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Coherent diffractive imaging experiments often collect incomplete datasets containing regions that lack any measurements. These regions can arise because of beamstops, gaps between detectors, or, in tomography experiments, a missing wedge of data due to a limited sample rotation range. We describe practical and effective approaches to mitigate reconstruction artifacts by bringing uniqueness back to the phase retrieval problem. This is accomplished by looking for a solution that both matches the data and has minimum total variation, which essentially sets the unconstrained modes to reduce oscillations within the reconstruction. Two algorithms are described. The first algorithm assumes that there is an accurate estimate of the phase and can be used for pre- and post-processing. The second algorithm attempts to simultaneously minimize the total variation and recover the phase. We demonstrate the utility of these algorithms with numerical simulations and, experimentally, on a large, three-dimensional dataset.

Coherent diffractive imaging with X‐ray free‐electron lasers could enable structural studies of macromolecules at room temperature. This type of experiment could provide a means to study structural dynamics on the femtosecond timescale. However, the diffraction from a single protein is weak compared with the incoherent scattering from background sources, which negatively affects the reconstruction analysis. This work evaluates the effects of the presence of background on the analysis pipeline. Background measurements from the European X‐ray Free‐Electron Laser were combined with simulated diffraction patterns and treated by a standard reconstruction procedure, including orientation recovery with the expand, maximize and compress algorithm and 3D phase retrieval. Background scattering did have an adverse effect on the estimated resolution of the reconstructed density maps. Still, the reconstructions generally worked when the signal‐to‐background ratio was 0.6 or better, in the momentum transfer shell of the highest reconstructed resolution. The results also suggest that the signal‐to‐background requirement increases at higher resolution. This study gives an indication of what is possible at current setups at X‐ray free‐electron lasers with regards to expected background strength and establishes a target for experimental optimization of the background. [ABSTRACT FROM AUTHOR]

New properties and exotic quantum phenomena can form due to periodic nanotextures, including Moire patterns, ferroic domains, and topologically protected magnetization and polarization textures. Despite the availability of powerful tools to characterize the atomic crystal structure, the visualization of nanoscale strain-modulated structural motifs remains challenging. Here, we develop nondestructive real-space imaging of periodic lattice distortions in thin epitaxial films and report an emergent periodic nanotexture in a Mott insulator. Specifically, we combine iterative phase retrieval with unsupervised machine learning to invert the diffuse scattering pattern from conventional X-ray reciprocal-space maps into real-space images of crystalline displacements. Our imaging in PbTiO3/SrTiO3 superlattices exhibiting checkerboard strain modulation substantiates published phase-field model calculations. Furthermore, the imaging of biaxially strained Mott insulator Ca2RuO4 reveals a strain-induced nanotexture comprised of nanometer-thin metallic-structure wires separated by nanometer-thin Mott-insulating-structure walls, as confirmed by cryogenic scanning transmission electron microscopy (cryo-STEM). The nanotexture in Ca2RuO4 film is induced by the metal-to-insulator transition and has not been reported in bulk crystals. We expect the phasing of diffuse X-ray scattering from thin crystalline films in combination with cryo-STEM to open a powerful avenue for discovering, visualizing, and quantifying the periodic strain-modulated structures in quantum materials. [ABSTRACT FROM AUTHOR]

Phase retrieval is an important optimization problem that occurs, for example, in the analysis of coherent diffraction patterns from isolated proteins. All iterative algorithms employed for phase retrieval in this context require some a priori knowledge of the object, usually in the form of a support that describes the extent of the particle. Phase retrieval is a time-consuming task that can often fail, particularly if the support is too loose or of bad quality. This paper presents a neural network that can produce low-resolution estimates of the phased object in a fraction of the time it takes for a full phase retrieval. It can also successfully be used as support for further analysis. Our network is trained on simulated data from biological macromolecules and is thus tailored to the type of data seen in a typical CDI experiment. Other approaches to support finding require very accurate data without missing regions or the full phase-retrieval algorithm to be run for a long time. Our network could speed up offline analysis and provide real-time feedback during data collection.

We present a deep learning-based generative model for the enhancement of partially coherent diffractive images. In lensless coherent diffractive imaging, a highly coherent X-ray illumination is required to image an object at high resolution. Non-ideal experimental conditions result in a partially coherent X-ray illumination, lead to imperfections of coherent diffractive images recorded on a detector, and ultimately limit the capability of lensless coherent diffractive imaging. The previous approaches, relying on the coherence property of illumination, require preliminary experiments or expensive computations. In this article, we propose a generative adversarial network (GAN) model to enhance the visibility of fringes in partially coherent diffractive images. Unlike previous approaches, the model is trained to restore the latent sharp features from blurred input images without finding coherence properties of illumination. We demonstrate that the GAN model performs well with both coherent diffractive imaging and ptychography. It can be applied to a wide range of imaging techniques relying on phase retrieval of coherent diffraction patterns.

Over the last decade ptychography has progressed rapidly from a specialist ultramicroscopy technique into a mature method accessible to non-expert users. However, to improve scientific value ptychography data must reconstruct reliably, with high image quality and at no cost to other correlative methods. Presented here is the implementation of high-speed ptychography used at the Australian Synchrotron on the XFM beamline, which includes a free-run data collection mode where dead time is eliminated and the scan time is optimized. It is shown that free-run data collection is viable for fast and high-quality ptychography by demonstrating extremely high data rate acquisition covering areas up to 352 000 µm2 at up to 140 µm2 s−1, with 13× spatial resolution enhancement compared with the beam size. With these improvements, ptychography at velocities up to 250 µm s−1 is approaching speeds compatible with fast-scanning X-ray fluorescence microscopy. The combination of these methods provides morphological context for elemental and chemical information, enabling unique scientific outcomes.

X‐ray coherent diffractive imaging (CDI) techniques have been applied with widespread impact to study nanoscale material properties. New fast framing detectors may reveal dynamics that occur at millisecond timescales. This work demonstrates by simulation that kilohertz synchrotron CDI is possible, by making use of redundant information from static parts of the image field. Reconstruction ambiguities are strongly suppressed by applying a spatiotemporal constraint, obviating the need for slower methods of introducing diversity such as ptychography. The relationship between image fidelity and time resolution is investigated and shows that dynamics an order of magnitude faster can be reconstructed, compared with conventional CDI. [ABSTRACT FROM AUTHOR]

We present a deep learning-based generative model for the enhancement of partially coherent diffractive images. In lensless coherent diffractive imaging, a highly coherent X-ray illumination is required to image an object at high resolution. Non-ideal experimental conditions result in a partially coherent X-ray illumination, lead to imperfections of coherent diffractive images recorded on a detector, and ultimately limit the capability of lensless coherent diffractive imaging. The previous approaches, relying on the coherence property of illumination, require preliminary experiments or expensive computations. In this article, we propose a generative adversarial network (GAN) model to enhance the visibility of fringes in partially coherent diffractive images. Unlike previous approaches, the model is trained to restore the latent sharp features from blurred input images without finding coherence properties of illumination. We demonstrate that the GAN model performs well with both coherent diffractive imaging and ptychography. It can be applied to a wide range of imaging techniques relying on phase retrieval of coherent diffraction patterns. [ABSTRACT FROM AUTHOR]

Over the last decade ptychography has progressed rapidly from a specialist ultramicroscopy technique into a mature method accessible to non‐expert users. However, to improve scientific value ptychography data must reconstruct reliably, with high image quality and at no cost to other correlative methods. Presented here is the implementation of high‐speed ptychography used at the Australian Synchrotron on the XFM beamline, which includes a free‐run data collection mode where dead time is eliminated and the scan time is optimized. It is shown that free‐run data collection is viable for fast and high‐quality ptychography by demonstrating extremely high data rate acquisition covering areas up to 352 000 µm2 at up to 140 µm2 s−1, with 13× spatial resolution enhancement compared with the beam size. With these improvements, ptychography at velocities up to 250 µm s−1 is approaching speeds compatible with fast‐scanning X‐ray fluorescence microscopy. The combination of these methods provides morphological context for elemental and chemical information, enabling unique scientific outcomes. [ABSTRACT FROM AUTHOR]

Single‐particle X‐ray diffractive imaging (SPI) of small (bio‐)nanoparticles (NPs) requires optimized injectors to collect sufficient diffraction patterns to allow for the reconstruction of the NP structure with high resolution. Typically, aerodynamic lens‐stack injectors are used for NP injection. However, current injectors were developed for larger NPs (>100 nm), and their ability to generate high‐density NP beams suffers with decreasing NP size. Here, an aerodynamic lens‐stack injector with variable geometry and a geometry‐optimization procedure are presented. The optimization for 50 nm gold‐NP (AuNP) injection using a numerical‐simulation infrastructure capable of calculating the carrier‐gas flow and the particle trajectories through the injector is also introduced. The simulations were experimentally validated using spherical AuNPs and sucrose NPs. In addition, the optimized injector was compared with the standard‐installation 'Uppsala injector' for AuNPs. Results for these heavy particles showed a shift in the particle‐beam focus position rather than a change in beam size, which results in a lower gas background for the optimized injector. Optimized aerodynamic lens‐stack injectors will allow one to increase NP beam density, reduce the gas background, discover the limits of current injectors and contribute to structure determination of small NPs using SPI. [ABSTRACT FROM AUTHOR]

In many fields of science, it is often impossible to preserve the information about the phase of the electromagnetic field, and only the information about the magnitude is available. This is known as the phase problem. Various algorithms have been proposed to recover the information about phase from intensity measurements. Nowadays, iterative algorithms of phase retrieval have become popular. Many of these algorithms are based on modulating the object under study with several masks and retrieving the missing information about the phase of an object by applying mathematical optimization methods. Several of these algorithms are able to retrieve not only the phase but also the magnitude of the object under study. In this study, we investigate the effect of the range of modulation of a mask on the accuracy of the retrieved magnitude and phase map. We conclude that there is a sharp boundary of the range of modulation separating the successfully retrieved magnitude and phase maps from those retrieved unsuccessfully. A decrease in the range of modulation affects the accuracy of the retrieved magnitude and phase map differently. [ABSTRACT FROM AUTHOR]

Phase retrieval occurs in many research areas. There are some classical phase retrieval methods such as hybrid input-output (HIO) and difference map (DM). However, phase retrieval results are sensitive to noise, and the reconstructed images always include artefacts. In this paper, we use the DM algorithm together with DNN to get better phase retrieval results. We train one deep neural network using amplitude images and phase images, respectively. First, using DM, we get initial reconstructed amplitude and phase results. Then, using DNN improves both amplitude and phase results. Finally, using the DM algorithm again improves the DNN results further. The numerical experimental results show that using DM gives better results than HIO, and using DNN improves phase information better than just using DNN to train for amplitude information alone. Compared with only using DNN improves amplitude methods, our method using DM plus DNN plus DM yields a better reconstruction performance for both amplitude and phase. [ABSTRACT FROM AUTHOR]

NanoMAX is the first hard X‐ray nanoprobe beamline at the MAX IV laboratory. It utilizes the unique properties of the world's first operational multi‐bend achromat storage ring to provide an intense and coherent focused beam for experiments with several methods. In this paper we present the beamline optics design in detail, show the performance figures, and give an overview of the surrounding infrastructure and the operational diffraction endstation. [ABSTRACT FROM AUTHOR]

With the emergence of X-ray free-electron lasers, it is possible to investigate the structure of nanoscale samples by employing coherent diffractive imaging in the X-ray spectral regime. In this work, we developed a refinement method for structure reconstruction applicable to low-quality coherent diffraction data. The method is based on the gradient search method and considers the missing region of a diffraction pattern and the small number of detected photons. We introduced an initial estimate of the structure in the method to improve the convergence. The present method is applied to an experimental diffraction pattern of an Xe cluster obtained in an X-ray scattering experiment at the SPring-8 Angstrom Compact free-electron LAser (SACLA) facility. It is found that the electron density is successfully reconstructed from the diffraction pattern with a large missing region, with a good initial estimate of the structure. The diffraction pattern calculated from the reconstructed electron density reproduced the observed diffraction pattern well, including the characteristic intensity modulation in each ring. Our refinement method enables structure reconstruction from diffraction patterns under difficulties such as missing areas and low diffraction intensity, and it is potentially applicable to the structure determination of samples that have low scattering power.

With the development of fourth‐generation synchrotron sources, coherent diffractive imaging (CDI) will be a mainstream method for 3D structure determination at nanometre resolution. The partial coherence of incident X‐rays plays a critical role in the reconstructed image quality. Here a wave optics model is proposed to analyze the effect of partial coherence on CDI for an actual beamline layout, based on the finite size of the source and the influence of the optics on the wavefront. Based on this model, the light field distribution at any plane, the coherence between any two points on this plane and CDI experiments can be simulated. The plane‐wave CDI simulation result also shows that in order to reconstruct good image quality of complex samples the visibility of the interference fringes of any two points in the horizontal and vertical directions of the incident light field at the sample needs to be higher than 0.95. [ABSTRACT FROM AUTHOR]

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.

Diffraction before destruction using X-ray free-electron lasers (XFELs) has the potential to determine radiation-damage-free structures without the need for crystallization. This article presents the three-dimensional reconstruction of the Melbournevirus from single-particle X-ray diffraction patterns collected at the LINAC Coherent Light Source (LCLS) as well as reconstructions from simulated data exploring the consequences of different kinds of experimental sources of noise. The reconstruction from experimental data suffers from a strong artifact in the center of the particle. This could be reproduced with simulated data by adding experimental background to the diffraction patterns. In those simulations, the relative density of the artifact increases linearly with background strength. This suggests that the artifact originates from the Fourier transform of the relatively flat background, concentrating all power in a central feature of limited extent. We support these findings by significantly reducing the artifact through background removal before the phase-retrieval step. Large amounts of blurring in the diffraction patterns were also found to introduce diffuse artifacts, which could easily be mistaken as biologically relevant features. Other sources of noise such as sample heterogeneity and variation of pulse energy did not significantly degrade the quality of the reconstructions. Larger data volumes, made possible by the recent inauguration of high repetition-rate XFELs, allow for increased signal-to-background ratio and provide a way to minimize these artifacts. The anticipated development of three-dimensional Fourier-volume-assembly algorithms which are background aware is an alternative and complementary solution, which maximizes the use of data.

Ptychography is a coherent diffractive imaging technique that can determine how an electron wave is transmitted through an object by probing it in many small overlapping regions and processing the diffraction data obtained at each point. The resulting electron transmission model describes both phase and amplitude changes to the electron wave. Ptychography has been adopted in transmission electron microscopy in recent years following advances in high-speed direct electron detectors and computer algorithms which now make the technique suitable for practical applications. Its ability to retrieve quantitative phase information at high spatial resolution makes it a plausible alternative or complement to electron holography. Furthermore, unlike off-axis electron holography, it can provide phase information without an electron bi-prism assembly or the requirement of a minimally structured region adjacent to the region of interest in the object. However, it does require a well-calibrated scanning transmission electron microscope and a well-managed workflow to manage the calibration, data acquisition and reconstruction process to yield a practical technique. Here we detail this workflow and highlight how this is greatly assisted by acquisition management software. Through experimental data and modelling we also explore the similarities and differences between high-resolution ptychography and electron holography. Both techniques show a dependence of the recovered phase on the crystalline orientation of the material which is attributable to dynamical scattering. However, the exact nature of the variation differs reflecting fundamental expectations, but nonetheless equally useful information is obtained from electron holography and the ptychographically determined object transmission function. [ABSTRACT FROM AUTHOR]

Basic coherent diffraction imaging methods strongly rely on having a highly coherent illumination in order to reconstruct the phase accurately. However, regardless of considering the turbulent transport medium, the instability of the system or the generation mechanism of the light source, partially coherent illumination is more common in real case. In this paper, we proposed an efficient microscopic phase imaging method to study normal and abnormal cervical exfoliated cells. By applying three phase modulations in a single point of the sample's transmitted field, the phase can be retrieved with correspoding three intensities under partially coherent illumination. Compared with intensity map, we can efficiently and clearly judge the proportion of high density shrinking abnormal cells from the phase distributions, which provides a confident analysis and evaluation basis for early medical diagnosis of cervical cancer. This study also has potential applications in noninvasive optical imaging of dynamic biological tissues. [ABSTRACT FROM AUTHOR]

The free expansion of a planar plasma surface is a fundamental non-equilibrium process relevant for various fields but as-yet experimentally still difficult to capture. The significance of the associated spatiotemporal plasma motion ranges from astrophysics and controlled fusion to laser machining, surface high-harmonic generation, plasma mirrors, and laser-driven particle acceleration. Here, we show that x-ray coherent diffractive imaging can surpass existing approaches and enables the quantitative real-time analysis of the sudden free expansion of laser-heated nanoplasmas. For laser-ionized SiO _2 nanospheres, we resolve the formation of the emerging nearly self-similar plasma profile evolution and expose the so far inaccessible shell-wise expansion dynamics including the associated startup delay and rarefaction front velocity. Our results establish time-resolved diffractive imaging as an accurate quantitative diagnostic platform for tracing and characterizing plasma expansion and indicate the possibility to resolve various laser-driven processes including shock formation and wave-breaking phenomena with unprecedented resolution.

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

X-ray diffraction is a technique to study the structure of materials at spatial resolutions up to an atomic scale. In the field of life science, the X-ray diffraction technique is especially suited to study materials having periodical structures, such as protein crystals, nucleic acids, and muscle. Among others, muscle is a dynamic structure and the molecular events occurring during muscle contraction have been the main interest among muscle researchers. In early days, the laboratory X-ray generators were unable to deliver X-ray flux strong enough to resolve the dynamic molecular events in muscle. This situation has dramatically been changed by the advent of intense synchrotron radiation X-rays and advanced detectors, and today X-ray diffraction patterns can be recorded from muscle at sub-millisecond time resolutions. In this review, we shed light mainly on the technical aspects of the history and the current status of the X-ray diffraction studies on muscle and discuss what will be made possible for muscle studies by the advance of new techniques. [ABSTRACT FROM AUTHOR]

During the last five years, serial femtosecond crystallography using X-ray laser pulses has been developed into a powerful technique for determining the atomic structures of protein molecules from micrometre- and sub-micrometre-sized crystals. One of the key reasons for this success is the `self-gating' pulse effect, whereby the X-ray laser pulses do not need to outrun all radiation damage processes. Instead, X-ray-induced damage terminates the Bragg diffraction prior to the pulse completing its passage through the sample, as if the Bragg diffraction were generated by a shorter pulse of equal intensity. As a result, serial femtosecond crystallography does not need to be performed with pulses as short as 5–10 fs, but can succeed for pulses 50–100 fs in duration. It is shown here that a similar gating effect applies to single-molecule diffraction with respect to spatially uncorrelated damage processes like ionization and ion diffusion. The effect is clearly seen in calculations of the diffraction contrast, by calculating the diffraction of the average structure separately to the diffraction from statistical fluctuations of the structure due to damage (`damage noise'). The results suggest that sub-nanometre single-molecule imaging with 30–50 fs pulses, like those produced at currently operating facilities, should not yet be ruled out. The theory presented opens up new experimental avenues to measure the impact of damage on single-particle diffraction, which is needed to test damage models and to identify optimal imaging conditions.

A structural understanding of whole cells in three dimensions at high spatial resolution remains a significant challenge and, in the case of X-rays, has been limited by radiation damage. By alleviating this limitation, cryogenic coherent diffractive imaging (cryo-CDI) can in principle be used to bridge the important resolution gap between optical and electron microscopy in bio-imaging. Here, the first experimental demonstration of cryo-CDI for quantitative three-dimensional imaging of whole frozen-hydrated cells using 8 keV X-rays is reported. As a proof of principle, a tilt series of 72 diffraction patterns was collected from a frozen-hydrated Neospora caninum cell and the three-dimensional mass density of the cell was reconstructed and quantified based on its natural contrast. This three-dimensional reconstruction reveals the surface and internal morphology of the cell, including its complex polarized sub-cellular structure. It is believed that this work represents an experimental milestone towards routine quantitative three-dimensional imaging of whole cells in their natural state with spatial resolutions in the tens of nanometres.

A numerical simulation infrastructure capable of calculating the flow of gas and the trajectories of particles through an aerodynamic lens injector is presented. The simulations increase the fundamental understanding and predict optimized injection geometries and parameters. Our simulation results were compared to previous reports and also validated against experimental data for 500 nm polystyrene spheres from an aerosol-beam-characterization setup. The simulations yielded a detailed understanding of the radial phase-space distribution and highlighted weaknesses of current aerosol injectors for single-particle diffractive imaging. With the aid of these simulations we developed new experimental implementations to overcome current limitations. [ABSTRACT FROM AUTHOR]

The present work reports novel soft X-ray Fresnel CDI ptychography results, demonstrating the potential of this method for dynamic in situ studies. Specifically, in situ ptychography experiments explored the electrochemical fabrication of Co-doped Mn-oxide/polypyrrole nanocomposites for sustainable and cost-effective fuel-cell air-electrodes. Oxygen-reduction catalysts based on Mn-oxides exhibit relatively high activity, but poor durability: doping with Co has been shown to improve both reduction rate and stability. In this study, we examine the chemical state distribution of the catalytically crucial Co dopant to elucidate details of the Co dopant incorporation into the Mn/polymer matrix. The measurements were performed using a custom-made three-electrode thin-layer microcell, developed at the TwinMic beamline of Elettra Synchrotron during a series of experiments that were continued at the SXRI beamline of the Australian Synchrotron. Our time-resolved ptychography-based investigation was carried out in situ after two representative growth steps, controlled by electrochemical bias. In addition to the observation of morphological changes, we retrieved the spectroscopic information, provided by multiple ptychographic energy scans across Co L3-edge, shedding light on the doping mechanism and demonstrating a general approach for the molecular-level investigation complex multimaterial electrodeposition processes. [ABSTRACT FROM AUTHOR]

By using phase retrieval, Bragg coherent diffractive imaging (BCDI) allows tracking of three-dimensional displacement fields inside individual nanocrystals. Nevertheless, during structural phase transformations, significant strains (1% and higher) are common, and BCDI fails due to the Bragg peak distortions. Here we present and advanced BCDI algorithm enabling imaging three-dimensional strain fields in highly strained crystals with separated structural phases. We test the algorithm on particles simulated to undergo a structural phase transformation. While the conventional algorithms fail in unambiguously reconstructing the phase morphology, our algorithm correctly retrieves the morphology of coexistent phases with a strain difference of 1%. The key novelty is the simultaneous reconstruction of multiple scans of the same nanoparticle at snapshots through the phase transformations. The algorithm enables visualizing phase transformations in nanoparticles of lithium-ion, sodium-ion nanoparticles, and other nanoparticulate materials in working conditions (operando).

The ability to record large field-of-view images without a loss in spatial resolution is of crucial importance for imaging science. For most imaging techniques however, an increase in field-of-view comes at the cost of decreased resolution. Here we present a novel extension to ptychographic coherent diffractive imaging that permits simultaneous full-field imaging of multiple locations by illuminating the sample with spatially separated, interfering probes. This technique allows for large field-of-view imaging in amplitude and phase while maintaining diffraction-limited resolution, without an increase in collected data i.e. diffraction patterns acquired. [ABSTRACT FROM AUTHOR]

A single-channel encryption method for color images is proposed using chessboard grating and a phase-retrieval algorithm in the Fresnel domain. The pixel sampling operation is introduced to convert the color image to be encrypted into a Bayer image. Thereafter, with a single channel, the Bayer image is encoded by the chessboard grating before being sent into a diffractive-imaging-based encryption scheme. The cryptosystem is simple owing to only one single intensity pattern being required during encryption. In the decryption procedure, the phase-retrieval algorithm and the chessboard grating are combined to extract the plaintext from the intensity pattern. This proposal not only can successfully encrypt a color image into a single diffractive intensity pattern but also can recover the primary color image with high quality from the one single diffraction pattern with a compact optical setup. Numerical simulations are carried out to prove the feasibility and validity of the proposal. [ABSTRACT FROM AUTHOR]

Coherent diffractive imaging (CDI) or lensless microscopy has recently been of great interest as a promising alternative to electron microscopy in achieving atomic spatial resolution. Reconstruction of images in real space from a single experimental diffraction pattern in CDI is based on applying iterative phase-retrieval (IPR) algorithms, such as the hybrid input-output and the error reduction algorithms. For noisy data, these algorithms might suffer from stagnation or trapping in local minima. Generally, the different local minima have many common as well as complementary features and might provide useful information for an improved estimate of the object. Therefore, a linear combination of a number of chosen minima, termed a basis set, gives an educated initial estimate, which might accelerate the search for the global solution. In this study, a genetic algorithm (GA) is combined with an IPR algorithm to tackle the stagnation and trapping in phase-retrieval problems. The combined GA-IPR has been employed to reconstruct an irregularly shaped hole and has proven to be reliable and robust. With the concept of basis set, it is strongly believed that many effective local and global optimization frameworks can be combined in a similar manner to solve the phase problem. [ABSTRACT FROM AUTHOR]

The paradigm shift of the semiconductor industry moving from deep ultraviolet to extreme ultraviolet lithography (EUVL) brought about new challenges in the fabrication of illumination and projection optics, which constitute one of the core sources of cost of ownership for many of the metrology tools needed in the lithography process. For this reason, lensless imaging techniques based on coherent diffractive imaging started to raise interest in the EUVL community. This paper presents an overview of currently on-going research endeavors that use a number of methods based on lensless imaging with coherent light. [ABSTRACT FROM AUTHOR]

An overview of several ptychographic phase retrieval methods and the theory behind them is presented. By looking into the theory behind more basic single-intensity pattern phase retrieval methods, a theoretical framework is provided for analyzing ptychographic algorithms. Extensions of ptychographic algorithms that deal with issues such as partial coherence, thick samples, or uncertainties of the probe or probe positions are also discussed. This introduction is intended for scientists and students without prior experience in the field of phase retrieval or ptychography to quickly get introduced to the theory, so that they can put the more specialized literature in context more easily. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A table-top coherent diffractive imaging experiment on a sample with biological-like characteristics using a focused narrow-bandwidth high harmonic source around 30 nm is performed. An approach involving a beam stop and a new reconstruction algorithm to enhance the quality of reconstructed the image is described. [ABSTRACT FROM AUTHOR]

This work presents a numerical study of the fluence-resolution behaviour for two coherent lensless X-ray imaging techniques. To this end the fluence-resolution relationship of inline near-field holography and far-field coherent diffractive imaging are compared in numerical experiments. To achieve this, the phase reconstruction is carried out using iterative phase-retrieval algorithms on simulated noisy data. Using the incident photon fluence on the specimen as the control parameter, the achievable resolution for two example phantoms (cell and bitmap) is studied. The results indicate the superior performance of holography compared with coherent diffractive imaging, for the same fluence and phase-reconstruction procedure. [ABSTRACT FROM AUTHOR]

Thermus thermophilus is reportedly polyploid and carries four to five identical genome copies per cell, based on molecular biological experiments. To directly detect polyploidy in this bacterium, we performed live cell imaging by X-ray free-electron laser (XFEL) diffraction and observed its internal structures. The use of femtosecond XFEL pulses enables snapshots of live, undamaged cells. For successful XFEL imaging, we developed a bacterial culture method using a starch- and casein-rich medium that produces a predominance of rod-shaped cells shorter than the focused XFEL beam size, which is slightly smaller than 2 µm. When cultured in the developed medium, the length of T. thermophilus cells, which is typically ~4 µm, was less than half its usual length. We placed living cells in a micro-liquid enclosure array and successively exposed each enclosure to a single XFEL pulse. A cell image was successfully obtained by the coherent diffractive imaging technique with iterative phase retrieval calculations. The reconstructed cell image revealed five peaks, which are most likely to be nucleoids, arranged in a row in the polyploid cell without gaps. This study demonstrates that XFELs offer a novel approach for visualizing the internal nanostructures of living, micrometer-sized, polyploid bacterial cells.

Understanding the lateral variations in the elemental and chemical state of constituents induced by electrochemical reactions at nanoscales is crucial for the advancement of electrochemical materials science. This requires in situ studies to provide observables that contribute to both modeling beyond the phenomenological level and exactly transducing the functionally relevant quantities. A range of X-ray coherent diffraction imaging (CDI) approaches have recently been proposed for imaging beyond the diffraction limit with potentially dramatic improvements in time resolution with chemical sensitivity. In this paper, we report a selection of ptychography results obtained in situ during the electrodeposition of a metal-polymer nanocomposite. Our selection includes dynamic imaging during electrochemically driven growth complemented with absorption and phase spectroscopy with high lateral resolution. We demonstrate the onset of morphological instability feature formation and correlate the chemical state of Mn with the local growth rate controlled by the current density distribution resulting from morphological evolution. [ABSTRACT FROM AUTHOR]

For the successful implementation of extreme ultraviolet (EUV) lithography in the upcoming technology nodes, a major challenge to overcome is the stable and reliable detection and characterization of mask defects. We have recently presented a reflective mode EUV mask scanning lensless imaging tool (RESCAN) which was installed at the XIL-II beamline of the swiss light source and showed reconstructed aerial images of test patterns on EUV masks. RESCAN uses scanning coherent diffractive imaging (SCDI) methods to obtain actinic aerial images of EUV photomasks and was designed for 80 nm onmask resolution. Our SCDI algorithm reconstructs the measured sample by iteratively solving the phase problem using overdetermined diffraction data gathered by scanning across the specimen with a finite illumination. It provides the phase and amplitude aerial images of EUV photomasks with high resolution without the need to use high numerical aperture (NA) lenses. Contrary to scanning microscopy and full-field microscopy, where the resolution is limited by the spot size or NA of the lens, the achievable resolution with our method depends on the detector noise and NA of the detector. To increase the resolution of our tool, we upgraded RESCAN with a detector and algorithms. Here, we present the results obtained with the tool that is capable of up to 40-nm onmask resolution. We believe that the realization of our prototype marks a significant step toward overcoming the limitations imposed by methods relying on imaging optics and shows a viable solution for actinic mask metrology. [ABSTRACT FROM AUTHOR]

The pressure dependent high-order harmonic generation in a semi-infinite gas cell with two different absorbing gaseous media (argon and helium) is analyzed to reveal the influence of absorption on the radiation process in the extreme ultraviolet region. The absorption cross section of a particular wavelength in this region is measured. Moreover, in consideration of macroscopic response, the geometrical phase mismatch and the dipole phase mismatch which are independent to the pressure are clearly studied. A Young's double slit experiment is also performed to indicate a high spatial coherence of the harmonic radiation. This measurement shows that a narrow bandwidth, bright, and highly coherent high harmonic source can be generated in gas cell filled with absorbing gases which could be useful for coherent diffractive imaging. [ABSTRACT FROM AUTHOR]

By introducing the theta modulation technique into the diffractive-imaging-based optical scheme, we propose a novel approach for color image encryption. For encryption, a color image is divided into three channels, i.e., red, green and blue, and thereafter these components are appended by redundant data before being sent to the encryption scheme. The carefully designed optical setup, which comprises of three 4f optical architectures and a diffractive-imaging-based optical scheme, could encode the three plaintexts into a single noise-like intensity pattern. For the decryption, an iterative phase retrieval algorithm, together with a filter operation, is applied to extract the primary color images from the diffraction intensity map. Compared with previous methods, our proposal has successfully encrypted a color rather than grayscale image into a single intensity pattern, as a result of which the capacity and practicability have been remarkably enhanced. In addition, the performance and the security of it are also investigated. The validity as well as feasibility of the proposed method is supported by numerical simulations. [ABSTRACT FROM AUTHOR]