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Ptychography is a scanning coherent diffraction imaging technique that provides high-resolution imaging and complete spatial information of the complex probe and object transmission function. The wavefront error caused by aberrated optics has previously been recovered using ptychography when a highly coherent source is used, but has not been demonstrated with partial coherence due to the multi-modal probe required. Here, we demonstrate that partial coherence can be accounted for in ptychographic reconstructions using the multi-modal approach and assuming that decoherence arises from either the probe or the object. This equivalence recovers coherent (or single state) reconstructions of both the probe and the object even in the presence of partial coherence. We demonstrate this experimentally by using hard x-ray ptychography with a partially coherent source to image a Siemens star test object and to also recover the wavefront error from an aberrated beryllium compound refractive lens. The source properties and resolving capabilities are analyzed, and the wavefront error results are compared with another at-wavelength metrology technique. Our work demonstrates the capability of ptychography to provide high-resolution imaging and optics characterization even in the presence of partial coherence.

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

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

The validity of the dose-fractionation theorem and the dependence of required dose on object size and resolution are analysed for various types of X-ray imaging, including coherent-, incoherent- and absorption-based methods. Estimates are given for the achievable resolutions for cells and other soft biological material., 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/d 4 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.

Coherent diffraction imaging (CDI) is a kind of computational technique seeking to reconstruct a complex wavefront from the measured intensity. To solve the phase retrieval problem, phase modulation is introduced to be a physical constraint. In this work, the alternative structured phase modulation (ASPM) and orbital angular momentum (OAM) are used to be the physical constraints. The ASPM can act as the phase grating. The modulated intensities are concentrated, which can be captured with a high signal-to-noise ratio (SNR). OAM is recently employed as a type of reliable modulation. The topological charge is robust during propagating in the atmosphere. The maximum value of the spectrum intensity is reduced by a factor of 170 under OAM modulation when topological charge is 50. The stagnation can be avoided using multiple ASPM and OAM modulations. The complex wavefront can be robustly reconstructed from redundant measurements without a priori knowledge.

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

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.

Ultrashort, coherent light pulses with wavelengths and durations on the atomic scale are now widely available due to the revolutionary advances made in x-ray free-electron laser (XFEL) technologies in the past few years [1] , [2] . The use of a free-electron gain medium, as opposed to discrete atomic transitions in traditional lasers, provides complete tunability from extreme ultraviolet (100 nm) to hard x-ray (1 Angstrom) wavelengths – enabling elemental, chemical site and spin selectivity to probe dynamics in complex systems. These ultrashort, tunable x-ray pulses have large energy content (10 12 -10 13 photons/pulse), particularly relative to high harmonic generation (HHG) sources – enabling focused intensities up to 10 20 W/cm 2 and exploration of nonlinear x-ray phenomena [3] - [5] . The transverse coherence of the x-ray pulses generated by self-amplified spontaneous emission (SASE) FELs is excellent [6] – enabling coherent diffraction imaging, x-ray holography and x-ray photon correlation spectroscopy. Going further, a fully coherent FEL pulse with longitudinal coherence is reliably achieved by seeding the source [7] – enabling time-domain coherent control using two phase-coherent waveforms delayed with attosecond precision [8] . The combination of all of these properties from advanced XFELs portend a bright future for multidimensional x-ray spectroscopies to elucidate nuclear and electronic dynamics on the atomic scale that probe not only charge densities and motions, but also quantum coherence and correlations between valence electrons and holes in systems of chemical importance [10] . This tutorial will review XFEL radiation properties and their origins, and illustrate their use via case studies involving molecular dynamics in the gas and liquid phase.

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.

Bragg coherent diffraction imaging has the potential to provide significant insight into the structure-properties relationship for crystalline materials by imaging, with nanoscale resolution, three-dimensional strain fields within individual grains and nanoparticles. The capability of present-day synchrotrons to locate and measure a multiplicity of Bragg reflections from a single grain makes it possible to recover the full strain tensor with nanometer resolution. Recent methods for coupling reconstructions from several peaks to determine the strain tensor have been developed and applied to synthetic data, but have not been applied to experimental data. Here, using a coupled genetic reconstruction algorithm, we reconstruct an experimental data set and demonstrate improvements in the ability to resolve vector-valued displacement fields internal to the particle as compared to what is achieved with a noncoupled approach. The coupled approach developed in this work was also validated on simulated data sets. In both simulated and experimental data, reconstructions from our coupled Bragg peak algorithm show improvements over the noncoupled independent reconstruction method of $5%$ in terms of accuracy and $53%$ in terms of consistency.

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.

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

In recent years coherent diffraction imaging (CDI) has evolved into a mature technology. Thanks to its lensless nature, it allowed to bypass the limitations of X-ray optics. At the same time, laser development in combination with high harmonic generation (HHG) has pushed the coherent XUV photon flux to values comparable to 3rd generation synchrotron facilities, which enables lensless imaging experiments that were previously only possible at large-scale facilities. Furthermore, the intrinsic short pulse duration of HHG radiation has potential for imaging experiments down to attosecond time scales. In this contribution, we present our latest results on lensless imaging using a fiber laser driven HHG source at 92 eV. A high photon flux source is used for scanning coherent diffractive imaging (ptychography) demonstrating sub-50 nm resolution. Further, an extension to Fourier transform holography is shown, which enables to increase the useable bandwidth by a factor of five without sacrificing spatial resolution. This paves the way for combing high-resolution table-top lensless imaging with attosecond pump-probe experiments.

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

Phase retrieval seeks to reconstruct the phase from the measured intensity, which is an ill-posed problem. A phase retrieval problem can be solved with physical constraints by modulating the investigated complex wavefront. Orbital angular momentum has been recently employed as a type of reliable modulation. The topological charge l is robust during propagation when there is atmospheric turbulence. In this work, topological modulation is used to solve the phase retrieval problem. Topological modulation offers an effective dynamic range of intensity constraints for reconstruction. The maximum intensity value of the spectrum is reduced by a factor of 173 under topological modulation when l is 50. The phase is iteratively reconstructed without a priori knowledge. The stagnation problem during the iteration can be avoided using multiple topological modulations.

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

Progress in nanotechnology and biotechnology are propelled by our ability to manipulate and resolve the structure of matter on fine scales. As imaging at higher resolution is limited by the probing light source and the numerical aperture, lensless imaging offers an advantage over lensed microscopy. Dispensing with lenses allows one to overcome certain intrinsic aberrations and to bypass fabrication costs, in the optical and the X-ray regimes. The long penetration depth of X-rays renders coherent X-ray diffraction imaging (CXDI) the method of choice for high resolution structure determination with broad applications from materials science to biology; moreover, the same methodology is extensible to electrons, optical photons, or even gamma rays or neutrons. Since coherent diffraction imaging (CDI) bypasses the need for focusing optics, it relies upon computer algorithms to reconstruct the structure of the scattering object. Currently, one of the main obstacles to nanometer resolution of biological imaging is noisy, incomplete data due to radiation damage. With the rapid development of new light source facilities and the advancement in image reconstruction techniques, determining the structure of individual virons or cells at high resolution is becoming more feasible. In particular, the femtosecond pulse of a free electron laser (FEL) is shorter than the coulomb explosion of the specimen, and thus, it is possible to collect diffraction data prior to radiation damage. However, to fully exploit the computational aspect of lensless imaging, prior knowledge about the object should be incorporated into the image reconstruction process and yet so far such methods are generally lacking. In this thesis, we develop tools that incorporate prior knowledge and reduce the amount of necessary data to recover the structure. We begin by a brief overview of lensless imaging and its place in the natural sciences. we then review the process of image formation in coherent X-ray scattering, the corresponding phase problem and the current state of image recovery. The contributions to this field are two fold. We first demonstrate that three dimensional information can be extracted from a two dimensional diffraction pattern collected at a high numerical aperture. Second, we present a framework for image discovery through Bayesian inference, where we introduce four general constraints: symmetry, sparsity and bounded local and total variation. Using simulated noisy, incomplete data, we recover the solution in situations where traditional algorithms fail. We anticipate that these results will encourage the broader application of Bayesian learning into the phase retrieval problem from noisy, incomplete diffraction data and further enhance the possibility of single shot three dimensional structure determination.

Diagnostics capable of interrogating dynamics in harsh environments such as plasma have remained essentially unchanged in recent decades. Developments in advanced microscopy techniques will improve our understanding of the physics involved in these events. Recently developed single-shot ptychography (SSP) provides a pathway towards sophisticated plasma metrologies. Here we introduce wavelength-multiplexed single-shot ptychography (WM-SSP), which allows for hyperspectral, spatially and temporally resolved phase and amplitude contrast imaging. Furthermore, we introduce a novel probe constraint common to all wavelength multiplexed modalities in the single-shot geometry and present modifications to SSP that improve reconstruction fidelity and robustness. WM-SSP was experimentally realized and simulations show the technique's ability to deconvolve the electron and neutral densities within the plasma. WM-SSP will pave the way to a new generation of quantitative plasma imaging techniques., 12 Pages, 6 Figures

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

A new instrument named COMET for COherent Magnetic scattering Experiments in Transmission using polarized soft X-rays has been designed and built. This high-vacuum setup is placed at the intermediate focal point of the elastic branch of the SEXTANTS beamline at Synchrotron SOLEIL. The main application is in solid state physics, the instrument being optimized for studying material properties using coherent scattering of soft X-rays with an emphasis on imaging, with chemical selectivity, the magnetic domains of artificially nano-structured materials. The instrument's principal features are presented and illustrated through recently performed experiments.

As a widely used lensless coherent diffraction imaging approach, ptychography has recently been implemented in Terahertz range. Combining with the unique penetration property of THz radiation, THz ptychography allows inspecting visually opaque samples and retrieving both amplitude and phase information. Here, we demonstrate for the first time to our knowledge, THz ptychography in reflective configuration. Due to the large wavelength (96.5 μm), THz ptychography requires small recording distance. Particular care has been taken in the experimental setup to minimize the recording distance. Extended ptychographic iterative engine (ePIE) is applied to reconstruct quantitatively the amplitude and phase information of the object wavefront. A lateral resolution of 180 μm and a depth resolution of 1.1μm are achieved.

With high-harmonic generation (HHG), spatially and temporally coherent XUV to soft x-ray (100 nm to 10 nm) table-top sources can be realized by focusing a driving infrared (IR) laser on a gas target. For applications such as coherent diffraction imaging, holography, plasma diagnostics, or pump–probe experiments, it is desirable to have control over the wave front (WF) of the HHs to maximize the number of XUV photons on target or to tailor the WF. Here, we demonstrate control of the XUV WF by tailoring the driving IR WF with a deformable mirror. The WFs of both IR and XUV beams are monitored with WF sensors. We present a systematic study of the dependence of the aberrations of the HHs on the aberrations of the driving IR laser and explain the observations with propagation simulations. We show that we can control the astigmatism of the HHs by changing the astigmatism of the driving IR laser without compromising the HH generation efficiency with a WF quality from λ / 8 to λ / 13.3 . This allows us to shape the XUV beam without changing any XUV optical element.

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

Improvement of spatial coherence in third generation synchrotron beamlines made possible the development of X-ray plane-wave coherent diffraction imaging technique (plane-wave cdi ), which enables 3D imaging at nanometric resolution. In this work, we first simulated the influence of detector geometry by comparing reconstruction quality of planar samples made of gold nanoparticles. We compared a commercially available detector geometry with the next Medipix3-based large area detector designed for the next fourth generation Brazilian synchrotron, sirius . The spatial resolution was highly improved, from 7.2 nm for the commercial geometry to 4.8 nm for the Medipix3 detector by keeping the same global image quality. Finally, global image qualities were compared by adjusting the sample-to-detectors distances at a given spatial resolution. For thick samples reconstruction at such high nanometric resolutions, the main limitation of current reconstruction approaches are due to the complex wave propagation within the sample, given by the inhomogeneous Helmholtz equation. We proposed an iterative method to reconstruct the complex refraction index. This method enables to keep the image quality almost constant beyond the resolution limit for thick samples made of gold nanoparticles in water.

The AXSIS project (Attosecond X-ray Science: Imaging and Spectroscopy) aims to develop a THz-driven compact X-ray source for applications e.g. in chemistry and biology by using ultrafast coherent diffraction imaging and spectroscopy. The key components of AXSIS are the THz-driven electron gun and THz-driven dielectric loaded linear accelerator as well as an inverse Compton scattering scheme for the X-rays production. This paper is focused on the prototype of the THz-driven electron gun which is capable of accelerating electrons up to tens of keV. Such a gun was manufactured and tested at the test-stand at DESY. Due to variations in gun fabrication and generation of THz-fields the gun is not exactly operated at design parameters. Extended simulations have been performed to understand the experimentally observed performance of the gun. A detailed comparison between simulations and experimental measurements is presented in this paper., EAAC proceeding at NIM-A

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

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.

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

Based on the extended Huygens–Fresnel integral and the theory of coherence of light field, we have investigated the correlated imaging by using the transverse normalized second-order intensity fluctuation correlation function with partially coherent light radiation. The imaging for a reflected object with relative long distance is determined by the feature of speckle-to-speckle correlation. By using the correlation function, we study the effects of imaging distance, the sizes of object lens and reference lens, the source’s transverse coherent width and its transverse size on the quality of correlated imaging. Numerical results show that the parameters of imaging system and the properties of partially coherent light source have significant influences on the imaging resolution and visibility. For an object lens with large enough diameter, the resolution is determined by the transverse coherent width of light source. On the contrary, it depends on the aperture of object lens. The magnification of the...

In this work the fluence efficiency of two coherent X-ray imaging techniques is studied by numerical experiments. The techniques surveyed are near-field holography and far-field diffraction imaging., 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.

We report on a novel non-iterative phase retrieval method with which the complex-valued transmission function of an object can be retrieved with a non-iterative computation, with a limited number of intensity measurements. The measurements are taken in either real space or Fourier space, and for each measurement the phase in its dual space is modulated according to a single optical parameter. The requirement found for the phase modulation function is a general one, which therefore allows for plenty of customization in this method. It is shown that quantitative Zernike phase contrast imaging is one special case of this general method. With simulations we investigate the sampling requirements for a microscopy setup and for a Coherent Diffraction Imaging (CDI) setup.

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

Ptychography has been developed and routinely employed as an at-wavelength metrology method on a low coherence dipole magnet beamline., Ptychography is a scanning coherent diffraction imaging technique which provides high resolution imaging and complete spatial information of the complex electric field probe and sample transmission function. Its ability to accurately determine the illumination probe has led to its use at modern synchrotrons and free-electron lasers as a wavefront-sensing technique for optics alignment, monitoring and correction. Recent developments in the ptychography reconstruction process now incorporate a modal decomposition of the illuminating probe and relax the restriction of using sources with high spatial coherence. In this article a practical implementation of hard X-ray ptychography from a partially coherent X-ray source with a large number of modes is demonstrated experimentally. A strongly diffracting Siemens star test sample is imaged using the focused beam produced by either a Fresnel zone plate or beryllium compound refractive lens. The recovered probe from each optic is back propagated in order to plot the beam caustic and determine the precise focal size and position. The power distribution of the reconstructed probe modes also allows the quantification of the beams coherence and is compared with the values predicted by a Gaussian–Schell model and the optics exit intensity.

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

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

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

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

To advance the frontiers of ultrafast X-ray science, Shanghai soft X-ray free-electron laser (SXFEL) user facility was proposed to develop which is now under construction as planned. The SXFEL facility provides ultraintense femtosecond X-ray pulses from 0.1 keV to 1 keV in a repetition rate of 50 Hz. The first phase of the SXFEL includes two beamlines and 5 experimental end-stations. The SXFEL user facility provides some advanced X-ray measurement tools in the research fields of biomaterial, condensed matters, atomic and molecular physics, and novel functional materials by means such as coherent diffraction imaging, time-resolved resonant X-ray scattering, and single-pulse time-resolved x-ray emission spectroscopy etc. In this presentation, I will report the latest status of the beamlines at Shanghai SXFEL.

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

Coherent diffractive imaging (CDI) is a lensless, high-resolution imaging method. In order to overcome the problems of poor-quality image and slow convergence of iterative algorithm in traditional CDI, an innovative setup for the multimode-based phase retrieval method is proposed. Here the multimode fiber source was selected as the light source to replace the traditional plane-wave incidence. Due to the nature of the multimode fiber, a speckle light field can be generated on the output fiber facet and then is used to illuminate the object. Thus the diffraction field can be rapidly changed at a very short distance so as to realize much higher resolution and consume less iteration time. Then a phase-only spatial light modulator (SLM) is used as a negative lens instead of a positive lens in a 4f imaging system for the advantage of larger detection space. This proposed setup has many advantages such as a simpler structure and static recording. The comparison experiments with plane waves confirm that our proposed method has higher reconstruction resolution and smaller iteration errors.

Coherent diffraction imaging (CDI) is a powerful method for visualizing the structure of an object with a high spatial resolution that exceeds the performance limits of the lens. Single-frame CDI in the X-ray region has potential use for probing dynamic phenomena with a high spatiotemporal resolution. Here, we experimentally demonstrate a general method for single-frame X-ray CDI using a triangular aperture and a Fresnel zone plate. Using 5 keV synchrotron radiation X-rays, we reconstructed the object image of the locally illuminated area with a spatial resolution of higher than 50 nm and an exposure time of more than 0.1 s without prior information about the sample. After a 10 s exposure, a resolution of 17 nm was achieved. The present method opens new frontiers in the study of dynamics at the nanoscale by using next-generation synchrotron radiation X-rays/free-electron lasers as light sources.