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The inherent ambiguity in reconstructed images from coherent diffraction imaging (CDI) poses an intrinsic challenge, as images derived from the same dataset under varying initial conditions often display inconsistencies. This study introduces a method that employs the Noise2Noise approach combined with neural networks to effectively mitigate these ambiguities. We applied this methodology to hundreds of ambiguous reconstructed images retrieved from a single diffraction pattern using a conventional retrieval algorithm. Our results demonstrate that ambiguous features in these reconstructions are effectively treated as inter-reconstruction noise and are significantly reduced. The post-Noise2Noise treated images closely approximate the average and singular value decomposition analysis of various reconstructions, providing consistent and reliable reconstructions.

The inherent ambiguity in reconstructed images from coherent diffraction imaging (CDI) poses an intrinsic challenge, as images derived from the same dataset under varying initial conditions often display inconsistencies. This study introduces a method that employs the Noise2Noise approach combined with neural networks to effectively mitigate these ambiguities. We applied this methodology to hundreds of ambiguous reconstructed images retrieved from a single diffraction pattern using a conventional retrieval algorithm. Our results demonstrate that ambiguous features in these reconstructions are effectively treated as inter‐reconstruction noise and are significantly reduced. The post‐Noise2Noise treated images closely approximate the average and singular value decomposition analysis of various reconstructions, providing consistent and reliable reconstructions. [ABSTRACT FROM AUTHOR]

Various X-ray techniques are employed to investigate specimens in diverse fields. Generally, scattering and absorption/emission processes occur due to the interaction of X-rays with matter. The output signals from these processes contain structural information and the electronic structure of specimens, respectively. The combination of complementary X-ray techniques improves the understanding of complex systems holistically. In this context, we introduce a multiplex imaging instrument that can collect small-/wide-angle X-ray diffraction and X-ray emission spectra simultaneously to investigate morphological information with nanoscale resolution, crystal arrangement at the atomic scale and the electronic structure of specimens.

Ptychography today is considered the most natural and effective method for approaching the diffraction limit of optical resolution. The principal scheme of a ptychoscope does not contain refractive or focusing elements and includes a coherent light source, a platform for moving (macroscopic) object, and a detector for registering radiation passed through or reflected by the object associated with a computer for processing diffraction patterns. In classical optics, the main task in achieving high spatial resolution is the correction and elimination of aberrations of optical systems, while in ptychography spatial resolution mainly depends on the reliability of registration and computer processing of diffraction patterns with large numerical apertures. The key idea of ptychography is to obtain an image by computer processing of overlapping diffraction patterns (scans). When moving the object it is assumed that the illuminating beam and the position of the detector remain unchanged. Ptychography is used in a wide range of radiation wavelengths from infrared to X-ray, and it is possible to do without imaging optics. In this work, the possibility of obtaining an amplitude-phase image of the surface relief of an object inclined to the incident one was studied. [ABSTRACT FROM AUTHOR]

We consider the 3D coefficient inverse problem for parabolic wave equation. It involves determining the spatial distribution of refractive and absorption indices by processing phase diffraction patterns obtained by irradiating an object with a set of Gaussian beams. Unlike tomography and ptychography, rotation or scanning of the sample is not required. The problem is solved by expanding the wave field and the complex dielectric constant ε r → over the full set of Gaussian beam functions. To determine ε r → , we obtain a nonlinear matrix equation. The condition of its solvability allows the selection of sampling frequencies by coordinates in accordance with the practical task. [ABSTRACT FROM AUTHOR]

We present a method for single-shot blind deconvolution in coherent diffraction imaging. Coherent diffraction imaging is a technique for non-interferometric quantitative phase imaging without reference light. In our method based on coherent diffraction imaging, a complex amplitude object is illuminated with coherent light, and light from the object is captured through unknown aberrating media and a coded aperture located on the pupil plane to reduce estimated variables on the aberrated pupil function. Both the amplitude and the phase of the object are recovered from the single captured intensity image by a phase retrieval algorithm in which the coded aperture is utilized as a support to estimate the sparse aberrated pupil function. We numerically and experimentally demonstrate the proposed method with complex amplitude objects under severe aberrating conditions. In the experiment, we quantitatively evaluate its performance with ptychography, which is a method for multi-shot coherent diffraction imaging. Our method enables quantitative phase imaging through turbulence by using simple and reference-free optical hardware without any invasive process. [ABSTRACT FROM AUTHOR]

Abstract—The progress in the computer science caused wide acceptance of lensless imaging methods, in particular, the phase reconstruction method. It allows phase and amplitude distribution reconstruction in the object plane by mathematical treatment of the diffraction pattern resulting from a coherent beam passage or reflection from an object. In this case, elements of conventional optical systems, i.e., lenses, focusing mirrors, and others are not used. The classical version of the method implies the detector position in the far-field region with respect to the object, which simplifies calculations. However, this condition is not always feasible; therefore, near-field method versions based on the direct application of the wave propagator were proposed in some studies. In this paper, a new version based on a virtual lens is proposed. Then the complexity and computation time remain at the same level as for the far zone, but it is possible to significantly reduce the distance to the detector. The effectiveness of the method is demonstrated in an experiment with a helium-neon laser. [ABSTRACT FROM AUTHOR]

The characterization of X-ray focal spots is of great significance for the diagnosis and performance optimization of focusing systems. X-ray free-electron lasers (XFELs) are the latest generation of X-ray sources with ultrahigh brilliance, ultrashort pulse duration and nearly full transverse coherence. Because each XFEL pulse is unique and has an ultrahigh peak intensity, it is difficult to characterize its focal spot size individually with full power. Herein, a method for characterizing the spot size at the focus position is proposed based on coherent diffraction imaging. A numerical simulation was conducted to verify the feasibility of the proposed method. The focal spot size of the Coherent Scattering and Imaging endstation at the Shanghai Soft X-ray Free Electron Laser Facility was characterized using the method. The full width at half-maxima of the focal spot intensity and spot size in the horizontal and vertical directions were calculated to be 2.10 ± 0.24 µm and 2.00 ± 0.20 µm, respectively. An ablation imprint on the silicon frame was used to validate the results of the proposed method.

The twin‐image problem, a persistent stagnation mode in iterative projection algorithms (IPAs) for coherent diffraction imaging, occurs when the ideal and twin images appear simultaneously in the reconstruction. Presented here is a methodological framework for IPAs termed the half‐cycle multigrid (HMG) for use in phase retrieval to alleviate the twin‐image problem during the iterative process. HMG reconstructs the low‐frequency phase first to reduce the impact of oscillation caused by phase retrieval in the higher‐frequency region of Fourier space during the iteration. The higher‐frequency Fourier magnitude is then added to the reconstruction stage by stage using the multigrid method. The unification of phase retrieval orientation in the low‐frequency region lays the foundation for that in the whole Fourier space. The reconstruction results of simulated and experimental diffraction patterns demonstrate that HMG effectively reduces the probability of the twin‐image problem occurring, enhances the accuracy of low‐frequency information, and achieves credible and faithful reconstruction results from noisy diffraction patterns. The combination of HMG with the oversampling smoothness framework allows more reliable reconstruction results, proving that the HMG framework has good extensibility. It is expected that HMG can be combined with other IPAs. [ABSTRACT FROM AUTHOR]

Coherent diffraction imaging (CDI) is a high-resolution technique that does not require x-ray lenses. With advances in scientific technology, such as synchrotron radiation, x-ray free-electron lasers, and coherent electron sources, CDI has been applied to diverse fields, such as biology, medicine, and semiconductors, as a high-resolution, nondestructive measure. With the rapid increase in demand for these applications, enhancing the efficiency of processing high-volume data has become a significant challenge for promotion. In this study, we proposed an algorithm that combines Kramers–Kronig (KK) relations with oversampling smoothness (OSS). The results were evaluated by introducing an error coefficient. We found that the error of the KK-OSS algorithm is always reduced by approximately 50% compared with the error reduction (ER) algorithm, hybrid input–output (HIO) algorithm, and OSS in real space. In the diffraction space, the error in the KK-OSS can be decreased to 0.11. With 100 iterations, KK-OSS spent 218.3 s on reconstructing most of the sample information, while ER was 258.1 s, HIO algorithm took 296.7 s and the reconstruction was still a random value. In Fraunhofer diffraction, it cost KK-OSS 58.8 s to reconstruct, while OSS took 61.9 s. Therefore, this method can reduce the reconstruction error, shorten the reconstruction time, and improve the efficiency compared with the ER, HIO, and OSS algorithms using a random phase as the initial value. [ABSTRACT FROM AUTHOR]

Fourier transform holography (FTH) is a lensless imaging technique where the wave scattered by an object is superimposed with the wave scattered by a reference source positioned in the same plane. The distribution of the object is then reconstructed by simply calculating the Fourier transform of the recorded hologram. In this study, we outline the basic principles of FTH and provide an overview of the different types of references and the associated reconstruction algorithms. Current applications of FTH with different waves (light, electron, and X-ray) are presented, and their relationships with other coherent imaging techniques are discussed. [ABSTRACT FROM AUTHOR]

Temporal compressive CDI utilizes single-exposure snapshot compression sampling in the frequency domain to visualize the dynamic process of CDI. Due to the lack of effective frequency domain prior information constraint, the traditional temporal compressive CDI method has limited imaging quality. In order to achieve high-quality dynamic reconstruction at high frame rates, a score-based diffusion model in frequency domain is used to extract the prior gradient distribution of the target in the complex frequency domain. Subsequently, this information is harmoniously woven into the physics-driven iterative phase recovery reconstruction process to restore multi-frame high-quality images. Simulation and experimental outcomes have demonstrated that the proposed technique surpasses conventional methods, delivering enhanced structural details and a reduction in artifact. The highest achieved PSNR and SSIM values are 37.25 dB and 0.997, respectively. The proposed method has equally well performance on targets across datasets, demonstrating the strong generalization of the method. [ABSTRACT FROM AUTHOR]

A fast charge-integrating detector has been showcased for high-resolution X-ray ptychography. The advancement in developing detectors of this kind, with rapid framing capabilities, holds paramount significance in harnessing the full potential of emerging diffraction-limited synchrotron sources for X-ray nanoimaging.

Radiation damage and a low signal-to-noise ratio are the primary factors that limit spatial resolution in coherent diffraction imaging (CDI) of biomaterials using X-ray sources. Introduced here is a clustering algorithm named ConvRe based on deep learning, and it is applied to obtain accurate and consistent image reconstruction from noisy diffraction patterns of weakly scattering biomaterials. To investigate the impact of X-ray radiation on soft biomaterials, CDI experiments were performed on mitochondria from human embryonic kidney cells using synchrotron radiation. Benefiting from the new algorithm, structural changes in the mitochondria induced by X-ray radiation damage were quantitatively characterized and analysed at the nanoscale with different radiation doses. This work also provides a promising approach for improving the imaging quality of biomaterials with XFEL-based plane-wave CDI.

In this paper, we present a method for single-shot phase imaging with a wide field of view based on coherent diffraction imaging. Coherent diffraction imaging can be implemented by compact optical hardware without any interferometric measurement, but one issue is a severely limited field of view. Although this limited field of view is extendable by introducing random optical processes, this solution increases the costs of optical hardware and computations. To solve this issue, we utilize a shift-invariant scattering process in coherent diffraction imaging. This optical process is implemented by inserting a scattering plate on the pupil plane in an imaging system. In the proposed method, a complex amplitude object is illuminated with coherent light, and a single diffraction intensity image from the object is captured through the convolution of the scattering point spread function, which is probed in advance. The object field is reconstructed from the captured intensity image based on the ptychographical iterative engine, taking into account the randomized convolution process. The proposed method is numerically analyzed and experimentally demonstrated. [ABSTRACT FROM AUTHOR]

The rapid growth of nanotechnology has increased the need for fast nanoscale imaging. X-ray free electron laser (XFEL) facilities currently provide such coherent sources of directional and high-brilliance X-ray radiation. These facilities require large financial investments for development, maintenance, and manpower, and thus, only a few exist worldwide. In this article, we present an automated table-top system for XUV coherent diffraction imaging supporting the capabilities for multispectral microscopy at high repetition rates, based on laser high harmonic generation from gases. This prototype system aims towards the development of an industrial table-top system of ultrafast soft X-ray multi-spectral microscopy imaging for nanostructured materials with enormous potential and a broad range of applications in current nanotechnologies. The coherent XUV radiation is generated in a semi-infinite gas cell via the high harmonic generation of the near-infrared femtosecond laser pulses. The XUV spectral selection is performed by specially designed multilayer XUV mirrors that do not affect the XUV phase front and pulse duration. [ABSTRACT FROM AUTHOR]

Single‐shot coherent diffraction imaging (CDI) is a powerful approach to characterize the structure and dynamics of isolated nanoscale objects such as single viruses, aerosols, nanocrystals and droplets. Using X‐ray wavelengths, the diffraction images in CDI experiments usually cover only small scattering angles of a few degrees. These small‐angle patterns represent the magnitude of the Fourier transform of the 2D projection of the sample's electron density, which can be reconstructed efficiently but lacks any depth information. In cases where the diffracted signal can be measured up to scattering angles exceeding ∼10°, i.e. in the wide‐angle regime, some 3D morphological information of the target is contained in a single‐shot diffraction pattern. However, the extraction of the 3D structural information is no longer straightforward and defines the key challenge in wide‐angle CDI. So far, the most convenient approach relies on iterative forward fitting of the scattering pattern using scattering simulations. Here the Scatman is presented, an approximate and fast numerical tool for the simulation and iterative fitting of wide‐angle scattering images of isolated samples. Furthermore, the open‐source software implementation of the Scatman algorithm, PyScatman, is published and described in detail. The Scatman approach, which has already been applied in previous work for forward‐fitting‐based shape retrieval, adopts the multi‐slice Fourier transform method. The effects of optical properties are partially included, yielding quantitative results for small, isolated and weakly interacting samples. PyScatman is capable of computing wide‐angle scattering patterns in a few milliseconds even on consumer‐level computing hardware, potentially enabling new data analysis schemes for wide‐angle coherent diffraction experiments. [ABSTRACT FROM AUTHOR]

• A single-intensity phase retrieval is proposed by generating reliable object supports using deep learning. • The convergence of iterative phase retrieval algorithms can be markedly enhanced with the generated support constraint. • The training features in the proposed method are binary-image supports, which provides the good generalization. • The method uses simulated data for training, eliminating the need for experimental data collection. Phase retrieval is an essential technique for imaging applications in many fields such as biology and materials science. The fundamental challenge lies in reconstructing objects from measured intensity patterns. A prevalent solution involves an iterative strategy that alternates projections between the object and detector planes. However, reconstructing objects from a single diffraction intensity pattern remains challenging due to the absence of constraints at the object plane. Here, we propose a learning-based approach that generates reliable object support in real time from its autocorrelation support. With the generated support as the constraint for the object plane, we show that the convergence of iterative phase retrieval algorithms can be markedly enhanced. Compared with the end-to-end learning-based methods, the proposed method has a unique character that the training features are binary supports, instead of the type and content of objects, so that our approach has better generalization. Furthermore, one of the advantages of our method is that it uses simulated data for training, eliminating the need for experimental data collection. [ABSTRACT FROM AUTHOR]

• R-CIMI expands CMI modes for accurate reflective surface measurement. • Optimized random masks enhance wavefront reconstruction and measurement precision. • Automatic positioning method ensures accurate distance determination. • Experimental validation demonstrates the robustness and accuracy of R-CIMI. This paper proposes a reflection-type surface coherent interferometric modulation imaging (R-CIMI) method based on reference light modulation, leveraging the interference light path generated by the reflected beam of the modulator and the target surface. Furthermore, we present a mask optimization strategy to enhance the similarity of diffraction pattern structures, as well as an automatic positioning approach based on optical field estimation. Owing to the anti-disturbance properties of coherent diffraction imaging, R-CIMI is less susceptible to environmental disturbances than conventional interference techniques. Simulations and experiments demonstrate that the proposed method is comparable to conventional interference methods in terms of measurement accuracy. [ABSTRACT FROM AUTHOR]

• The underlying mathematics was investigated for the first time to prove the existence of the unique solution of extended ptychographic iterative engine imaging. • A linear mathematical model was set up to reconstruct the illumination and sample simultaneously from only seven frames of recorded diffraction intensities directly. • An efficient computing method without limitation of spectrum size was developed to improve computing efficiency, and the mathematical relationship between the reconstruction results and imaging system was illustrated. • Experimental factors were also considered and it was demonstrated theoretically and numerically that the proposed method had a strong robustness to detecting noise and positioning error. A linear model by writing the recorded diffractive intensities as a set of linear equations was put forwarded to determine the complex amplitude of the illumination and sample analytically for the extended ptychographic iterative engine (ePIE) imaging. An efficient computing method that can process large matrices was proposed to improve computing efficiency. The influences of detector noise and the positioning error of the sample were studied to explain why satisfactory reconstruction can be obtained experimentally when the linear equations of diffractive intensities are incorrect. This study demonstrates for the first time that ePIE technique has a unique and deterministic solution even with noisy experimental data, overcoming the main obstacle hindering the application of the ePIE algorithm in optical measurement and optical metrology, where a mathematically unique solution is crucial. [ABSTRACT FROM AUTHOR]

Crystallography is the standard for determining the atomic structure of molecules. Unfortunately, many interesting molecules, including an extensive array of biological macromolecules, do not form crystals. While ultrashort and intense X-ray pulses from free-electron lasers are promising for imaging single isolated molecules with the so-called "diffraction before destruction" technique, nanocrystals are still needed for producing sufficient scattering signal for structure retrieval as implemented in serial femtosecond crystallography. Here, we show that a femtosecond laser pulse train may be used to align an ensemble of isolated molecules to a high level transiently, such that the diffraction pattern from the highly aligned molecules resembles that of a single molecule, allowing one to retrieve its atomic structure with a coherent diffraction imaging technique. In our experiment with CO2 molecules, a high degree of alignment is maintained for about 100 fs, and a precisely timed ultrashort relativistic electron beam from a table-top instrument is used to record the diffraction pattern within that duration. The diffraction pattern is further used to reconstruct the distribution of CO2 molecules with atomic resolution. Our results mark a significant step toward imaging noncrystallized molecules with atomic resolution and open opportunities in the study and control of dynamics in the molecular frame that provide information inaccessible with randomly oriented molecules. [ABSTRACT FROM AUTHOR]

To reconstruct the wavefront in a single-lens coherent diffraction imaging (CDI) system, we propose a closed-loop cascaded iterative engine (CIE) algorithm based on the known information of the imaging planes. The precision of diffraction distance is an important prerequisite for a perfect reconstruction of samples. For coherent diffraction imaging with a lens, autofocus is investigated to accurately determine the object distance and image distance. For the case of only the object distance being unknown, a diffuser is used to scatter the coherent beam for speckle illumination to improve the performance of autofocus. The optimal object distance is obtained stably and robustly by combing speckle imaging with clarity evaluation functions. SSIM and MSE, using the average pixel value of the reconstructed data set as a reference, are applied on two-unknown-distance autofocus. Simulation and experiment results are presented to prove the feasibility of the CIE and proposed auto-focusing method. [ABSTRACT FROM AUTHOR]

X-ray imaging of soft materials is often difficult because of the low contrast of the components. This particularly applies to frozen hydrated biological cells where the feature of interest can have a similar density to the surroundings. As a consequence, a high dose is often required to achieve the desired resolution. However, the maximum dose that a specimen can tolerate is limited by radiation damage. Results from 3D coherent diffraction imaging (CDI) of frozen hydrated specimens have given resolutions of ∼80 nm compared with the expected resolution of 10 nm predicted from theoretical considerations for identifying a protein embedded in water. Possible explanations for this include the inapplicability of the dose-fractionation theorem, the difficulty of phase determination, an overall object-size dependence on the required fluence and dose, a low contrast within the biological cell, insufficient exposure, and a variety of practical difficulties such as scattering from surrounding material. A recent article [Villaneuva-Perez et al. (2018), Optica, 5, 450–457] concluded that imaging by Compton scattering gave a large dose advantage compared with CDI because of the object-size dependence for CDI. An object-size dependence would severely limit the applicability of CDI and perhaps related coherence-based methods for structural studies. This article specifically includes the overall object size in the analysis of the fluence and dose requirements for coherent imaging in order to investigate whether there is a dependence on object size. The applicability of the dose-fractionation theorem is also discussed. The analysis is extended to absorption-based imaging and imaging by incoherent scattering (Compton) and fluorescence. This article includes analysis of the dose required for imaging specific low-contrast cellular organelles as well as for protein against water. This article concludes that for both absorption-based and coherent diffraction imaging, the dose-fractionation theorem applies and the required dose is independent of the overall size of the object. For incoherent-imaging methods such as Compton scattering, the required dose depends on the X-ray path length through the specimen. For all three types of imaging, the dependence of fluence and dose on a resolution d goes as 1/d4 when imaging uniform-density voxels. The independence of CDI on object size means that there is no advantage for Compton scattering over coherent-based imaging methods. The most optimistic estimate of achievable resolution is 3 nm for imaging protein molecules in water/ice using lensless imaging methods in the water window. However, the attainable resolution depends on a variety of assumptions including the model for radiation damage as a function of resolution, the efficiency of any phase-retrieval process, the actual contrast of the feature of interest within the cell and the definition of resolution itself. There is insufficient observational information available regarding the most appropriate model for radiation damage in frozen hydrated biological material. It is advocated that, in order to compare theory with experiment, standard methods of reporting results covering parameters such as the feature examined (e.g. which cellular organelle), resolution, contrast, depth of the material (for 2D), estimate of noise and dose should be adopted.

Fourier transform holography (FTH) is a lensless imaging technique where the wave scattered by an object is superimposed with the wave scattered by a reference source positioned in the same plane. The distribution of the object is then reconstructed by simply calculating the Fourier transform of the recorded hologram. In this study, we outline the basic principles of FTH and provide an overview of the different types of references and the associated reconstruction algorithms. Current applications of FTH with different waves (light, electron, and X-ray) are presented, and their relationships with other coherent imaging techniques are discussed.

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. [ABSTRACT FROM AUTHOR]

The rapid growth of nanotechnology has increased the need for fast nanoscale imaging. X-ray free electron laser (XFEL) facilities currently provide such coherent sources of directional and high-brilliance X-ray radiation. These facilities require large financial investments for development, maintenance, and manpower, and thus, only a few exist worldwide. In this article, we present an automated table-top system for XUV coherent diffraction imaging supporting the capabilities for multispectral microscopy at high repetition rates, based on laser high harmonic generation from gases. This prototype system aims towards the development of an industrial table-top system of ultrafast soft X-ray multi-spectral microscopy imaging for nanostructured materials with enormous potential and a broad range of applications in current nanotechnologies. The coherent XUV radiation is generated in a semi-infinite gas cell via the high harmonic generation of the near-infrared femtosecond laser pulses. The XUV spectral selection is performed by specially designed multilayer XUV mirrors that do not affect the XUV phase front and pulse duration.

Autofocus technology is a crucial technique in computational optical imaging. The clarity evaluation function (CEF) serves as the criterion for autofocus, making it the core of the autofocus algorithm. In this paper, we propose a CEF based on amplitude differences of fractional Fourier transform (ADFrFT). ADFrFT extracts information from the fractional domain, which corresponds to the fusion of the spatial and frequency domains. This renders ADFrFT highly accurate and robust to noise, making it suitable for various types of sample images. Additionally, ADFrFT provides an added dimension of flexibility to address different autofocus requirements for distinct sample image types and focusing scenarios. Simulations and experiments confirmed the effectiveness of ADFrFT, and we improved the imaging resolution via distance calibration in the coaxial multi-distance coherent diffraction imaging (MDCDI) experiment. • We propose a novel autofocus based on fractional Fourier amplitude differences, which is flexible and universal. • This autofocus provides additional flexibility to address different requirements for various sample types. • The autofocusing scheme is highly accurate and robust to noise. • We have improved image quality in coaxial multi-distance coherent diffraction imaging by distance calibration. [ABSTRACT FROM AUTHOR]

In cancer treatment, it is highly desirable to classify single cancer cells in real time. The standard method is polymerase chain reaction requiring a substantial amount of resources and time. Here, we present an innovative approach for rapidly classifying different cell types: we measure the diffraction pattern of a single cell illuminated with coherent extreme ultraviolet (XUV) laser-generated radiation. These patterns allow distinguishing different breast cancer cell types in a subsequent step. Moreover, the morphology of the object can be retrieved from the diffraction pattern with submicron resolution. In a proof-of-principle experiment, we prepared single MCF7 and SKBR3 breast cancer cells on gold-coated silica slides. The output of a laser-driven XUV light source is focused onto a single unstained and unlabeled cancer cell. With the resulting diffraction pattern, we could clearly identify the different cell types. With an improved setup, it will not only be feasible to classify circulating tumor cells with a high throughput, but also to identify smaller objects such as bacteria or even viruses.

For tiny crystals, their diffraction intensities at and between the Bragg peaks become measurable due to the limited number of the unit cells, which can in principle be used to directly phase the crystal structures.

The hybrid input-output algorithm is a phase retrieval method that provides solution for the phase problem of coherent X-ray diffraction imaging of micro- and nano-objects from the diffraction pattern alone without using any focusing optics. In this paper, we have studied a tolerance of this algorithm to missing information at the center of the diffraction pattern, which is a frequent problem in problems of small-angle scattering. We considered the particular problem of the stability of the algorithm in the case of scattering from an ordered structure and provided a qualitative and quantitative description of the degradation of image reconstruction with an increase in the amount of missing information.

We developed a single-shot coherent X-ray imaging instrument at the hard X-ray beamline of the Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL). This experimental platform was established to conduct a variety of XFEL experiments, including coherent diffraction imaging (CDI), X-ray photon correlation spectroscopy (XPCS), and coherent X-ray scattering (CXS). Based on the forward-scattering geometry, this instrument utilizes a fixed-target method for sample delivery. It is well optimized for single-shot-based experiments in which one expects to observe the ultrafast phenomena of nanoparticles at picosecond temporal and nanometer spatial resolutions. In this paper, we introduce a single-shot coherent X-ray imaging instrument and report pump–probe coherent diffraction imaging (PPCDI) of Ag nanoparticles as an example of its applications. [ABSTRACT FROM AUTHOR]

In coherent diffraction imaging (CDI) experiments, the intensity of the scattered wave impinging on an object is measured on an array of detectors. These measurements can be interpreted as samples of the square of the modulus of the Fourier transform of the unknown scattering density. A beamstop obstructs the forward scattered wave and, hence, the modulus Fourier data from a neighborhood of k = 0 cannot be measured. In this note, we describe a linear method for recovering this unmeasured modulus Fourier data from the measured values and an estimate of the support of the image's autocorrelation function without consideration of phase retrieval. We analyze the effects of noise, and the conditioning of this problem, which grows exponentially with the modulus of the maximum spatial frequency not measured. [ABSTRACT FROM AUTHOR]

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

Various X-ray techniques are employed to investigate specimens in diverse fields. Generally, scattering and absorption/emission processes occur due to the interaction of X-rays with matter. The output signals from these processes contain structural information and the electronic structure of specimens, respectively. The combination of complementary X-ray techniques improves the understanding of complex systems holistically. In this context, we introduce a multiplex imaging instrument that can collect small-/wide-angle X-ray diffraction and X-ray emission spectra simultaneously to investigate morphological information with nanoscale resolution, crystal arrangement at the atomic scale and the electronic structure of specimens., (open access.)

We explore the light induced dynamics in superfluid helium nanodroplets with wide-angle scattering in a pump–probe measurement scheme. The droplets are doped with xenon atoms to facilitate the ignition of a nanoplasma through irradiation with near-infrared laser pulses. After a variable time delay of up to 800 ps, we image the subsequent dynamics using intense extreme ultraviolet pulses from the FERMI free-electron laser. The recorded scattering images exhibit complex intensity fluctuations that are categorized based on their characteristic features. Systematic simulations of wide-angle diffraction patterns are performed, which can qualitatively explain the observed features by employing model shapes with both randomly distributed as well as structured, symmetric distortions. This points to a connection between the dynamics and the positions of the dopants in the droplets. In particular, the structured fluctuations might be governed by an underlying array of quantized vortices in the superfluid droplet as has been observed in previous small-angle diffraction experiments. Our results provide a basis for further investigations of dopant–droplet interactions and associated heating mechanisms.

To reconstruct the wavefront in a single-lens coherent diffraction imaging (CDI) system, we propose a closed-loop cascaded iterative engine (CIE) algorithm based on the known information of the imaging planes. The precision of diffraction distance is an important prerequisite for a perfect reconstruction of samples. For coherent diffraction imaging with a lens, autofocus is investigated to accurately determine the object distance and image distance. For the case of only the object distance being unknown, a diffuser is used to scatter the coherent beam for speckle illumination to improve the performance of autofocus. The optimal object distance is obtained stably and robustly by combing speckle imaging with clarity evaluation functions. SSIM and MSE, using the average pixel value of the reconstructed data set as a reference, are applied on two-unknown-distance autofocus. Simulation and experiment results are presented to prove the feasibility of the CIE and proposed auto-focusing method.

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

Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. In this work, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the ptychographical iterative engine, a workhorse in the optics community. [ABSTRACT FROM AUTHOR]

The problem of the dynamic diffraction of X-rays from a point source on the spatial lattice of a crystal weakly deformed by a temperature gradient is considered. The Theoretical study is based on the asymptotic representation of the Green-Riemann function for a pair of Takagi equations of the hyperbolic type. The Experimental studies were carried out on the quartz crystals in the presence of a temperature gradient that is perpendicular to the reflecting planes. The conditions and characteristics of focusing are considered, taking into account the distances source-crystal-detector and the parameter of the deformation field. [ABSTRACT FROM AUTHOR]

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.

We developed a single-shot coherent X-ray imaging instrument at the hard X-ray beamline of the Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL). This experimental platform was established to conduct a variety of XFEL experiments, including coherent diffraction imaging (CDI), X-ray photon correlation spectroscopy (XPCS), and coherent X-ray scattering (CXS). Based on the forward-scattering geometry, this instrument utilizes a fixed-target method for sample delivery. It is well optimized for single-shot-based experiments in which one expects to observe the ultrafast phenomena of nanoparticles at picosecond temporal and nanometer spatial resolutions. In this paper, we introduce a single-shot coherent X-ray imaging instrument and report pump–probe coherent diffraction imaging (PPCDI) of Ag nanoparticles as an example of its applications.

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. [ABSTRACT FROM AUTHOR]

With only one piece of the power-spectrum pattern, the single-shot coherent power-spectrum imaging can provide a clear object image for real-time applications even if the object is hidden by opaque scattering media, in which the feedback coefficient β value for the reconstruction with least retrievals and fastest speed has to be pre-estimated through time-consuming iterative loops. Here we report a method for estimating the optimal β value from the captured raw power-spectrum images adaptively to optimize the single-shot coherent power-spectrum imaging for practical exposure conditions. The results demonstrate that, based on exposure level analysis of the captured raw power-spectrum images even of underexposure, moderate exposure, and overexposure cases, the β value could be quickly determined with a compact expression for the algorithm to achieve clear reconstruction output efficiently. The proposed method helps to push ahead of the coherent diffractive imaging devices for real-time imaging through turbid mediums in Artificial Intelligence (AI), driving assistance, and flight assistance applications. [ABSTRACT FROM AUTHOR]