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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.

Bragg coherent diffraction imaging (BCDI) provides a powerful tool for obtaining high-resolution structural information from nanocrystalline materials. Here a BCDI sample consisting of a large number of randomly oriented nanoscale crystals is considered. Ideally, only one crystal is oriented to produce a Bragg peak on the detector. However, diffraction from other crystals often produces additional signals on the detector. Before the measured diffraction patterns can be processed into structural images, scientists routinely need to manually identify and remove the `alien' intensities from sources other than the intended crystal. With the development of modern high-coherence storage rings, such as the upgraded Advanced Photon Source (APS), the already slow process of manual preprocessing will be untenable for the large volumes of data that will be produced. An automated method of identifying and deleting alien intensities is proposed. This method exploits the fact that BCDI of a perfect crystal produces diffraction data with inversion symmetry around the Bragg peak. This approach uses the machine learning clustering method DBSCAN to distinguish between diffraction from multiple sources, and then calculates cluster size and inversion symmetry to assess whether clusters of intensity belong to desired data or alien signals. This approach can dramatically reduce the amount of time spent manually processing data, allowing BCDI data processing capabilities to keep pace with the technological advances of fourth-generation synchrotron light sources.

How Compton scattering can reduce the real space resolution achievable with the Bragg coherent diffraction imaging technique is analysed., Compton scattering is generally neglected in diffraction experiments because the incoherent radiation it generates does not give rise to interference effects and therefore is negligible at Bragg peaks. However, as the scattering volume is reduced, the difference between the Rayleigh (coherent) and Compton (incoherent) contributions at Bragg peaks diminishes and the incoherent part may become substantial. The consequences can be significant for coherent diffraction imaging at high scattering angles: the incoherent radiation produces background that smears out the secondary interference fringes, affecting thus the achievable resolution of the technique. Here, a criterion that relates the object shape and the resolution is introduced. The Compton contribution for several object shapes is quantified, and it is shown that the maximum achievable resolution along different directions has a strong dependence on the crystal shape and size.

A method is presented for inferring missing low-frequency data in coherent diffraction imaging via the least-squares solution of a linear system. This gives rise to improved image reconstruction when solving the phase retrieval problem.

Coherent precipitation of ordered phases is responsible for providing exceptional high temperature mechanical properties in a wide range of compositionally complex alloys (CCAs). Ordered phases are also essential to enhance the magnetic or catalytic properties of alloyed nanoparticles. The present work aims at demonstrating the relevance of Bragg coherent diffraction imaging (BCDI) to study bulk and thin film samples or isolated nanoparticles containing coherent nanoprecipitates / ordered phases. Crystals of a few tens of nanometres are modelled with realistic interatomic potentials and relaxed after introduction of coherent ordered nanoprecipitates. Diffraction patterns from fundamental and superstructure reflections are calculated in the kinematic approximation and used as input to retrieve the strain fields using algorithmic inversion. We first tackle the case of single nanoprecipitates and show that the strain field distribution from the ordered phase is retrieved very accurately. Then, we investigate the influence of the order parameter S on the strain field retrieved from the superstructure reflections and evidence that a very accurate strain distribution can be retrieved for partially ordered phases with large and inhomogeneous strains. In a subsequent section, we evaluate the relevance of BCDI for the study of systems containing many precipitates and demonstrate that the technique is relevant for such systems. Finally, we discuss the experimental feasibility of using BCDI to image ordered phases, in the light of the new possibilities offered by the 4 th generation synchrotron sources., Comment: 33 pages, 12 figures

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.

With the transition of EUV lithography to high volume manufacturing, EUV mask metrology has become a critical requirement. At PSI, we are developing RESCAN, a lensless actinic microscope dedicated to EUV mask inspection. RESCAN is based on coherent diffraction imaging (CDI), a method that reconstructs the complex image of the sample through its diffraction spectrum measured with a CCD detector. While this approach can overcome the cons and limitations of traditional optical imaging systems, in CDI, the quality of the recorded diffraction data is crucial for the reliable reconstruction of a high-resolution image. Ultimately, the signal-to-noise ratio of the recorded diffraction data depends on several parameters, such as the reflectance of the sample, the quantum efficiency of the detector, its full well capacity, and the intensity of the illumination. This paper investigates the optimal photon flux for RESCAN and analyzes the relation between the image quality and the EUV illumination intensity for a CDI-based imaging tool dedicated to EUV mask inspection and review.

High-resolution imaging at short wavelengths from extreme ultraviolet to hard X-rays has many applications in a plethora of fields from astronomy to biology and semiconductor metrology. Unfortunately, efficient optics for these wavelengths are difficult to manufacture or have limited resolution. For this reason, in the past few years, coherent diffraction imaging (CDI) applications become widely used. In CDI, the object is illuminated by a coherent beam and the diffraction intensity is collected by a 2D pixel detector. In this process, the phase information of the diffracted light is lost. A phase retrieval algorithm is then used to reconstruct the object’s complex amplitude. Ptychography is a scanning version of coherent diffraction imaging and it is based on an iterative reconstruction algorithm that relies on the quality of the recorded diffraction intensity to converge. To obtain diffraction patterns with a high signal-to-noise ratio, a beam stop is used in many ptychography setups to avoid over-saturation and blooming effects on the detector. While using a beam stop in a ptychography setup has become common practice, the limits of affordable data loss due to beam stop have not been systematically investigated. Pixel masking is the conventional method to recover the lost frequencies. In this method, when enforcing the Fourier domain constraint, the invalid pixels are ignored. In the missing data region, the algorithm is allowed to keep the guess from the previous iteration. The illumination conditions of the ptychography experiment play a critical role in the signal recovery procedure. The diffraction pattern on the detector is the convolution of the Fourier transform of the object and the illumination. An illumination with a finite numerical aperture encodes the object information over a larger detector area. This makes the reconstruction algorithm more robust to pixel loss. We provide simulation and experimental results to demonstrate this theory.

In a coherent diffraction imaging (CDI) system, the information of the sample is retrieved from the diffraction patterns recorded by the image sensor via multiple iterations. The limited dynamic range of the image sensor restricts the resolution of the reconstructed sample information. To alleviate this problem, the high dynamic range imaging technology is adopted to increase the signal-to-noise ratio of the diffraction patterns. A sequence of raw diffraction images with differently exposure time are recorded by the image sensor. Then, they are fused to generate a high quality diffraction pattern based on the response function of the image sensor. With the fused diffraction patterns, the resolution of the coherent diffraction imaging can be effectively improved. The experiments on USAF resolution card is carried out to verify the effectiveness of our proposed method, in which the spatial resolution is improved by 1.8 times using the high dynamic range imaging technology.

In this paper, a phase retrieval method is proposed to reconstruct the high-quality image free from undesired terms in on-axis digital holography (DH) with modified coherent diffraction imaging (MCDI). A random phase plate (RPP) is applied to generate a modulated diffraction pattern which forms an on-axis digital hologram with a plane reference wave, and a proper iterative algorithm is designed to reconstruct high-quality object information from both on-axis digital hologram and modulated diffraction pattern. Numerical simulations and experiments prove that both modulus and phase distributions can be accurately reconstructed within 100 iterations while the undesired twin image and zero-order diffraction can be effectively removed, thus demonstrating the feasibility of the suggested method.

Arising in coherent diffraction imaging (CDI), the phase retrieval problem is to reconstruct a complex object by measuring only diffraction intensity patterns. Existing approaches, such as iterative Fourier algorithm (IFA), transport intensity equation (TIE) methods and matrix optimisation, result in near-optimal solutions rather than exact solutions. This paper proposes an analytic method to get the exact phase retrieval solution without relying on direct reference waves. Based on structured template windows, the object far-field phase is solved analytically from the recorded Fourier intensities, from which the exact object reconstruction can be achieved. Sufficient conditions for obtaining exact phase retrieval solution are analysed rigorously and verified by numerical simulations, which also show the robustness of the method through simulations under noises, dynamic range, nonlinear response and bad alignment. A simple experimental result is provided to demonstrate the practical feasibility of the method. It achieves analytic phase retrieval for arbitrary complex-valued objects and may be applicable to quick phase imaging.

Bragg coherent diffraction imaging (BCDI) experiments have been carried out at the Advanced Photon Source using a new cryostat system developed to achieve high mechanical stability and low vibrations. We measured the (012)LTO Bragg peak which is unique to the low-temperature orthorhombic (LTO) phase of micron-sized crystals of the high-temperature superconductor La2−xBaxCuO4 (LBCO) to study the formation of structural domains. Each time the sample was cooled into the orthorhombic phase, the diffraction pattern of domains was different. This confirms the interpretation of pinning of the lower-temperature charge density Wave domains observed in coherent resonant X-ray speckle correlation analysis experiments.

This article presents a combined approach where quantitative forward-scattering coherent diffraction imaging (CDI) is supported by crystal diffraction using 8.1 keV synchrotron X-ray radiation. The method allows the determination of the morphology, mass density and crystallinity of an isolated microscopic specimen. This approach is tested on three homogeneous samples made of different materials with different degrees of crystallinity. The mass density and morphology are revealed using three-dimensional coherent diffraction imaging with a resolution better than 36 nm. The crystallinity is extracted from the diffraction profiles measured simultaneously with coherent diffraction patterns. The presented approach extends CDI to structural characterization of samples when crystallinity aspects are of interest.

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.

The quest for understanding the structural mechanisms of material properties and biological cell functions has led to the active development of coherent diffraction imaging (CDI) and its variants in the hard X-ray regime. Herein, we propose multiple-shot CDI, a full-field CDI technique dedicated to the visualisation of local nanostructural dynamics in extended objects at a spatio-temporal resolution beyond that of current instrumentation limitations. Multiple-shot CDI reconstructs a “movie” of local dynamics from time-evolving diffraction patterns, which is compatible with a robust scanning variant, ptychography. We developed projection illumination optics to produce a probe with a well-defined illumination area and a phase retrieval algorithm, establishing a spatio-temporal smoothness constraint for the reliable reconstruction of dynamic images. The numerical simulations and proof-of-concept experiment using synchrotron hard X-rays demonstrated the capability of visualising a dynamic nanostructured object at a frame rate of 10 Hz or higher. Coherent diffraction imaging (CDI) is a lensless technique for 2D or 3D reconstruction of nanoscale structure images, where a highly coherent beam of x-rays, electrons or other wavelike particle or photon is incident on an object. The authors present a phase retrieval algorithm that takes advantage of the continuity of physical phenomena and uses it as a temporal constraint for CDI, and also present an illumination optics suitable for the method, which allow them to follow dynamic processes, as demonstrate in their proof-of-principle experiment.

We proposed a self-referenced technique for measuring the spatiotemporal characteristics of ultrashort pulses using the coherent diffraction imaging. This technique includes the wavelength spatial multiplexing coherent diffraction imaging measurement and the three-dimensional spatiotemporal amplitude and phase reconstruction. In experiment, we verified the feasibility of this technique by measuring a pulse from the femtosecond laser oscillator. Wavelength spatial multiplexing was realized by the combination of two-dimensional diffracted optical element and narrow-band-pass filter, and the amplitude and phase information of each wavelength was recovered by ePIE (extended Ptychographic Iterative Engine) algorithm. This technique can measure the three-dimensional spatiotemporal amplitude and phase information of ultrashort pulses with high resolution and simplicity. In the future, it is expected to be an effective method for the comprehensive monitoring of the spatiotemporal optical field of ultrashort pulse lasers, and will be helpful for the laser performance improvement.

Phase retrieval, or signal recovery from magnitude-only measurements, is a challenging signal processing problem. Recent progress has revealed that measurement- and computational-complexity challenges can be alleviated if the underlying signal belongs to certain low-dimensional model families, including sparsity, low-rank, or neural generative models. However, the remaining bottleneck in most of these approaches is the requirement of a carefully chosen initial signal estimate. In this paper, we assume that a portion of the signal is already known a priori as "side information" (this assumption is natural in applications such as holographic coherent diffraction imaging). When such side information is available, we show that a much simpler initialization can provably succeed with considerably reduced costs. We supplement our theory with a range of simulation results.

Bragg coherent diffractive imaging (BCDI) is a noninvasive microscopy technique that can visualize the morphology and internal lattice deviations of crystals with nanoscale spatial resolution and picometer deformation sensitivity. While BCDI has been successfully applied in various studies of materials, it is less successful for highly strained crystals. Specifically, it is difficult to correctly reconstruct the electron density of a highly strained object using conventional phase retrieval algorithms. Although various algorithms have been developed to overcome this challenge, most of them require a priori knowledge that is not always available in practice. Here we report a phase retrieval workflow that can invert diffraction patterns from multiple Bragg peaks simultaneously. The workflow is explored via simulated diffraction from crystals with various strain conditions. Reconstructions from the workflow consistently demonstrate more accurate electron density maps, in comparison with the conventional method. For highly strained crystals, the workflow improves the reliability and consistency of BCDI phase retrieval significantly.

Modern microscopy techniques are developing towards high-resolution imaging, and tremendous progress has been made in past decades; however, the imaging of individual biological macromolecules at atomic resolution using short-wavelength radiation such as electrons or X-rays has not yet been achieved. The construction of free-electron lasers in many countries around the world arises from the desire to develop new imaging techniques by employing coherent radiation to image individual macromolecules. This work deals with coherent imaging and related phase retrieval techniques, with an emphasis on their application in the imaging of individual biological macromolecules. An introduction to the imaging of non-crystalline objects with coherent waves is provided in Section 1 . An overview of experimental schemes for realizing coherent imaging is given in Section 2 . These schemes use no optical elements between the sample and the detector, in order to avoid aberrations and to achieve the highest possible resolution, limited only by diffraction. The images of samples are created using numerical reconstruction, an unusual aspect compared to conventional microscopy techniques. In coherent diffraction imaging, the result is equally dependent on the experimental setup and the numerical procedure used to recreate the structure. Section 3 describes the achievements of Professor Hans-Werner Fink's group at the University of Zurich, whose main interest is in coherent imaging with low-energy electrons. Examples of reconstructed holograms and diffraction patterns recorded with low-energy electrons are given. Section 4 describes the relevant advances that have been achieved in numerical analysis, such as three-dimensional deconvolution in holography, merging holography and CDI, and the extrapolation of recorded coherent images. The final section summarizes the future prospects of the coherent imaging of non-crystalline objects in general, and discusses prospective applications for the methods described in this work.

A learning-based dual alternating direction method of multipliers is proposed to solve the phase retrieval problem. Numerical simulations of the coded holographic coherent diffraction imaging system show the efficiency of proposed method.

To understand the function of macromolecules like proteins it helps to know the structure of the molecule. Coherent diffraction imaging is an emerging method that might be used to figure out the structures of macromolecules. In this method diffraction patterns of the macromolecule are recorded by shining light on the molecule from many unknown orientations and detecting the pattern of the diffracted photons. By assembling the diffraction patterns in a specific way and finding the phase of the photons that gave rise to the diffraction patterns, it is theoretically possible to obtain the electronstructure of the molecule and thus the molecular structure. The assembling of several thousand diffraction patterns representing unknown orientations of the molecule is hard to do by hand, but there are several methods that can be used. The EMC (Expand-Maximize-Compress) algorithm is one of those methods. It is an iterative algorithm that tries to create a model describing the Fourier Transform of the electron density of the molecule by maximizing each diffraction patterns fit to the model. This work examines how sensitive the EMC algorithm is to datasets with few diffraction patterns or a low intensity of the light being diffracted by the molecule, for the proteins phytochrome and lysozyme. The result of the work could be used to make sure enough data in collected in real experiments. Diffraction patterns simulated with the program Condor is used in this work, instead of diffraction patterns from real experiments.EMC finds the correct model when the data set contains about 1/3 fewer photons for the smaller more symmetrical molecule lysozyme than it does for phytochrome. This might be because the shapes in lysozymes diffraction patterns are larger than in phyochrome’s patterns. For phytochrome the EMC algorithm assembled the diffraction patterns correctly, with fewest photons for the light intensity 0.764 J/μm2 and 1250 diffraction patterns. For lysozyme it was with an intensity 1.910 J/μm2 and 1425 diffraction patterns. More investigation of the data is needed to understand what factors that affect the EMC algorithms ability to assemble the diffraction patterns correctly. För att förstå makromolekylers kemiska eller biologiska funktion so underlättar det om man känner till molekylens kemiska struktur. Med den nya tekniken “coherent diffraction imaging” ska det vara möjligt att lista ut makromolekylers struktur. I denna teknik detekterar man diffraktionsmönster av molekylen genom att belysa molekylen med ljus från många olika okända vinklar and registrera mönstret som skapas av det diffrakterade ljuset. Genom att sätta ihop alla dessa diffraktionsmönster på rätt sätt och sen återskapa fasen för ljuset i diffraktionsmönstret så kan man generera molekylens elektronstruktur och från elektronstrukturen kan man få tag i molekylens struktur. Att sätta ihop tio tusentals diffraktionsmönster med okända vinklar på rätt sätt är väldigt svårt att göra, men det finns flera olika metoder som kan användas. EMC (Expand-Maximize-Compress) är en sådan metod. EMC är en iterativ algoritm som skapar en modell av (Fourier transformen av) molekylens elektronstruktur genom att maximera hur bra diffraktionsmönstren passar med modellen. Detta arbete utreder hur bra EMC algoritmen är på att hitta rätt (Fourier transform av) elektronstruktur när väldigt få diffraktionsmönster används eller när intensiteten på ljuset som sprids av molekylen är lågt. Programmet Condor används för att generera teoretiska diffraktionsmönster för de 2 molekylerna lysozym och fytokrom. EMC används sedan med olika uppsättningar av intensitet och antal diffraktionsmönster för att skapa en modell av elektronstrukturen. EMC behövde ca 1/3 färre antal fotoner i sin modell för att hittar den rätta modellen av elektronstrukturen för den lilla symmetriskt formade molekylen lysozym än för fytokrom. Att det är lättare för EMC algoritmen att hitta den korrekta modellen för lysozym än fytokrom kan bero på att lysozyms diffraktionsmönster har större former/features eller på lysozyms storlek och form. EMC körningen som behövde minst antal fotoner för att hitta den korrekta elektronstrukturen för fytokrom hade intensiteten 0,764 J/μm2 på det inkommande ljuset och behövde 1250 diffraktionsmönster. För lysozym behövdes det 1,910 J/μm2 och 1425 diffraktionsmönster för att EMC algoritmen skulle hitta rätt modell av elektronstrukturen.

A deep decoder neural network is applied towards the enhancement of recent algorithms for holographic Coherent Diffraction Imaging (CDI). This method does not re- quire training data, and provides improved imaging given noisy low-photon CDI data.

Bragg coherent diffraction imaging is a powerful strain imaging tool, often limited by beam-induced sample instability for small particles and high power densities. Here, we devise and validate an adapted diffraction volume assembly algorithm, capable of recovering three-dimensional datasets from particles undergoing uncontrolled and unknown rotations. We apply the method to gold nanoparticles which rotate under the influence of a focused coherent x-ray beam, retrieving their three-dimensional shapes and strain fields. The results show that the sample instability problem can be overcome, enabling the use of fourth generation synchrotron sources for Bragg coherent diffraction imaging to their full potential. Research conducted at MAX IV, a Swedish national user facility, is supported by the Swedish Research council under Contract No. 2018-07152, the Swedish Governmental Agency for Innovation Systems under Contract No. 2018-04969, and Formas under Contract No. 2019-02496. This work has also received funding from the ÅForsk Foundation (Contract No. 17-408), the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Contract No. 801847), from the Olle Engkvist Foundation, from the Swedish Research council (Contract No. 2018-00234), and from NanoLund.

RESCAN is a coherent diffraction imaging based APMI microscope prototype. A complex image of the EUV reticle is reconstructed from diffraction patterns collected on a CCD detector. With the next upgrade of the tool, the resolution will be enhanced from the current 34 nm down to 20 nm on mask. Also the illumination NA value will change from the current range of 0.002 to 0.02 to a value of 0.035. Here, we study how a change of the illumination NA affects the EUV mask inspection in simulation. We observe a better image quality, lower object error and higher defect sensitivity with increasing illumination NA.

Conventional coherent diffraction imaging (CDI) suffers from inherent phase retrieval ambiguity due to limited intensity-only measurements. Coded illumination with multiple modulations has been introduced to tackle the underdetermination challenge, which however slows down imaging speed. In addition, the required high-dynamic-range acquisition at the Fourier plane is also time consuming. To increase imaging speed, we report an accelerated coded CDI method in this Letter. It requires only three binarized intensity patterns to illuminate the full field, which can be implemented at ∼ 22 kHz using a digital micromirror device. Each diffraction pattern at the Fourier plane is acquired in a single shot without high-dynamic-range synthesis, resulting in three intensity-only images corrupted with underexposed pixels. We develop an adaptive phase retrieval algorithm to adaptively remove the negative influence of underexposure and recover both the object’s amplitude and phase. Both simulations and experiments validate that the method enables fast and high-fidelity complex-field 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.

In this paper, we present the theoretical background to electron scattering in an atomic potential and the differences between low- and high-energy electrons interacting with matter. We discuss several interferometric techniques that can be realized with low- and high-energy electrons and which can be applied to the imaging of non-crystalline samples and individual macromolecules, including in-line holography, point projection microscopy, off-axis holography, and coherent diffraction imaging. The advantages of using low- and high-energy electrons for particular experiments are examined, and experimental schemes for holography and coherent diffraction imaging are compared.

Phase defect detection with micrometer scale on large aperture optical elements is one of the challenges in precision optical systems. An efficient scheme is proposed to detect phase defects. First, the defects are positioned in a large aperture by dark-field imaging based on large aperture photon sieves to improve the detection efficiency with a relatively low cost. Second, static multiplanar coherent diffraction imaging is used to retrieve the phase of the positioned defects in a small field of view. Here, a spatial light modulator is used as a multifocal negative lens to eliminate the mechanical errors in multiplanar imaging. The use of a negative lens instead of a positive lens has the advantage of a larger imaging space for the system configuration. Compared to the traditional interferometry system, this diffraction detection system has a simpler optical path and doesn’t require sparse distribution of the defects. Experiment results demonstrate the success of the proposed scheme with a detection resolution better than 50 µm. We believe this work provides an effective method to rapidly detect phase defects on large aperture optics with high accuracy and high resolution.

X-ray Bragg coherent diffraction imaging (BCDI) has been demonstrated as a powerful 3D microscopy approach for the investigation of sub-micrometre-scale crystalline particles. The approach is based on the measurement of a series of coherent Bragg diffraction intensity patterns that are numerically inverted to retrieve an image of the spatial distribution of the relative phase and amplitude of the Bragg structure factor of the diffracting sample. This 3D information, which is collected through an angular rotation of the sample, is necessarily obtained in a non-orthogonal frame in Fourier space that must be eventually reconciled. To deal with this, the approach currently favored by practitioners (detailed in Part I) is to perform the entire inversion in conjugate non-orthogonal real- and Fourier-space frames, and to transform the 3D sample image into an orthogonal frame as a post-processing step for result analysis. In this article, which is a direct follow-up of Part I, two different transformation strategies are demonstrated, which enable the entire inversion procedure of the measured data set to be performed in an orthogonal frame. The new approaches described here build mathematical and numerical frameworks that apply to the cases of evenly and non-evenly sampled data along the direction of sample rotation (i.e. the rocking curve). The value of these methods is that they rely on the experimental geometry, and they incorporate significantly more information about that geometry into the design of the phase-retrieval Fourier transformation than the strategy presented in Part I. Two important outcomes are (1) that the resulting sample image is correctly interpreted in a shear-free frame and (2) physically realistic constraints of BCDI phase retrieval that are difficult to implement with current methods are easily incorporated. Computing scripts are also given to aid readers in the implementation of the proposed formalisms.

The commissioning of a movable X-ray monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported. The new instrument allows indexing of nanocrystals with Laue diffraction and collecting multi-reflection BCDI data., Measurement modalities in Bragg coherent diffraction imaging (BCDI) rely on finding a signal from a single nanoscale crystal object which satisfies the Bragg condition among a large number of arbitrarily oriented nanocrystals. However, even when the signal from a single Bragg reflection with (hkl) Miller indices is found, the crystallographic axes on the retrieved three-dimensional (3D) image of the crystal remain unknown, and thus localizing in reciprocal space other Bragg reflections becomes time-consuming or requires good knowledge of the orientation of the crystal. Here, the commissioning of a movable double-bounce Si (111) monochromator at the 34-ID-C endstation of the Advanced Photon Source is reported, which aims at delivering multi-reflection BCDI as a standard tool in a single beamline instrument. The new instrument enables, through rapid switching from monochromatic to broadband (pink) beam, the use of Laue diffraction to determine crystal orientation. With a proper orientation matrix determined for the lattice, one can measure coherent diffraction patterns near multiple Bragg peaks, thus providing sufficient information to image the full strain tensor in 3D. The design, concept of operation, the developed procedures for indexing Laue patterns, and automated measuring of Bragg coherent diffraction data from multiple reflections of the same nanocrystal are discussed.

Signal-to-noise ratio, spatial resolution and information capacity of tomographic coherent diffractive imaging are investigated; the results are expected to be useful for the design and analysis of synchrotron and XFEL-based diffractive imaging experiments., It is shown that the average signal-to-noise ratio (SNR) in the three-dimensional electron-density distribution of a sample reconstructed by coherent diffractive imaging cannot exceed twice the square root of the ratio of the mean total number of scattered photons detected during the scan and the number of spatially resolved voxels in the reconstructed volume. This result leads to an upper bound on Shannon’s information capacity of this imaging method by specifying the maximum number of distinguishable density distributions within the reconstructed volume when the radiation dose delivered to the sample and the spatial resolution are both fixed. If the spatially averaged SNR in the reconstructed electron density is fixed instead, the radiation dose is shown to be proportional to the third or fourth power of the spatial resolution, depending on the sampling of the three-dimensional diffraction space and the scattering power of the sample.

It has been proposed that the radiation damage to biological particles and soft condensed matter can be overcome by ultrafast and ultraintense X-ray free-electron lasers (FELs) with short pulse durations. The successful demonstration of the "diffraction-before-destruction" concept has made single-shot diffraction imaging a promising tool to achieve high resolutions under the native states of samples. However, the resolution is still limited because of the low signal-to-noise ratio, especially for biological specimens such as cells, viruses, and macromolecular particles. Here, we present a demonstration single-shot diffraction imaging experiment of DNA-based structures at SPring-8 Angstrom Compact Free Electron Laser (SACLA), Japan. Through quantitative analysis of the reconstructed images, the scattering abilities of gold and DNA were demonstrated. Suggestions for extracting valid DNA signals from noisy diffraction patterns were also explained and outlined. To sketch out the necessary experimental conditions for the 3D imaging of DNA origami or DNA macromolecular particles, we carried out numerical simulations with practical detector noise and experimental geometry using the Linac Coherent Light Source (LCLS) at the SLAC National Accelerator Laboratory, USA. The simulated results demonstrate that it is possible to capture images of DNA-based structures at high resolutions with the technique development of current and next-generation X-ray FEL facilities.

In a traditional single beam multiple-intensity reconstruction(SBMIR) system, error is accumulated by multiple translational image sensors, which reduces the imaging effect and the effective resolution of the photoelectric imaging system. In this paper, a three-step coherent diffraction imaging system based on parallel plates is proposed. Three different diffraction planes are obtained by inserting or extracting two parallel plates and imaging and restoration reconstruction of complex amplitude objects are achieved. The numerical simulation and experiments show that the system overcomes the error accumulation problem of several translations in the SBMIR system, and one only needs to record three diffraction surfaces to avoid oversampling. The proposed optical system is easy to implement and has high repeatability.

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.

We report the improvement of an apparatus for Bragg coherent x-ray diffraction imaging (Bragg-CDI) at BL22XU in SPring-8 to expand the applicable particle size and the application of the Bragg-CDI technique for Pd and ferroelectric barium titanate (BaTiO3) fine crystals with particle sizes of 40–500 nm. Preparing a vacuum environment around the sample enabled us to obtain the high-contrast diffraction pattern of a 40-nm particle. The reconstructed three-dimensional image showed the outer shape, size, and internal phase (strain) for a single particle. A single 500-nm BaTiO3 particle showed a straight and sharp antiphase-boundary shape, whereas smaller BaTiO3 particles showed different phase boundary shapes. The present Bragg-CDI apparatus, thus, allows the observation of the outer shape, size, and inner phase distribution for a single particle with a size of 40–500 nm.

Highlights • Pulse-plating of Mn-oxide/polypyrrole nanocomposite studied in situ by ptychography. • Electrocrystallization followed in operando by dynamic coherent diffractive imaging. • Morphology and chemical state evolutions monitored in situ during electrodeposition. • Spectroscopic ptychography reveals valence distribution with nanometric resolution. • Local magnitude and phase spectra extracted from recostructued ptychographic images. Abstract Crucial for the advancement of electrochemical materials science is understanding the lateral variations in the elemental and chemical state of constituents induced by electrochemical reactions at nanoscales. This requires in situ studies to provide observables that contribute to both modeling beyond the phenomenological level and transducing exactly the functionally relevant quantities A range of X-ray coherent diffraction imaging (CDI) approaches has recently been proposed for imaging beyond the diffraction limit with potentially dramatic improvements of time resolution with chemical sensitivity. In this paper we report a selection of ptychography results obtained in situ after successive steps of electrochemically driven growth, complemented with absorption and phase spectroscopy at high lateral resolution. We demonstrate the onset of morphological instability feature formation and correlate the chemical state of Mn with local growth rate controlled by the current density distribution resulting from morphological evolution.

Coherent X-ray diffraction imaging (CXDI) is a technique for visualizing the structures of non-crystalline particles with size in the submicrometer to micrometer range in material sciences and biology. In the structural analysis of CXDI, the electron density map of a specimen particle projected along the direction of the incident X-rays can be reconstructed only from the diffraction pattern by using phase-retrieval (PR) algorithms. However, in practice, the reconstruction, relying entirely on the computational procedure, sometimes fails because diffraction patterns miss the data in small-angle regions owing to the beam stop and saturation of the detector pixels, and are modified by Poisson noise in X-ray detection. To date, X-ray free-electron lasers have allowed us to collect a large number of diffraction patterns within a short period of time. Therefore, the reconstruction of correct electron density maps is the bottleneck for efficiently conducting structure analyses of non-crystalline particles. To automatically address the correctness of retrieved electron density maps, a data analysis protocol to extract the most probable electron density maps from a set of maps retrieved from 1000 different random seeds for a single diffraction pattern is proposed. Through monitoring the variations of the phase values during PR calculations, the tendency for the PR calculations to succeed when the retrieved phase sets converged on a certain value was found. On the other hand, if the phase set was in persistent variation, the PR calculation tended to fail to yield the correct electron density map. To quantify this tendency, here a figure of merit for the variation of the phase values during PR calculation is introduced. In addition, a PR protocol to evaluate the similarity between a map of the highest figure of merit and other independently reconstructed maps is proposed. The protocol is implemented and practically examined in the structure analyses for diffraction patterns from aggregates of gold colloidal particles. Furthermore, the feasibility of the protocol in the structure analysis of organelles from biological cells is examined.

The developed reconstruction method can successfully identify the orientations of coherent X-ray diffraction patterns of an aerosol nanoparticle., The three-dimensional (3D) structural analysis of single particles using an X-ray free-electron laser (XFEL) is a new structural biology technique that enables observations of molecules that are difficult to crystallize, such as flexible biomolecular complexes and living tissue in the state close to physiological conditions. In order to restore the 3D structure from the diffraction patterns obtained by the XFEL, computational algorithms are necessary as the orientation of the incident beam with respect to the sample needs to be estimated. A program package for XFEL single-particle analysis based on the Xmipp software package, that is commonly used for image processing in 3D cryo-electron microscopy, has been developed. The reconstruction program has been tested using diffraction patterns of an aerosol nanoparticle obtained by tomographic coherent X-ray diffraction microscopy.

In recent years, X-ray ptychography has been established as a valuable tool for high-resolution imaging. Nevertheless, the spatial resolution and sensitivity in coherent diffraction imaging are limited by the signal that is detected over noise and over background scattering. Especially, coherent imaging of weakly scattering specimens suffers from incoherent background that is generated by the interaction of the central beam with matter along its propagation path in particular close to and inside of the detector. Common countermeasures entail evacuated flight tubes or detector-side beamstops, which improve the experimental setup in terms of background reduction or better coverage of high dynamic range in the diffraction patterns. Here, we discuss an alternative approach: we combine two ptychographic scans with and without beamstop and reconstruct them simultaneously taking advantage of the complementary information contained in the two scans. We experimentally demonstrate the potential of this scheme for hard X-ray ptychography by imaging a weakly scattering object composed of catalytic nanoparticles and provide the analysis of the signal-to-background ratio in the diffraction patterns.

Solid-phase epitaxy (SPE) and other three-dimensional epitaxial crystallization processes pose challenging structural and chemical characterization problems. The concentration of defects, the spatial distribution of elastic strain, and the chemical state of ions each vary with nanoscale characteristic length scales and depend sensitively on the gas environment and elastic boundary conditions during growth. The lateral or three-dimensional propagation of crystalline interfaces in SPE has nanoscale or submicron characteristic distances during typical crystallization times. An in situ synchrotron hard x-ray instrument allows these features to be studied during deposition and crystallization using diffraction, resonant scattering, nanobeam and coherent diffraction imaging, and reflectivity. The instrument incorporates a compact deposition system allowing the use of short-working-distance x-ray focusing optics. Layers are deposited using radio-frequency magnetron sputtering and evaporation sources. The deposition system provides control of the gas atmosphere and sample temperature. The sample is positioned using a stable mechanical design to minimize vibration and drift and employs precise translation stages to enable nanobeam experiments. Results of in situ x-ray characterization of the amorphous thin film deposition process for a SrTiO3/BaTiO3 multilayer illustrate implementation of this instrument., Comment: 28 pages, 6 figures

Coherent diffraction imaging using third generation synchrotron sources and x-ray free-electron lasers has been demonstrated to be an excellent tool for revealing the inner structures of a single particle. The primary challenge in imaging pure, tiny, and isolated biological specimens is obtaining a reliable reconstruction from diffraction data that have a poor signal-to-noise ratio. Thus, we developed a robust method that yields the internal density distribution of liposome vesicles immersed in a solution. By combining the guided hybrid input-output method and a new order parameter defined by the consistency of the reconstruction, we, without prior knowledge, retrieved both pure and drug-containing liposome vesicles from individual diffraction patterns. This result is currently the smallest noncrystalline biological specimen resolved by single-shot coherent diffraction microscopy.

Based on experiment and simulation results, we find that the spatial power spectrum pattern gray-level distortion has much influence on the CDI reconstruction, and the acquired pattern distortion rate should be less than 0.1.

Ptychography is a widely used lensless coherent diffraction imaging approach, in which the complex transmittance function of the object is retrieved from a set of diffraction patterns originating from overlapping sample illumination area. In this paper, we propose a normal-incidence reflection ptychographic system. The sample and detector are located on each side of the beam splitter similarly to Michelson interferometer without reference beam. This system can reveal the topographic structure of reflective samples. Compared with Michelson interferometer based off-axis digital holography, the field-of-view of the proposed reflective ptychography is unlimited by the aperture of the detector.

It is demonstrated that an object distribution can be successfully retrieved from its diffraction pattern or hologram, even if some of the measured intensity samples are missing. The maximum allowable number of missing values depends on the linear oversampling ratio σ , where the higher the value of σ , the more intensity samples can be missing. For a real-valued object, the ratio of missing pixels to the total number of pixels should not exceed (1 - 2/ σ 2 ) or (1 - 1/ σ 2 ) in the acquired diffraction pattern or hologram, respectively. For example, even 5% of the measured intensity values at an oversampling ratio of σ = 8 are sufficient to simultaneously retrieve the object distribution and the missing intensity values. It is important that the missing intensity values should not be concentrated in the centre, but should be randomly distributed over the acquired diffraction pattern.

Different studies in X-ray microscopy have arrived at conflicting conclusions about the dose efficiency of near- and far-field imaging approaches. X-ray far-field ptychography is compared with near-field holography and near-field ptychography in computer simulations. All three methods are highly dose efficient, with far-field ptychography offering slightly better low-dose imaging characteristics., 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.

Physical Review E, 99 (6), ISSN:1539-3755, ISSN:1063-651X, ISSN:1095-3787, ISSN:1550-2376

Fourier ptychography microscopy (FPM) is a recently developed computational imaging approach which surpasses the resolution barrier of a low numerical aperture (NA) imaging system. It is a powerful tool due to its ability to achieve super resolution of complex sample function, pupil aberration, LED misalignment, and beyond. However, recent studies have focused more on the optimization algorithms and set-ups instead of its theoretical background. Although some imaging laws about FPM have already been set forth, the formulas and laws are not fully defined, and the connection between diffraction theory and Fourier optics has a gap. Therefore, there exist a need for comprehensive research on physical and mathematical basis of FPM for future applications. Keeping this goal in mind, this manuscript utilizes scalar field diffraction theory to rigorously study the relationship between wavelength, the propagation mode, illumination direction of the incident wave, sample structure information and the direction of the output wave. The theoretical analysis of diffraction imaging in FPM provides a clear physical basis for not only the FPM systems, but also for the ptychography iterative engine (PIE) and any other coherent diffraction imaging techniques and systems. It can help to find the source of noise and therefore improve image quality in FPM technique and systems.

Bragg coherent diffraction imaging (BCDI) is a powerful technique to explore the local strain state and morphology of microscale crystals. The method can potentially reach nanometer-scale spatial resolution thanks to the advances in synchrotron design that dramatically increase coherent flux. However, there are experimental bottlenecks that may limit the image reconstruction quality from future high signal-to-noise ratio measurements. In this work we show that angular uncertainty of the sample orientation with respect to a fixed incoming beam is one example of such a factor, and we present a method to mitigate the resulting artifacts. On the basis of an alternative formulation of the forward problem, we design a phase retrieval algorithm which enables the simultaneous reconstruction of the object and determination of the exact angular position corresponding to each diffraction pattern in the data set. We have tested the algorithm performance on simulated data for different degrees of angular uncertainty and signal-to-noise ratio.

Optical trapping has been implemented in many areas of physics and biology as a noncontact sample manipulation technique to study the structure and dynamics of nano- and mesoscale objects. It provides a unique approach for manipulating microscopic objects without inducing undesired changes in structure. Combining optical trapping with hard X-ray microscopy techniques, such as coherent diffraction imaging and crystallography, provides a nonperturbing environment where electronic and structural dynamics of an individual particle in solution can be followed in situ. It was previously shown that optical trapping allows the manipulation of micrometer-sized objects for X-ray fluorescence imaging. However, questions remain over the ability of optical trapping to position objects for X-ray diffraction measurements, which have stringent requirements for angular stability. Our work demonstrates that dynamic holographic optical tweezers are capable of manipulating single micrometer-scale anisotropic particles in a microfluidic environment with the precision and stability required for X-ray Bragg diffraction experiments-thus functioning as an "optical goniometer." The methodology can be extended to a variety of X-ray experiments and the Bragg coherent diffractive imaging of individual particles in solution, as demonstrated here, will be markedly enhanced with the advent of brighter, coherent X-ray sources.