, lensless imaging through MCFs was made possible by correcting the core-to-core phase distortions pre-measured in a calibration procedure. However, temporally varying wavefront distortions, for instance, due to dynamic fiber bending, pose a challenge for such approaches. Here, we demonstrate a coherent lensless imaging technique based on intensity-only measurements insensitive to core-to-core phase distortions. We leverage a ptychographic reconstruction algorithm to retrieve the phase and amplitude profiles of reflective objects placed at a distance from the fiber tip, using as input a set of diffracted intensity patterns reflected from the object when the illumination is scanned over the MCF cores. Our approach thus utilizes an acquisition process equivalent to confocal microendoscopy, only replacing the single detector with a camera.

Unsupervised physics-informed deep learning-based reconstruction for time-resolved imaging by multiplexed ptychography

We explore numerically an unsupervised, physics-informed, deep learning-based reconstruction technique for time-resolved imaging by multiplexed ptychography. In our method, the untrained deep learning model replaces the iterative algorithm's update step, yielding superior reconstructions of multiple dynamic object frames compared to conventional methodologies. More precisely, we demonstrate improvements in image quality and resolution, while reducing sensitivity to the number of recorded frames, the mutual orthogonality of different probe modes, overlap between neighboring probe beams and the cutoff frequency of the ptychographic microscope - properties that are generally of paramount importance for ptychographic reconstruction algorithms.

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.

Noise-robust latent vector reconstruction in ptychography using deep generative models

Computational imaging is increasingly vital for a broad spectrum of applications, ranging from biological to material sciences. This includes applications where the object is known and sufficiently sparse, allowing it to be described with a reduced number of parameters. When no explicit parameterization is available, a deep generative model can be trained to represent an object in a low-dimensional latent space. In this paper, we harness this dimensionality reduction capability of autoencoders to search for the object solution within the latent space rather than the object space. We demonstrate what we believe to be a novel approach to ptychographic image reconstruction by integrating a deep generative model obtained from a pre-trained autoencoder within an automatic differentiation ptychography (ADP) framework. This approach enables the retrieval of objects from highly ill-posed diffraction patterns, offering an effective method for noise-robust latent vector reconstruction in ptychography. Moreover, the mapping into a low-dimensional latent space allows us to visualize the optimization landscape, which provides insight into the convexity and convergence behavior of the inverse problem. With this work, we aim to facilitate new applications for sparse computational imaging such as when low radiation doses or rapid reconstructions are essential.

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.

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.

Deep reinforcement learning for data-driven adaptive scanning in ptychography

We present a method that lowers the dose required for an electron ptychographic reconstruction by adaptively scanning the specimen, thereby providing the required spatial information redundancy in the regions of highest importance. The proposed method is built upon a deep learning model that is trained by reinforcement learning, using prior knowledge of the specimen structure from training data sets. We show that using adaptive scanning for electron ptychography outperforms alternative low-dose ptychography experiments in terms of reconstruction resolution and quality.

Near-field multi-slice ptychography: quantitative phase imaging of optically thick samples with visible light and X-rays

Ptychography is a form of lens-free coherent diffractive imaging now used extensively in electron and synchrotron-based X-ray microscopy. In its near-field implementation, it offers a route to quantitative phase imaging at an accuracy and resolution competitive with holography, with the added advantages of extended field of view and blind deconvolution of the illumination beam profile from the sample image. In this paper we show how near-field ptychography can be combined with a multi-slice model, adding to this list of advantages the unique ability to recover high-resolution phase images of larger samples, whose thickness places them beyond the depth of field of alternative methods.

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.

Machine learning in electron microscopy for advanced nanocharacterization: current developments, available tools and future outlook

In the last few years, electron microscopy has experienced a new methodological paradigm aimed to fix the bottlenecks and overcome the challenges of its analytical workflow. Machine learning and artificial intelligence are answering this call providing powerful resources towards automation, exploration, and development. In this review, we evaluate the state-of-the-art of machine learning applied to electron microscopy (and obliquely, to materials and nano-sciences). We start from the traditional imaging techniques to reach the newest higher-dimensionality ones, also covering the recent advances in spectroscopy and tomography. Additionally, the present review provides a practical guide for microscopists, and in general for material scientists, but not necessarily advanced machine learning practitioners, to straightforwardly apply the offered set of tools to their own research. To conclude, we explore the state-of-the-art of other disciplines with a broader experience in applying artificial intelligence methods to their research (e.g., high-energy physics, astronomy, Earth sciences, and even robotics, videogames, or marketing and finances), in order to narrow down the incoming future of electron microscopy, its challenges and outlook.

Complete alignment of a KB-mirror system guided by ptychography

We demonstrate how the individual mirrors of a high-quality Kirkpatrick-Baez (KB) mirror system can be aligned to each other to create an optimally focused beam, through minimizing aberrations in the phase of the ptychographically reconstructed pupil function. Different sources of misalignment and the distinctive phase artifacts they create are presented via experimental results from the alignment of the KB mirrors at the NanoMAX diffraction endstation. The catalog of aberration artifacts can be used to easily identify which parameter requires further tuning in the alignment of any KB mirror system.

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.

Environmental control for X-ray nanotomography

The acquisition speed and spatial resolution of X-ray nanotomography have continuously improved over the last decades. Coherent diffraction-based techniques breach the 10 nm resolution barrier frequently and thus pose stringent demands on sample positioning accuracy and stability. At the same time there is an increasing desire to accommodate in situ or operando measurements. Here, an environmental control system for X-ray nanotomography is introduced to regulate the temperature of a sample from room temperature up to 850°C in a controlled atmospheric composition. The system allows for a 360° sample rotation, permitting tomographic studies in situ or operando free of missing wedge constraints. The system is implemented and available at the flOMNI microscope at the Swiss Light Source. In addition to the environmental control system itself, the related modifications of flOMNI are described. Tomographic measurements of a nanoporous gold sample at 50°C and 600°C at a resolution of sub-20 nm demonstrate the performance of the device.

Single-shot ptychography at a soft X-ray free-electron laser

In this work, single-shot ptychography was adapted to the XUV range and, as a proof of concept, performed at the free-electron laser FLASH at DESY to obtain a high-resolution reconstruction of a test sample. Ptychography is a coherent diffraction imaging technique capable of imaging extended samples with diffraction-limited resolution. However, its scanning nature makes ptychography time-consuming and also prevents its application for mapping of dynamical processes. Single-shot ptychography can be realized by collecting the diffraction patterns of multiple overlapping beams in one shot and, in recent years, several concepts based on two con-focal lenses were employed in the visible regime. Unfortunately, this approach cannot be extended straightforwardly to X-ray wavelengths due to the use of refractive optics. Here, a novel single-shot ptychography setup utilizes a combination of X-ray focusing optics with a two-dimensional beam-splitting diffraction grating. It facilitates single-shot imaging of extended samples at X-ray wavelengths.

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.

Phase retrieval based on a total-variation-regularized Poisson model for X-ray ptychographic imaging of low-contrast objects

Hard X-ray ptychography has become an indispensable tool for observing the microscopic structure of a thick specimen. It measures diffraction patterns by scanning an X-ray beam and visualizes the complex-valued refractive index of the specimen by a computational reconstruction called phase retrieval. The quality of imaging is dependent on the used phase-retrieval algorithm, especially when the intensity of the diffraction patterns in the high-spatial-frequency range is low and/or when the spatial overlap of the illumination area is small. In this paper, a phase-retrieval algorithm, AMPAM, based on the Poisson model and total variation (TV) is proposed. It applies alternating minimization using primal-dual splitting and gradient-descent algorithms to compute the result without matrix inversion. The imaging capability of the proposed algorithm from low-dose and/or sparsely scanned data was investigated by numerical simulations. The proposed algorithm was compared with ADPr, which is the state-of-the-art algorithm based on the TV-regularized Poisson model. The results indicated that AMPAM can provide good-quality images with a computational cost 7–11 times less than ADPr. In addition, ink toner and macroporous silica particles were imaged at SPring-8 BL24XU to confirm the applicability of the algorithm to actual measurements.

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.

Material-specific high-resolution table-top extreme ultraviolet microscopy

Microscopy with extreme ultraviolet (EUV) radiation holds promise for high-resolution imaging with excellent material contrast, due to the short wavelength and numerous element-specific absorption edges available in this spectral range. At the same time, EUV radiation has significantly larger penetration depths than electrons. It thus enables a nano-scale view into complex three-dimensional structures that are important for material science, semiconductor metrology, and next-generation nano-devices. Here, we present high-resolution and material-specific microscopy at 13.5 nm wavelength. We combine a highly stable, high photon-flux, table-top EUV source with an interferometrically stabilized ptychography setup. By utilizing structured EUV illumination, we overcome the limitations of conventional EUV focusing optics and demonstrate high-resolution microscopy at a half-pitch lateral resolution of 16 nm. Moreover, we propose mixed-state orthogonal probe relaxation ptychography, enabling robust phase-contrast imaging over wide fields of view and long acquisition times. In this way, the complex transmission of an integrated circuit is precisely reconstructed, allowing for the classification of the material composition of mesoscopic semiconductor systems.

Wavelength-multiplexed single-shot ptychography

We present the first experimental demonstration of wavelength-multiplexing in single-shot ptychography. Specifically, we experimentally reconstruct the complex transmission profile of a wavelength-independent and wavelength-dependent object simultaneously for 532 nm and 633 nm probing wavelengths. In addition, we discuss the advantages of a more general approach to detector segmentation in single-shot ptychography. A minimization to correct for uncertainties in a priori information that is required for single-shot geometries is presented along with a novel probe constraint. Furthermore, this technique is complementary to dual-wavelength interferometry without the need for an external reference. This work is enabling to imaging technologies and applications such as broadband single-shot ptychography, time-resolved imaging by multiplexed ptychography, real-time inspection for laser micro-machining, and plasma imaging.

Terahertz ptychography using a long-distance diffraction-free beam as the probe

We have implemented a terahertz (THz) ptychographic technique using a long-distance diffraction-free beam (DFB) instead of traditional low-energy pinhole-defined illumination as the probe. The DFB generating system containing two lens-axicon doublets is very easily realized. Measured transverse intensities of such a DFB display an Airy-pattern-like distribution. Based on the well-developed extended ptychographic iterative engine, we simultaneously reconstruct a phase object and the DFB probe with both simulated and real data. Further calculation shows that the DFB has abundant spatial high-frequency components that guarantee high coherence of the illuminating probe beam in our THz ptychographic system. In addition, we firmly believe that the proposed approach can be easily transplanted to the ptychography at other frequency bands as both lens and axicon are very common optical elements.

Numerical and experimental study of partial coherence for near-field and far-field ptychography

High degree of coherence is essential in coherent diffraction imaging (CDI). The coherence requirement on the light source varies with the experimental configuration. As a scanning variant of CDI, ptychography has shown great potential for extensive applications. To determine the influence of partially temporal and spatial coherence on near- and far-field ptychography, we have performed a series of numerical simulations and visible light optical experiments. We demonstrated that the near-field is more robust to spatial and temporal decoherence than the far-field. In addition, the far-field is found to be more sensitive to spatial decoherence than to temporal decoherence. Our experiments also show that a known probe estimate with good spatial coherence enables the retrieval qualities to be enhanced dramatically and helps prevent falling into the local minimums in the reconstruction process. Our work would provide a valuable reference for implementing ptychography with sources of limited coherence.

Hard X-ray ptychography at Taiwan Photon Source at 11-20 nm spatial resolution

X-ray ptychography, a technique based on scanning and processing of coherent diffraction patterns, is a non-destructive imaging technique with a high spatial resolution far beyond the focused beam size. Earlier demonstrations of hard X-ray ptychography at Taiwan Photon Source (TPS) using an in-house program successfully recorded the ptychographic diffraction patterns from a gold-made Siemens star as a test sample and retrieved the finest inner features of 25 nm. Ptychography was performed at two beamlines with different focusing optics: a pair of Kirkpatrick-Baez mirrors and a pair of nested Montel mirrors, for which the beam sizes on the focal planes were 3 µm and 200 nm and the photon energies were from 5.1 keV to 9 keV. The retrieved spatial resolutions are 20 nm to 11 nm determined by the 10-90% line-cut method and half-bit threshold of Fourier shell correlation. This article describes the experimental conditions and compensation methods, including position correction, mixture state-of-probe, and probe extension methods, of the aforementioned experiments. The discussions will highlight the criteria of ptychographic experiments at TPS as well as the opportunity to characterize beamlines by measuring factors such as the drift or instability of beams or stages and the coherence of beams. Besides, probe functions, the full complex fields illuminated on samples, can be recovered simultaneously using ptychography. Theoretically, the wavefield at any arbitrary position can be estimated from one recovered probe function undergoing wave-propagating. The verification of probe-propagating has been carried out by comparing the probe functions obtained by ptychography and undergoing wave-propagating located at 0, 500 and 1000 µm relative to the focal plane.

Imaging of retina cellular and subcellular structures using ptychographic hard X-ray tomography

Ptychographic hard X-ray computed tomography (PXCT) is a recent method allowing imaging with quantitative electron-density contrast. Here, we imaged, at cryogenic temperature and without sectioning, cellular and subcellular structures of a chemically fixed and stained wild-type mouse retina, including axons and synapses, with complete isotropic 3D information over tens of microns. Comparison with tomograms of degenerative retina from a mouse model of retinitis pigmentosa illustrates the potential of this method for analyzing disease processes like neurodegeneration at sub-200 nm resolution. As a non-destructive imaging method, PXCT is very suitable for correlative imaging. Within the outer plexiform layer containing the photoreceptor synapses, we identified somatic synapses. We used a small region inside the X-ray-imaged sample for further high-resolution focused ion beam/scanning electron microscope tomography. The subcellular structures of synapses obtained with the X-ray technique matched the electron microscopy data, demonstrating that PXCT is a powerful scanning method for tissue volumes of more than 60 cells and sensitive enough for identification of regions as small as 200 nm, which remain available for further structural and biochemical investigations.

Spatiospectral characterization of ultrafast pulse-beams by multiplexed broadband ptychography

Ultrafast pulse-beam characterization is critical for diverse scientific and industrial applications from micromachining to generating the highest intensity laser pulses. The four-dimensional structure of a pulse-beam, E~(x,y,z,ω), can be fully characterized by coupling spatiospectral metrology with spectral phase measurement. When temporal pulse dynamics are not of primary interest, spatiospectral characterization of a pulse-beam provides crucial information even without spectral phase. Here we demonstrate spatiospectral characterization of pulse-beams via multiplexed broadband ptychography. The complex spatial profiles of multiple spectral components, E~(x,y,ω), from modelocked Ti:sapphire and from extreme ultra-violet pulse-beams are reconstructed with minimum intervening optics and no refocusing. Critically, our technique does not require spectral filters, interferometers, or reference pulses.

Mechanical adaptation of brachiopod shells via hydration-induced structural changes

The function-optimized properties of biominerals arise from the hierarchical organization of primary building blocks. Alteration of properties in response to environmental stresses generally involves time-intensive processes of resorption and reprecipitation of mineral in the underlying organic scaffold. Here, we report that the load-bearing shells of the brachiopod Discinisca tenuis are an exception to this process. These shells can dynamically modulate their mechanical properties in response to a change in environment, switching from hard and stiff when dry to malleable when hydrated within minutes. Using ptychographic X-ray tomography, electron microscopy and spectroscopy, we describe their hierarchical structure and composition as a function of hydration to understand the structural motifs that generate this adaptability. Key is a complementary set of structural modifications, starting with the swelling of an organic matrix on the micron level via nanocrystal reorganization and ending in an intercalation process on the molecular level in response to hydration.

Quantitative phase measurements of human cell nuclei using X-ray ptychography

The human cell nucleus serves as an important organelle holding the genetic blueprint for life. In this work, X-ray ptychography was applied to assess the masses of human cell nuclei using its unique phase shift information. Measurements were carried out at the I13-1 beamline at the Diamond Light Source that has extremely large transverse coherence properties. The ptychographic diffractive imaging approach allowed imaging of large structures that gave quantitative measurements of the phase shift in 2D projections. In this paper a modified ptychography algorithm that improves the quality of the reconstruction for weak scattering samples is presented. The application of this approach to calculate the mass of several human nuclei is also demonstrated.

Sparse ab initio x-ray transmission spectrotomography for nanoscopic compositional analysis of functional materials

The performance of functional materials is either driven or limited by nanoscopic heterogeneities distributed throughout the material's volume. To better our understanding of these materials, we need characterization tools that allow us to determine the nature and distribution of these heterogeneities in their native geometry in 3D. Here, we introduce a method based on x-ray near-edge spectroscopy, ptychographic x-ray computed nanotomography, and sparsity techniques. The method allows the acquisition of quantitative multimodal tomograms of representative sample volumes at sub-30 nm half-period spatial resolution within practical acquisition times, which enables local structure refinements in complex geometries. To demonstrate the method's capabilities, we investigated the transformation of vanadium phosphorus oxide catalysts with industrial use. We observe changes from the micrometer to the atomic level and the formation of a location-specific defect so far only theorized. These results led to a reevaluation of these catalysts used in the production of plastics.

Direct evidence for eoarchean iron metabolism?

Metasedimentary rocks from Isua, West Greenland (> 3,700 million years old) contain carbonaceous compounds, compatible with a biogenic origin (Hassenkam, Andersson, Dalby, Mackenzie, & Rosing, 2017; Ohtomo, Kakegawa, Ishida, Nagase, & Rosing, 2014; Rosing, 1999). The metamorphic mineral assemblage with garnet and quartz intergrowths contains layers of carbonaceous inclusions contiguous with carbon-rich sedimentary beds in the host rock. Previous studies (Hassenkam et al., 2017; Ohtomo et al., 2014; Rosing, 1999) on Isua rocks focused on testing the biogenic origin of the carbonaceous material, but here we searched for evidence which could provide new insights into the nature of the life that generated this carbonaceous material. We studied material trapped in inclusions armoured within quartz grains inside garnet porphyroblasts by non-destructive ptychographic X-ray nanotomography (PXCT). The 3D electron density maps generated by PXCT were correlated with maps from X-ray fluorescence tomography and micro-Raman spectroscopy. We found that the material trapped inside inclusions in the quartz grains consist of disordered carbon material encasing domains of iron-rich carbonaceous material. These results corroborate earlier claims (Hassenkam et al., 2017; Ohtomo et al., 2014; Rosing, 1999) for biogenic origins and are compatible with relics of metamorphosed biological material originally containing high iron/carbon ratios, comparable to ratios found in most extant organisms. These iron-rich domains represent the oldest evidence for organic iron complexes in the geologic record and are consistent with Fe-isotopic evidence for metabolic iron fractionation in > 3,700 Ma Isua banded iron formation (Czaja et al., 2013; Whitehouse & Fedo, 2007).

Upscaling X-ray nanoimaging to macroscopic specimens

Upscaling X-ray nanoimaging to macroscopic specimens has the potential for providing insights across multiple length scales, but its feasibility has long been an open question. By combining the imaging requirements and existing proof-of-principle examples in large-specimen preparation, data acquisition and reconstruction algorithms, the authors provide imaging time estimates for howX-ray nanoimaging can be scaled to macroscopic specimens. To arrive at this estimate, a phase contrast imaging model that includes plural scattering effects is used to calculate the required exposure and corresponding radiation dose. The coherent X-ray flux anticipated from upcoming diffraction-limited light sources is then considered. This imaging time estimation is in particular applied to the case of the connectomes of whole mouse brains. To image the connectome of the whole mouse brain, electron microscopy connectomics might require years, whereas optimized X-ray microscopy connectomics could reduce this to one week. Furthermore, this analysis points to challenges that need to be overcome (such as increased X-ray detector frame rate) and opportunities that advances in artificial-intelligence-based 'smart' scanning might provide. While the technical advances required are daunting, it is shown that X-ray microscopy is indeed potentially applicable to nanoimaging of millimetre- or even centimetre-size specimens.

Ptychographic optical coherence tomography

Ptychography is a robust computational imaging technique that can reconstruct complex light fields beyond conventional hardware limits. However, for many wide-field computational imaging techniques, including ptychography, depth sectioning remains a challenge. Here we demonstrate a high-resolution three-dimensional (3D) computational imaging approach, which combines ptychography with spectral-domain imaging, inspired by optical coherence tomography (OCT). This results in a flexible imaging system with the main advantages of OCT, such as depth-sectioning without sample rotation, decoupling of transverse and axial resolution, and a high axial resolution only determined by the source bandwidth. The interferometric reference needed in OCT is replaced by computational methods, simplifying hardware requirements. As ptychography is capable of deconvolving the illumination contributions in the observed signal, speckle-free images are obtained. We demonstrate the capabilities of ptychographic optical coherence tomography (POCT) by imaging an axially discrete lithographic structure and an axially continuous mouse brain sample.

Hard X-ray omnidirectional differential phase and dark-field imaging

Ever since the discovery of X-rays, tremendous efforts have been made to develop new imaging techniques for unlocking the hidden secrets of our world and enriching our understanding of it. X-ray differential phase contrast imaging, which measures the gradient of a sample's phase shift, can reveal more detail in a weakly absorbing sample than conventional absorption contrast. However, normally only the gradient's component in two mutually orthogonal directions is measurable. In this article, omnidirectional differential phase images, which record the gradient of phase shifts in all directions of the imaging plane, are efficiently generated by scanning an easily obtainable, randomly structured modulator along a spiral path. The retrieved amplitude and main orientation images for differential phase yield more information than the existing imaging methods. Importantly, the omnidirectional dark-field images can be simultaneously extracted to study strongly ordered scattering structures. The proposed method can open up new possibilities for studying a wide range of complicated samples composed of both heavy, strongly scattering atoms and light, weakly scattering atoms.

Nondestructive, high-resolution, chemically specific 3D nanostructure characterization using phase-sensitive EUV imaging reflectometry

Next-generation nano- and quantum devices have increasingly complex 3D structure. As the dimensions of these devices shrink to the nanoscale, their performance is often governed by interface quality or precise chemical or dopant composition. Here, we present the first phase-sensitive extreme ultraviolet imaging reflectometer. It combines the excellent phase stability of coherent high-harmonic sources, the unique chemical sensitivity of extreme ultraviolet reflectometry, and state-of-the-art ptychography imaging algorithms. This tabletop microscope can nondestructively probe surface topography, layer thicknesses, and interface quality, as well as dopant concentrations and profiles. High-fidelity imaging was achieved by implementing variable-angle ptychographic imaging, by using total variation regularization to mitigate noise and artifacts in the reconstructed image, and by using a high-brightness, high-harmonic source with excellent intensity and wavefront stability. We validate our measurements through multiscale, multimodal imaging to show that this technique has unique advantages compared with other techniques based on electron and scanning probe microscopies.

Fast digital lossy compression for X-ray ptychographic data

Increases in X-ray brightness from synchrotron light sources lead to a requirement for higher frame rates from hybrid pixel array detectors (HPADs), while also favoring charge integration over photon counting. However, transfer of the full uncompressed data will begin to constrain detector design, as well as limit the achievable continuous frame rate. Here a data compression scheme that is easy to implement in a HPAD's application-specific integrated circuit (ASIC) is described, and how different degrees of compression affect image quality in ptychography, a commonly employed coherent imaging method, is examined. Using adaptive encoding quantization, it is shown in simulations that one can digitize signals up to 16383 photons per pixel (corresponding to 14 bits of information) using only 8 or 9 bits for data transfer, with negligible effect on the reconstructed image.

Alterations in Sub-Axonal Architecture Between Normal Aging and Parkinson's Diseased Human Brains Using Label-Free Cryogenic X-ray Nanotomography

Gaining insight to pathologically relevant processes in continuous volumes of unstained brain tissue is important for a better understanding of neurological diseases. Many pathological processes in neurodegenerative disorders affect myelinated axons, which are a critical part of the neuronal circuitry. Cryo ptychographic X-ray computed tomography in the multi-keV energy range is an emerging technology providing phase contrast at high sensitivity, allowing label-free and non-destructive three dimensional imaging of large continuous volumes of tissue, currently spanning up to 400,000 μm3. This aspect makes the technique especially attractive for imaging complex biological material, especially neuronal tissues, in combination with downstream optical or electron microscopy techniques. A further advantage is that dehydration, additional contrast staining, and destructive sectioning/milling are not required for imaging. We have developed a pipeline for cryo ptychographic X-ray tomography of relatively large, hydrated and unstained biological tissue volumes beyond what is typical for the X-ray imaging, using human brain tissue and combining the technique with complementary methods. We present four imaged volumes of a Parkinson's diseased human brain and five volumes from a non-diseased control human brain using cryo ptychographic X-ray tomography. In both cases, we distinguish neuromelanin-containing neurons, lipid and melanic pigment, blood vessels and red blood cells, and nuclei of other brain cells. In the diseased sample, we observed several swellings containing dense granular material resembling clustered vesicles between the myelin sheaths arising from the cytoplasm of the parent oligodendrocyte, rather than the axoplasm. We further investigated the pathological relevance of such swollen axons in adjacent tissue sections by immunofluorescence microscopy for phosphorylated alpha-synuclein combined with multispectral imaging. Since cryo ptychographic X-ray tomography is non-destructive, the large dataset volumes were used to guide further investigation of such swollen axons by correlative electron microscopy and immunogold labeling post X-ray imaging, a possibility demonstrated for the first time. Interestingly, we find that protein antigenicity and ultrastructure of the tissue are preserved after the X-ray measurement. As many pathological processes in neurodegeneration affect myelinated axons, our work sets an unprecedented foundation for studies addressing axonal integrity and disease-related changes in unstained brain tissues.

Fast reconstruction tools for ptychography at Sirius, the fourth-generation Brazilian synchrotron

Described here are image reconstruction optimizations for ptychographic coherent X-ray scattering data and X-ray fluorescence, which have been developed for the new fourth-generation synchrotron light source, Sirius, at the Brazilian Synchrotron Light Laboratory. The optimization strategy has been applied to the standard experimental strategy for ptychographic and fluorescence experiments on the Carnaúba beamline which involves the use of high-speed continuous scans (fly scans) for a fast acquisition time over large areas through the use of a newly proposed trajectory named the alternating linear trajectory. The scientific computing developments presented here target an efficient use of graphical processing units (GPUs) to the point where large fly-scan acquisitions can be processed in real time on a local high-performance computer. Some optimizations involving a custom fast Fourier transform implementation and use of mixed precision can be applied to other algorithms and phase-retrieval techniques, and therefore this work provides a general optimization scheme. Finally, the optimization strategy presented here has improved performance by a factor of ∼2.5 times faster when compared with non-optimized GPU implementations.

Metrology of a Focusing Capillary Using Optical Ptychography

The focusing property of an ellipsoidal monocapillary has been characterized using the ptychography method with a 405 nm laser beam. The recovered wavefront gives a 12.5×10.4μm2 focus. The reconstructed phase profile of the focused beam can be used to estimate the height error of the capillary surface. The obtained height error shows a Gaussian distribution with a standard deviation of 1.3 μm. This approach can be used as a quantitative tool for evaluating the inner functional surfaces of reflective optics, complementary to conventional metrology methods.

Three-dimensional single-shot ptychography

Here we introduce three-dimensional single-shot ptychography (3DSSP). 3DSSP leverages an additional constraint unique to the single-shot geometry to deconvolve multiple 2D planes of a 3D object. Numeric simulations and analytic calculations demonstrate that 3DSSP reconstructs multiple planes in an extended 3D object with a minimum separation consistent with the depth of field for a conventional microscope. We experimentally demonstrate 3DSSP by reconstructing orthogonal hair strands axially separated by 5 mm. 3DSSP provides a pathway towards volumetric imaging of dynamically evolving systems on ultrafast timescales.

2D MEMS-based multilayer Laue lens nanofocusing optics for high-resolution hard x-ray microscopy

We report on the development of 2D integrated multilayer Laue lens (MLL) nanofocusing optics used for high-resolution x-ray microscopy. A Micro-Electro-Mechanical-Systems (MEMS) - based template has been designed and fabricated to accommodate two linear MLL optics in pre-aligned configuration. The orthogonality requirement between two MLLs has been satisfied to a better than 6 millidegrees level, and the separation along the x-ray beam direction was controlled on a micrometer scale. Developed planar 2D MLL structure has demonstrated astigmatism free point focus of ∼14 nm by ∼13 nm in horizontal and vertical directions, respectively, at 13.6 keV photon energy. Approaching 10 nm resolution with integrated 2D MLL optic is a significant step forward in applications of multilayer Laue lenses for high-resolution hard x-ray microscopy and their adoption by the general x-ray microscopy community.

Near, far, wherever you are: simulations on the dose efficiency of holographic and ptychographic coherent imaging

Different studies in X-ray microscopy have arrived at conflicting conclusions about the dose efficiency of imaging modes involving the recording of intensity distributions in the near (Fresnel regime) or far (Fraunhofer regime) field downstream of a specimen. A numerical study is presented on the dose efficiency of near-field holography, near-field ptychography and far-field ptychography, where ptychography involves multiple overlapping finite-sized illumination positions. Unlike what has been reported for coherent diffraction imaging, which involves recording a single far-field diffraction pattern, it is found that all three methods offer similar image quality when using the same fluence on the specimen, with far-field ptychography offering slightly better spatial resolution and a lower mean error. These results support the concept that (if the experiment and image reconstruction are done properly) the sample can be near or far; wherever you are, photon fluence on the specimen sets one limit to spatial resolution.

Nanoscale 3D quantitative imaging of 1.88 Ga Gunflint microfossils reveals novel insights into taphonomic and biogenic characters

Precambrian cellular remains frequently have simple morphologies, micrometric dimensions and are poorly preserved, imposing severe analytical and interpretational challenges, especially for irrefutable attestations of biogenicity. The 1.88 Ga Gunflint biota is a Precambrian microfossil assemblage with different types and qualities of preservation across its numerous geological localities and provides important insights into the Proterozoic biosphere and taphonomic processes. Here we use synchrotron-based ptychographic X-ray computed tomography to investigate well-preserved carbonaceous microfossils from the Schreiber Beach locality as well as poorly-preserved, iron-replaced fossil filaments from the Mink Mountain locality, Gunflint Formation. 3D nanoscale imaging with contrast based on electron density allowed us to assess the morphology and carbonaceous composition of different specimens and identify the minerals associated with their preservation based on retrieved mass densities. In the Mink Mountain filaments, the identification of mature kerogen and maghemite rather than the ubiquitously described hematite indicates an influence from biogenic organics on the local maturation of iron oxides through diagenesis. This non-destructive 3D approach to microfossil composition at the nanoscale within their geological context represents a powerful approach to assess the taphonomy and biogenicity of challenging or poorly preserved traces of early microbial life, and may be applied effectively to extraterrestrial samples returned from upcoming space missions.

Measuring laser beam quality, wavefronts, and lens aberrations using ptychography

We report on an approach for quantitative characterization of laser beam quality, wavefronts, and lens aberrations using ptychography with a near-infrared supercontinuum laser. Ptychography is shown to offer a powerful alternative for both beam propagation ratio M² and wavefront measurements compared with existing techniques. In addition, ptychography is used to recover the transmission function of a microlens array for aberration analysis. The results demonstrate ptychography's flexibility in wavefront metrology and optical shop testing.

Super-resolution near-field ptychography

Compared to far-field ptychography, near-field ptychography can reduce the requirement on the detector dynamic range, while it is able to cover a larger field of view with a fewer number of sample scans. However, its spatial resolution is limited by the detector pixel size. Here, we utilize a pixel-super-resolved approach to overcome this limitation. The method has been applied to four types of experiment configurations using planar and divergent illuminations together with two different cameras with highly contrast specifications. The proposed method works effectively for up-sampling up to 6 times. Meanwhile, it can achieve ∼5.9-fold and ∼3.1-fold resolution improvement over the 6.5-μm and 2.4-μm detector pixel size. We also demonstrate the precisely quantitative phase imaging capability of the method by using a phase resolution target. The presented method is believed to have great potential in X-ray tomography and on-chip flow cytometry.

A Monte Carlo ray-tracing simulation of coherent X-ray diffractive imaging

Coherent diffractive imaging (CDI) experiments are adequately simulated assuming the thin sample approximation and using a Fresnel or Fraunhofer wavefront propagator to obtain the diffraction pattern. Although this method is used in wave-based or hybrid X-ray simulators, here the applicability and effectiveness of an alternative approach that is based solely on ray tracing of Huygens wavelets are investigated. It is shown that diffraction fringes of a grating-like source are accurately predicted and that diffraction patterns of a ptychography dataset from an experiment with realistic parameters can be sampled well enough to be retrieved by a standard phase-retrieval algorithm. Potentials and limits of this approach are highlighted. It is suggested that it could be applied to study imperfect or non-standard CDI configurations lacking a satisfactory theoretical formulation. The considerable computational effort required by this method is justified by the great flexibility provided for easy simulation of a large-parameter space.