Hard-x-ray lensless imaging of extended objects

High-speed X-ray ptychographic tomography

X-ray ptychography is a coherent scanning imaging technique widely used at synchrotron facilities for producing quantitative phase images beyond the resolution limit of conventional x-ray optics. The scanning nature of the technique introduces an inherent overhead to the collection at every scan position and limits the acquisition time of each 2D projection. The overhead associated with motion can be minimised with a continuous-scanning approach. Here we present an acquisition architecture based on continuous-scanning and up-triggering which allows to record ptychographic datasets at up to 9 kHz. We demonstrate the method by applying it to record 2D scans at up to 273 µm²/s and 3D scans of a (20 µm)³ volume in less than three hours. We discuss the current limitations and the outlook toward the development of sub-second 2D acquisition and minutes-long 3D ptychographic tomograms.

Single-exposure X-ray phase imaging microscopy with a grating interferometer

The advent of hard X-ray free-electron lasers enables nanoscopic X-ray imaging with sub-picosecond temporal resolution. X-ray grating interferometry offers a phase-sensitive full-field imaging technique where the phase retrieval can be carried out from a single exposure alone. Thus, the method is attractive for imaging applications at X-ray free-electron lasers where intrinsic pulse-to-pulse fluctuations pose a major challenge. In this work, the single-exposure phase imaging capabilities of grating interferometry are characterized by an implementation at the I13-1 beamline of Diamond Light Source (Oxfordshire, UK). For comparison purposes, propagation-based phase contrast imaging was also performed at the same instrument. The characterization is carried out in terms of the quantitativeness and the contrast-to-noise ratio of the phase reconstructions as well as via the achievable spatial resolution. By using a statistical image reconstruction scheme, previous limitations of grating interferometry regarding the spatial resolution can be mitigated as well as the experimental applicability of the technique.

Scalable and accurate multi-GPU-based image reconstruction of large-scale ptychography data

While the advances in synchrotron light sources, together with the development of focusing optics and detectors, allow nanoscale ptychographic imaging of materials and biological specimens, the corresponding experiments can yield terabyte-scale volumes of data that can impose a heavy burden on the computing platform. Although graphics processing units (GPUs) provide high performance for such large-scale ptychography datasets, a single GPU is typically insufficient for analysis and reconstruction. Several works have considered leveraging multiple GPUs to accelerate the ptychographic reconstruction. However, most of these works utilize only the Message Passing Interface to handle the communications between GPUs. This approach poses inefficiency for a hardware configuration that has multiple GPUs in a single node, especially while reconstructing a single large projection, since it provides no optimizations to handle the heterogeneous GPU interconnections containing both low-speed (e.g., PCIe) and high-speed links (e.g., NVLink). In this paper, we provide an optimized intranode multi-GPU implementation that can efficiently solve large-scale ptychographic reconstruction problems. We focus on the maximum likelihood reconstruction problem using a conjugate gradient (CG) method for the solution and propose a novel hybrid parallelization model to address the performance bottlenecks in the CG solver. Accordingly, we have developed a tool, called PtyGer (Ptychographic GPU(multiple)-based reconstruction), implementing our hybrid parallelization model design. A comprehensive evaluation verifies that PtyGer can fully preserve the original algorithm's accuracy while achieving outstanding intranode GPU scalability.

An achromatic X-ray lens

Diffractive and refractive optical elements have become an integral part of most high-resolution X-ray microscopes. However, they suffer from inherent chromatic aberration. This has to date restricted their use to narrow-bandwidth radiation, essentially limiting such high-resolution X-ray microscopes to high-brightness synchrotron sources. Similar to visible light optics, one way to tackle chromatic aberration is by combining a focusing and a defocusing optic with different dispersive powers. Here, we present the first successful experimental realisation of an X-ray achromat, consisting of a focusing diffractive Fresnel zone plate (FZP) and a defocusing refractive lens (RL). Using scanning transmission X-ray microscopy (STXM) and ptychography, we demonstrate sub-micrometre achromatic focusing over a wide energy range without any focal adjustment. This type of X-ray achromat will overcome previous limitations set by the chromatic aberration of diffractive and refractive optics and paves the way for new applications in spectroscopy and microscopy at broadband X-ray tube sources.

X-ray diffractive and refractive optical elements suffer from chromatic aberrations, limiting high-resolution X-ray microscopes mainly to bright synchrotron sources. Here, the authors experimentally realise an achromatic X-ray lens by combing a focusing diffractive Fresnel zone plate and a defocusing refractive lens.

Evolution of Hierarchically Porous Nickel Alumina Catalysts Studied by X-Ray Ptychography

The synthesis of hierarchically porous materials usually requires complex experimental procedures, often based around extensive trial and error approaches. One common synthesis strategy is the sol-gel method, although the relation between synthesis parameters, material structure and function has not been widely explored. Here, in situ 2D hard X-ray ptychography (XRP) and 3D ptychographic X-ray computed tomography (PXCT) are applied to monitor the development of hierarchical porosity in Ni/Al2 O3 and Al2 O3 catalysts with connected meso- and macropore networks. In situ XRP allows to follow textural changes of a dried gel Ni/Al2 O3 sample as a function of temperature during calcination, activation and CO2 methanation reaction. Complementary PXCT studies on dried gel particles of Ni/Al2 O3 and Al2 O3 provide quantitative information on pore structure, size distribution, and shape with 3D spatial resolution approaching 50 nm, while identical particles are imaged ex situ before and after calcination. The X-ray imaging results are correlated with N2 -sorption, Hg porosimetry and He pycnometry pore characterization. Hard X-ray nanotomography is highlighted to derive fine structural details including tortuosity, branching nodes, and closed pores, which are relevant in understanding transport phenomena during chemical reactions. XRP and PXCT are enabling technologies to understand complex synthesis pathways of porous materials.

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.

Advances in laboratory-scale ptychography using high harmonic sources [Invited]

Extreme ultraviolet microscopy and wavefront sensing are key elements for next-generation ultrafast applications, such as chemically-resolved imaging, focal spot diagnostics in pump-and-probe experiments, and actinic metrology for the state-of-the-art lithography node at 13.5 nm wavelength. Ptychography offers a robust solution to the aforementioned challenges. Originally adapted by the electron and synchrotron communities, advances in the stability and brightness of high-harmonic tabletop sources have enabled the transfer of ptychography to the laboratory. This review covers the state of the art in tabletop ptychography with high harmonic generation sources. We consider hardware options such as illumination optics and detector concepts as well as algorithmic aspects in the analysis of multispectral ptychography data. Finally, we review technological application cases such as multispectral wavefront sensing, attosecond pulse characterization, and depth-resolved imaging.

Methods of Coherent X-Ray Diffraction Imaging

Abstract

Methods of coherent X-ray diffraction imaging of the spatial structure of noncrystalline objects and nanocrystals (nanostructures) are considered. Particular attention is paid to the methods of scanning-based coherent diffraction imaging (ptychography), visualization based on coherent surface scattering with application of correlation spectroscopy approaches, and specific features of visualization using X-ray free-electron laser radiation. The corresponding data in the literature are analyzed to demonstrate the state of the art of the methods of coherent diffraction imaging and fields of their application.

Dual energy X-ray beam ptycho-fluorescence imaging

X-ray ptychography and X-ray fluorescence are complementary nanoscale imaging techniques, providing structural and elemental information, respectively. Both methods acquire data by scanning a localized beam across the sample. X-ray ptychography processes the transmission signal of a coherent illumination interacting with the sample, to produce images with a resolution finer than the illumination spot and step size. By enlarging both the spot and the step size, the technique can cover extended regions efficiently. X-ray fluorescence records the emitted spectra as the sample is scanned through the localized beam and its spatial resolution is limited by the spot and step size. The requisites for fast ptychography and high-resolution fluorescence appear incompatible. Here, a novel scheme that mitigates the difference in requirements is proposed. The method makes use of two probes of different sizes at the sample, generated by using two different energies for the probes and chromatic focusing optics. The different probe sizes allow to reduce the number of acquisition steps for the joint fluorescence-ptychography scan compared with a standard single beam scan, while imaging the same field of view. The new method is demonstrated experimentally using two undulator harmonics, a Fresnel zone plate and an energy discriminating photon counting detector.

Dynamic coherent diffractive imaging with a physics-driven untrained learning method

Reconstruction of a complex field from one single diffraction measurement remains a challenging task among the community of coherent diffraction imaging (CDI). Conventional iterative algorithms are time-consuming and struggle to converge to a feasible solution because of the inherent ambiguities. Recently, deep-learning-based methods have shown considerable success in computational imaging, but they require large amounts of training data that in many cases are difficult to obtain. Here, we introduce a physics-driven untrained learning method, termed Deep CDI, which addresses the above problem and can image a dynamic process with high confidence and fast reconstruction. Without any labeled data for pretraining, the Deep CDI can reconstruct a complex-valued object from a single diffraction pattern by combining a conventional artificial neural network with a real-world physical imaging model. To our knowledge, we are the first to demonstrate that the support region constraint, which is widely used in the iteration-algorithm-based method, can be utilized for loss calculation. The loss calculated from support constraint and free propagation constraint are summed up to optimize the network's weights. As a proof of principle, numerical simulations and optical experiments on a static sample are carried out to demonstrate the feasibility of our method. We then continuously collect 3600 diffraction patterns and demonstrate that our method can predict the dynamic process with an average reconstruction speed of 228 frames per second (FPS) using only a fraction of the diffraction data to train the weights.

Off-axis multilayer zone plate with 16 nm × 28 nm focus for high-resolution X-ray beam induced current imaging

Using multilayer zone plates (MZPs) as two-dimensional optics, focal spot sizes of less than 10 nm can be achieved, as we show here with a focus of 8.4 nm × 9.6 nm, but the need for order-sorting apertures prohibits practical working distances. To overcome this issue, here an off-axis illumination of a circular MZP is introduced to trade off between working distance and focal spot size. By this, the working distance between order-sorting aperture and sample can be more than doubled. Exploiting a 2D focus of 16 nm × 28 nm, real-space 2D mapping of local electric fields and charge carrier recombination using X-ray beam induced current in a single InP nanowire is demonstrated. Simulations show that a dedicated off-axis MZP can reach sub-10 nm focusing combined with reasonable working distances and low background, which could be used for in operando imaging of composition, carrier collection and strain in nanostructured devices.

Development and application of a tender X-ray ptychographic coherent diffraction imaging system on BL27SU at SPring-8

Ptychographic coherent diffraction imaging (CDI) allows the visualization of both the structure and chemical state of materials on the nanoscale, and has been developed for use in the soft and hard X-ray regions. In this study, a ptychographic CDI system with pinhole or Fresnel zone-plate optics for use in the tender X-ray region (2-5 keV) was developed on beamline BL27SU at SPring-8, in which high-precision pinholes optimized for the tender energy range were used to obtain diffraction intensity patterns with a low background, and a temperature stabilization system was developed to reduce the drift of the sample position. A ptychography measurement of a 200 nm thick tantalum test chart was performed at an incident X-ray energy of 2.500 keV, and the phase image of the test chart was successfully reconstructed with approximately 50 nm resolution. As an application to practical materials, a sulfur polymer material was measured in the range of 2.465 to 2.500 keV including the sulfur K absorption edge, and the phase and absorption images were successfully reconstructed and the nanoscale absorption/phase spectra were derived from images at multiple energies. In 3 GeV synchrotron radiation facilities with a low-emittance storage ring, the use of the present system will allow the visualization on the nanoscale of the chemical states of various light elements that play important roles in materials science, biology and environmental science.

Hard X-ray nanoprobe scanner

X-ray scientists are continually striving to improve the quality of X-ray microscopy, due to the fact that the information obtained from X-ray microscopy of materials can be complementary to that obtained from optical and electron microscopes. In contrast to the ease with which one can deflect electron beams, the relative difficulty to deflect X-ray has constrained the development of scanning X-ray microscopes (SXMs) based on a scan of an X-ray small probe. This restriction has caused severe complications that hinder progress toward achieving ultimate resolution. Here, a simple and innovative method for constructing an SXM equipped with a nanoprobe scanner is proposed. The nanoprobe scanner combines X-ray prisms and advanced Kirkpatrick-Baez focusing mirrors. By rotating the prisms on the order of degrees, X-ray probe scanning with single-nanometre accuracy can be easily achieved. The validity of the concept was verified by acquiring an SXM image of a test pattern at a photon energy of 10 keV, where 50 nm line-and-space structures were resolved. This method is readily applicable to an SXM with a single-nanometre resolution and will assist effective utilization of increasing brightness of fourth-generation synchrotron radiation sources.

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained "blind" ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

Parameter retrieval of small particles in dark-field Fourier ptychography and a rectangle in real-space ptychography

We present a parameter retrieval method which incorporates prior knowledge about the object into ptychography. The proposed method is applied to two applications: (1) parameter retrieval of small particles from Fourier ptychographic dark field measurements; (2) parameter retrieval of a rectangular structure with real-space ptychography. The influence of Poisson noise is discussed in the second part of the paper. The Cramér Rao Lower Bound in both applications is computed and Monte Carlo analysis is used to verify the calculated lower bound. With the computation results we report the lower bound for various noise levels and analyze the correlation of particles in application 1. For application 2 the correlation of parameters of the rectangular structure is discussed.

Virtual depth-scan multi-slice ptychography for improved three-dimensional imaging

Multi-slice ptychography (MSP) is a fast three-dimensional ptychography technology developed on the basis of conventional ptychography. With this method, three-dimensional imaging can be achieved without rotating the sample. The prototype multi-slice algorithm can only reconstruct three-dimensional samples with a limited number of slices, which greatly limits the depth range and resolution of sample imaging. Here we reported a virtual depth-scan scheme of MSP in which a thick sample is scanned virtually in the depth direction across its whole thickness range within the reconstruction process, thereby eliminating the restriction on slice number and potentially improving the depth resolution of MSP. This new approach also improves the flexibility of multi-slice ptychography. Both the simulation and experimental results validate the feasibility of our new approach.

X-Ray Ptychography with a Laboratory Source

X-ray ptychography has revolutionized nanoscale phase contrast imaging at large-scale synchrotron sources in recent years. We present here the first successful demonstration of the technique in a small-scale laboratory setting. An experiment was conducted with a liquid metal-jet x-ray source and a single photon-counting detector with a high spectral resolution. The experiment used a spot size of 5  μm to produce a ptychographic phase image of a Siemens star test pattern with a submicron spatial resolution. The result and methodology presented show how high-resolution phase contrast imaging can now be performed at small-scale laboratory sources worldwide.

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.

Adorym: a multi-platform generic X-ray image reconstruction framework based on automatic differentiation

We describe and demonstrate an optimization-based X-ray image reconstruction framework called Adorym. Our framework provides a generic forward model, allowing one code framework to be used for a wide range of imaging methods ranging from near-field holography to fly-scan ptychographic tomography. By using automatic differentiation for optimization, Adorym has the flexibility to refine experimental parameters including probe positions, multiple hologram alignment, and object tilts. It is written with strong support for parallel processing, allowing large datasets to be processed on high-performance computing systems. We demonstrate its use on several experimental datasets to show improved image quality through parameter refinement.

X-ray Ptychography Imaging of Human Chromosomes After Low-dose Irradiation

Studies of the structural and functional role of chromosomes in cytogenetics have spanned more than 10 decades. In this work, we take advantage of the coherent X-rays available at the latest synchrotron sources to extract the individual masses of all 46 chromosomes of metaphase human B and T cells using hard X-ray ptychography. We have produced 'X-ray karyotypes' of both heavy metal-stained and unstained spreads to determine the gain or loss of genetic material upon low-level X-ray irradiation doses due to radiation damage. The experiments were performed at the I-13 beamline, Diamond Light Source, Didcot, UK, using the phase-sensitive X-ray ptychography method.

Wave field reconstruction and phase imaging by electron diffractive imaging

In electron diffractive imaging, the phase image of a sample is reconstructed from its diffraction intensity through iterative calculations. The principle of this method is based on the Fourier transform relation between the real-space wave field transmitted by the sample and its Fraunhofer diffraction wave field. Since Gerchberg's experimental work in 1972, various advancements have been achieved, which have substantially improved the quality of the reconstructed phase images and extended the applicable range of the method. In this review article, the principle of diffractive imaging, various experimental processes using electron beams and application to specific samples are explained in detail.

Single-pulse phase-contrast imaging at free-electron lasers in the hard X-ray regime

X-ray free-electron lasers (XFELs) have opened up unprecedented opportunities for time-resolved nano-scale imaging with X-rays. Near-field propagation-based imaging, and in particular near-field holography (NFH) in its high-resolution implementation in cone-beam geometry, can offer full-field views of a specimen's dynamics captured by single XFEL pulses. To exploit this capability, for example in optical-pump/X-ray-probe imaging schemes, the stochastic nature of the self-amplified spontaneous emission pulses, i.e. the dynamics of the beam itself, presents a major challenge. In this work, a concept is presented to address the fluctuating illumination wavefronts by sampling the configuration space of SASE pulses before an actual recording, followed by a principal component analysis. This scheme is implemented at the MID (Materials Imaging and Dynamics) instrument of the European XFEL and time-resolved NFH is performed using aberration-corrected nano-focusing compound refractive lenses. Specifically, the dynamics of a micro-fluidic water-jet, which is commonly used as sample delivery system at XFELs, is imaged. The jet exhibits rich dynamics of droplet formation in the break-up regime. Moreover, pump-probe imaging is demonstrated using an infrared pulsed laser to induce cavitation and explosion of the jet.

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.

Broadband X-ray ptychography using multi-wavelength algorithm

Ptychography is a rapidly developing scanning microscopy which is able to view the internal structures of samples at a high resolution beyond the illumination size. The achieved spatial resolution is theoretically dose-limited. A broadband source can provide much higher flux compared with a monochromatic source; however, it conflicts with the necessary coherence requirements of this coherent diffraction imaging technique. In this paper, a multi-wavelength reconstruction algorithm has been developed to deal with the broad bandwidth in ptychography. Compared with the latest development of mixed-state reconstruction approach, this multi-wavelength approach is more accurate in the physical model, and also considers the spot size variation as a function of energy due to the chromatic focusing optics. Therefore, this method has been proved in both simulation and experiment to significantly improve the reconstruction when the source bandwidth, illumination size and scan step size increase. It is worth mentioning that the accurate and detailed information of the energy spectrum for the incident beam is not required in advance for the proposed method. Further, we combine multi-wavelength and mixed-state approaches to jointly solve temporal and spatial partial coherence in ptychography so that it can handle various disadvantageous experimental effects. The significant relaxation in coherence requirements by our approaches allows the use of high-flux broadband X-ray sources for high-efficient and high-resolution ptychographic imaging.

Multi-beam X-ray ptychography for high-throughput coherent diffraction imaging

X-ray ptychography is a rapidly developing coherent diffraction imaging technique that provides nanoscale resolution on extended field-of-view. However, the requirement of coherence and the scanning mechanism limit the throughput of ptychographic imaging. In this paper, we propose X-ray ptychography using multiple illuminations instead of single illumination in conventional ptychography. Multiple locations of the sample are simultaneously imaged by spatially separated X-ray beams, therefore, the obtained field-of-view in one scan can be enlarged by a factor equal to the number of illuminations. We have demonstrated this technique experimentally using two X-ray beams focused by a house-made Fresnel zone plate array. Two areas of the object and corresponding double illuminations were successfully reconstructed from diffraction patterns acquired in one scan, with image quality similar with those obtained by conventional single-beam ptychography in sequence. Multi-beam ptychography approach increases the imaging speed, providing an efficient way for high-resolution imaging of large extended specimens.

Nanoscale Visualization of Phase Transition in Melting of Sn-Bi Particles by In situ Hard X-ray Ptychographic Coherent Diffraction Imaging

The phase transition in the melting of Sn–Bi eutectic solder alloy particles was observed by in situ hard X-ray ptychographic coherent diffraction imaging with a pin-point heating system. Ptychographic diffraction patterns of micrometer-sized Sn–Bi particles were collected at temperatures from room temperature to 540 K. The projection images of each particle were reconstructed at a spatial resolution of 25 nm, showing differences in the phase shifts due to two crystal phases in the Sn–Bi alloy system and the Sn/Bi oxides at the surface. By quantitatively evaluating the Bi content, it became clear that the nonuniformity of the composition of Sn and Bi at the single-particle level exists when the particles are synthesized by centrifugal atomization.

PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators

The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.

Overcoming information reduced data and experimentally uncertain parameters in ptychography with regularized optimization

The overdetermination of the mathematical problem underlying ptychography is reduced by a host of experimentally more desirable settings. Furthermore, reconstruction of the sample-induced phase shift is typically limited by uncertainty in the experimental parameters and finite sample thicknesses. Presented is a conjugate gradient descent algorithm, regularized optimization for ptychography (ROP), that recovers the partially known experimental parameters along with the phase shift, improves resolution by incorporating the multislice formalism to treat finite sample thicknesses, and includes regularization in the optimization process, thus achieving reliable results from noisy data with severely reduced and underdetermined information.

Ptychography at the Linac Coherent Light Source in a parasitic geometry

X-ray free-electron lasers (FELs) are being recognized as a powerful tool in an ever-increasing number of research fields, but are very limited as to the number of experiments that they can support. This work shows that more beamtime could be made available by using `parasitic' geometries, where a secondary experiment uses the X-ray beam that the primary experiment does not utilize. The first successful ptychography experiment, a scanning coherent diffractive imaging technique, in a parasitic geometry at an X-ray FEL is demonstrated. Utilizing the CXI hutch at the Linac Coherent Light Source (LCLS), it is shown that the obtained data are of high quality and that characterizing the beam using ptychography can be much faster than traditional imprinting methods.

Potential of Attosecond Coherent Diffractive Imaging

Attosecond science has been transforming our understanding of electron dynamics in atoms, molecules, and solids. However, to date almost all of the attoscience experiments have been based on spectroscopic measurements because attosecond pulses have intrinsically very broad spectra due to the uncertainty principle and are incompatible with conventional imaging systems. Here we report an important advance towards achieving attosecond coherent diffractive imaging. Using simulated attosecond pulses, we simultaneously reconstruct the spectrum, 17 probes, and 17 spectral images of extended objects from a set of ptychographic diffraction patterns. We further confirm the principle and feasibility of this method by successfully performing a ptychographic coherent diffractive imaging experiment using a light-emitting diode with a broad spectrum. We believe this work clears the way to an unexplored domain of attosecond imaging science, which could have a far-reaching impact across different disciplines.

High-speed coherent diffraction imaging by varying curvature of illumination with a focus tunable lens

A high-speed coherent diffraction imaging method is proposed by varying the curvature of illumination with a focus tunable lens. The imaging setup is free of conventional mechanical translation and takes only milliseconds to refocus by changing the electric signal applied on the lens. It is more compact and also an inexpensive alternative to coherent diffraction imaging with computerized translational stages. A detector that is kept at a fixed distance from the sample records diffraction patterns each time the spherical wavefront illuminations on the sample is changed with a control current. The complex wavefront of the object is then quantitatively recovered from the diffraction intensity measurements using an iterative phase retrieval algorithm. The feasibility of the proposed method is experimentally verified using various samples. Extremely short response time of the focus tunable lens makes the proposed method highly suitable for applications that requires high speed imaging.

PtyNAMi: ptychographic nano-analytical microscope

Ptychographic X-ray imaging at the highest spatial resolution requires an optimal experimental environment, providing a high coherent flux, excellent mechanical stability and a low background in the measured data. This requires, for example, a stable performance of all optical components along the entire beam path, high temperature stability, a robust sample and optics tracking system, and a scatter-free environment. This contribution summarizes the efforts along these lines to transform the nanoprobe station on beamline P06 (PETRA III) into the ptychographic nano-analytical microscope (PtyNAMi).

Iterative X-ray spectroscopic ptychography

Spectroscopic ptychography is a powerful technique to determine the chemical composition of a sample with high spatial resolution. In spectro-ptychography, a sample is rastered through a focused X-ray beam with varying photon energy so that a series of phaseless diffraction data are recorded. Each chemical component in the material under investigation has a characteristic absorption and phase contrast as a function of photon energy. Using a dictionary formed by the set of contrast functions of each energy for each chemical component, it is possible to obtain the chemical composition of the material from high-resolution multi-spectral images. This paper presents SPA (spectroscopic ptychography with alternating direction method of multipliers), a novel algorithm to iteratively solve the spectroscopic blind ptychography problem. First, a nonlinear spectro-ptychography model based on Poisson maximum likelihood is designed, and then the proposed method is constructed on the basis of fast iterative splitting operators. SPA can be used to retrieve spectral contrast when considering either a known or an incomplete (partially known) dictionary of reference spectra. By coupling the redundancy across different spectral measurements, the proposed algorithm can achieve higher reconstruction quality when compared with standard state-of-the-art two-step methods. It is demonstrated how SPA can recover accurate chemical maps from Poisson-noised measurements, and its enhanced robustness when reconstructing reduced-redundancy ptychography data using large scanning step sizes is shown.

Low-dose phase retrieval of biological specimens using cryo-electron ptychography

Cryo-electron microscopy is an essential tool for high-resolution structural studies of biological systems. This method relies on the use of phase contrast imaging at high defocus to improve information transfer at low spatial frequencies at the expense of higher spatial frequencies. Here we demonstrate that electron ptychography can recover the phase of the specimen with continuous information transfer across a wide range of the spatial frequency spectrum, with improved transfer at lower spatial frequencies, and as such is more efficient for phase recovery than conventional phase contrast imaging. We further show that the method can be used to study frozen-hydrated specimens of rotavirus double-layered particles and HIV-1 virus-like particles under low-dose conditions (5.7 e/Å2) and heterogeneous objects in an Adenovirus-infected cell over large fields of view (1.14 × 1.14 μm), thus making it suitable for studies of many biologically important structures.

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.

X-ray ptychographic mode of self-assembled CdSe/CdS octapod-shaped nanocrystals in thick polymers

This work describes the application of X-ray ptychography for the inspection of complex assemblies of highly anisotropic nanocrystals embedded in a thick polymer matrix. More specifically, this case deals with CdSe/CdS octapods, with pod length L = 39 ± 2 nm and pod diameter D = 12 ± 2 nm, dispersed in free-standing thick films (24 ± 4 µm) of polymethyl methacrylate and polystyrene, with different molecular weights. Ptychography is the only imaging method available to date that can be used to study architectures made by these types of nanocrystals in thick polymeric films, as any other alternative direct method, such as scanning/transmission electron microscopy, can be definitively ruled out as a result of the large thickness of the free-standing films. The electron density maps of the investigated samples are reconstructed by combining iterative difference map algorithms and a maximum likelihood optimization algorithm. In addition, post image processing techniques are applied to both reduce noise and provide a better visualization of the material morphological details. Through this process, at a final resolution of 27 nm, the reconstructed maps allow us to visualize the intricate network of octapods inside the polymeric matrices.

Tunable hard x-ray nanofocusing with Fresnel zone plates fabricated using deep etching

Fresnel zone plates are widely used for x-ray nanofocusing, due to their ease of alignment and energy tunability. Their spatial resolution is limited in part by their outermost zone width dr N , while their efficiency is limited in part by their thickness t zp. We demonstrate the use of Fresnel zone plate optics for x-ray nanofocusing with dr N = 16 nm outermost zone width and a thickness of about t zp = 1.8 μm (or an aspect ratio of 110) with an absolute focusing efficiency of 4.7% at 12 keV, and 6.2% at 10 keV. Using partially coherent illumination at 12 keV, the zone plate delivered a FWHM focus of 46 × 60 nm at 12 keV, with the first order coherent mode in a ptychographic reconstruction showing a probe size of 16 nm FWHM. These optics were fabricated using a combination of metal assisted chemical etching and atomic layer deposition for the diffracting structures, and silicon wafer back-thinning to produce optics useful for real applications. This approach should enable new higher resolution views of thick materials, especially when energy tunability is required.

Edge-subtraction X-ray ptychographic imaging with pink beam synchrotron radiation and a single photon-counting detector

We present here a new method of performing X-ray edge-subtraction ptychographic imaging by combining multiple harmonics from an undulator synchtrotron source and an energy discriminating photon counting detector. Conventionally, monochromatic far-field X-ray ptychography is used to perform edge subtraction through the use of multiple monochromatic energy scans to obtain spectral information for a variety of applications. Here, we use directly the undulator spectrum from a synchrotron source, selecting two separate harmonics post sample using the Pixirad-1/Pixie-III detector. The result is two monochromatic images, above and below an absorption edge of interest. The proposed method is applied to obtain Au L-edge subtraction imaging of a Au-Ni grid test sample. The Au L-edge subtraction is particularly relevant for the identification of gold nanoparticles for biomedical applications. Switching the energy scan mechanism from a mechanical monochromator to an electronic detector threshold allows for faster spectral data collection with improved stability.

Direct 2D spatial-coherence determination using the Fourier-analysis method: multi-parameter characterization of the P04 beamline at PETRA III

We present a systematic 2D spatial-coherence analysis of the soft-X-ray beamline P04 at PETRA III for various beamline configurations. The influence of two different beam-defining apertures on the spatial coherence properties of the beam is discussed and optimal conditions for coherence-based experiments are found. A significant degradation of the spatial coherence in the vertical direction has been measured and sources of this degradation are identified and discussed. The Fourier-analysis method, which gives fast and simple access to the 2D spatial coherence function of the X-ray beam, is used for the experiment. Here, we exploit the charge scattering of a disordered nanodot sample allowing the use of arbitrary X-ray photon energies with this method.

Nanoscale determination of interatomic distance by ptychography-EXAFS method using advanced Kirkpatrick-Baez mirror focusing optics

This work demonstrates a combination technique of X-ray ptychography and the extended X-ray absorption fine structure (ptychography-EXAFS) method, which can determine the interatomic distances of bulk materials at the nanoscale. In the high-resolution ptychography-EXAFS method, it is necessary to use high-intense coherent X-rays with a uniform wavefront in a wide energy range, hence a ptychographic measurement system installed with advanced Kirkpatrick-Baez mirror focusing optics is developed and its performance is evaluated. Ptychographic diffraction patterns of micrometre-size MnO particles are collected by using this system at 139 energies between 6.504 keV and 7.114 keV including the Mn K absorption edge, and then the EXAFS of MnO is derived from the reconstructed images. By analyzing the EXAFS spectra obtained from a 48 nm × 48 nm region, the nanoscale bond lengths of the first and second coordination shells of MnO are determined. The present approach has great potential to elucidate the unclarified relationship among the morphology, electronic state and atomic arrangement of inhomogeneous bulk materials with high spatial resolution.

Three dimensions, two microscopes, one code: Automatic differentiation for x-ray nanotomography beyond the depth of focus limit

Conventional tomographic reconstruction algorithms assume that one has obtained pure projection images, involving no within-specimen diffraction effects nor multiple scattering. Advances in x-ray nanotomography are leading toward the violation of these assumptions, by combining the high penetration power of x-rays, which enables thick specimens to be imaged, with improved spatial resolution that decreases the depth of focus of the imaging system. We describe a reconstruction method where multiple scattering and diffraction effects in thick samples are modeled by multislice propagation and the 3D object function is retrieved through iterative optimization. We show that the same proposed method works for both full-field microscopy and for coherent scanning techniques like ptychography. Our implementation uses the optimization toolbox and the automatic differentiation capability of the open-source deep learning package TensorFlow, demonstrating a straightforward way to solve optimization problems in computational imaging with flexibility and portability.

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.

Multibeam ptychography with synchrotron hard X-rays

We report the first demonstration of multibeam ptychography using synchrotron hard X-rays, which can enlarge the field of view of the reconstructed image of objects by efficiently using partially coherent X-rays. We measured the ptychographic diffraction patterns of a Pt test sample and MnO particles using three mutually incoherent coherent beams with a high intensity that were produced by using both the multiple slits and a pair of focusing mirrors. We successfully reconstructed the phase map of the samples at a spatial resolution of 25 nm in a field of view about twice as wide as that in the single-beam ptychography. We also computationally simulated a feasible experimental setup using random modulators to further enlarge the field of view by increasing the number of available beams. The present method has the potential to enable the high spatial resolution and large field-of-view observation of specimens in materials science and biology.

Translative lens-based full-field coherent X-ray imaging

A full-field coherent imaging approach suitable for hard X-rays based on a classical (i.e. Galilean) X-ray microscope is described. The method combines a series of low-resolution images acquired at different transverse lens positions into a single high-resolution image, overcoming the spatial resolution limit set by the numerical aperture of the objective lens. The optical principles of the approach are described, the successful reconstruction of simulated phantom data is demonstrated, and aspects of the reconstruction are discussed. The authors believe that this approach offers some potential benefits over conventional scanning X-ray ptychography in terms of spatial bandwidth and radiation dose rate.

Ptychography with multiple wavelength illumination

For performing phase retrieval in the extreme ultraviolet (EUV) regime more efficiently, developing polychromatic ptychography is desirable. As an alternative to the existing ptychographic information multiplexing (PIM) method, we present an another scheme where all monochromatic exit waves are expressed in terms of the amplitude of the transmission function and the thickness function of the object. Our proposed algorithm is a gradient based method and its validity is studied numerically. In addition, the sampling issue which appears in the polychromatic ptychography scheme and its influence to the reconstruction quality are discussed.

Towards a quantitative determination of strain in Bragg Coherent X-ray Diffraction Imaging: artefacts and sign convention in reconstructions

Bragg coherent X-ray diffraction imaging (BCDI) has emerged as a powerful technique to image the local displacement field and strain in nanocrystals, in three dimensions with nanometric spatial resolution. However, BCDI relies on both dataset collection and phase retrieval algorithms that can induce artefacts in the reconstruction. Phase retrieval algorithms are based on the fast Fourier transform (FFT). We demonstrate how to calculate the displacement field inside a nanocrystal from its reconstructed phase depending on the mathematical convention used for the FFT. We use numerical simulations to quantify the influence of experimentally unavoidable detector deficiencies such as blind areas or limited dynamic range as well as post-processing filtering on the reconstruction. We also propose a criterion for the isosurface determination of the object, based on the histogram of the reconstructed modulus. Finally, we study the capability of the phasing algorithm to quantitatively retrieve the surface strain (i.e., the strain of the surface voxels). This work emphasizes many aspects that have been neglected so far in BCDI, which need to be understood for a quantitative analysis of displacement and strain based on this technique. It concludes with the optimization of experimental parameters to improve throughput and to establish BCDI as a reliable 3D nano-imaging technique.

Ptychography of pure quantum states

Ptychography is an imaging technique in which a localized illumination scans overlapping regions of an object and generates a set of diffraction intensities used to computationally reconstruct its complex-valued transmission function. We propose a quantum analogue of this technique designed to reconstruct d-dimensional pure states. A set of n rank-r projectors “scans” overlapping parts of an input state and the moduli of the d Fourier amplitudes of each part are measured. These nd outcomes are fed into an iterative phase retrieval algorithm that estimates the state. Using d up to 100 and r around d / 2, we performed numerical simulations for single systems in an economic (n = 4) and a costly (n = d) scenario, as well as for multiqubit systems (n = 6logd). This numeric study included realistic amounts of depolarization and poissonian noise, and all scenarios yielded, in general, reconstructions with infidelities below 10⁻². The method is shown, therefore, to be resilient to noise and, for any d, requires a simple and fast postprocessing algorithm. We show that the algorithm is equivalent to an alternating gradient search, which ensures that it does not suffer from local-minima stagnation. Unlike traditional approaches to state reconstruction, the ptychographic scheme uses a single measurement basis; the diversity and redundancy in the measured data—key for its success—are provided by the overlapping projections. We illustrate the simplicity of this scheme with the paradigmatic multiport interferometer.

Semi-implicit relaxed Douglas-Rachford algorithm (sDR) for ptychography

Alternating projection based methods, such as ePIE and rPIE, have been used widely in ptychography. However, they only work well if there are adequate measurements (diffraction patterns); in the case of sparse data (i.e. fewer measurements) alternating projection underperforms and might not even converge. In this paper, we propose semi-implicit relaxed Douglas-Rachford (sDR), an accelerated iterative method, to solve the classical ptychography problem. Using both simulated and experimental data, we show that sDR improves the convergence speed and the reconstruction quality relative to extended ptychographic iterative engine (ePIE) and regularized ptychographic iterative engine (rPIE). Furthermore, in certain cases when sparsity is high, sDR converges while ePIE and rPIE fail or encounter slow convergence. To facilitate others to use the algorithm, we post the Matlab source code of sDR on a public website (www.physics.ucla.edu/research/imaging/sDR/index.html). We anticipate that this algorithm can be generally applied to the ptychographic reconstruction of a wide range of samples in the physical and biological sciences.

Angular X-Ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.