Use of a complex constraint in coherent diffractive imaging

Evaluation of the Weighted Mean X-ray Energy for an Imaging System Via Propagation-Based Phase-Contrast Imaging

For imaging events of extremely short duration, like shock waves or explosions, it is necessary to be able to image the object with a single-shot exposure. A suitable setup is given by a laser-induced X-ray source such as the one that can be found at GSI (Helmholtzzentrum für Schwerionenforschung GmbH) in Darmstadt (Society for Heavy Ion Research), Germany. There, it is possible to direct a pulse from the high-energy laser Petawatt High Energy Laser for Heavy Ion eXperiments (PHELIX) on a tungsten wire to generate a picosecond polychromatic X-ray pulse, called backlighter. For grating-based single-shot phase-contrast imaging of shock waves or exploding wires, it is important to know the weighted mean energy of the X-ray spectrum for choosing a suitable setup. In propagation-based phase-contrast imaging the knowledge of the weighted mean energy is necessary to be able to reconstruct quantitative phase images of unknown objects. Hence, we developed a method to evaluate the weighted mean energy of the X-ray backlighter spectrum using propagation-based phase-contrast images. In a first step wave-field simulations are performed to verify the results. Furthermore, our evaluation is cross-checked with monochromatic synchrotron measurements with known energy at Diamond Light Source (DLS, Didcot, UK) for proof of concepts.

Multimodal x-ray and electron microscopy of the Allende meteorite

Multimodal microscopy that combines complementary nanoscale imaging techniques is critical for extracting comprehensive chemical, structural, and functional information, particularly for heterogeneous samples. X-ray microscopy can achieve high-resolution imaging of bulk materials with chemical, magnetic, electronic, and bond orientation contrast, while electron microscopy provides atomic-scale spatial resolution with quantitative elemental composition. Here, we combine x-ray ptychography and scanning transmission x-ray spectromicroscopy with three-dimensional energy-dispersive spectroscopy and electron tomography to perform structural and chemical mapping of an Allende meteorite particle with 15-nm spatial resolution. We use textural and quantitative elemental information to infer the mineral composition and discuss potential processes that occurred before or after accretion. We anticipate that correlative x-ray and electron microscopy overcome the limitations of individual imaging modalities and open up a route to future multiscale nondestructive microscopies of complex functional materials and biological systems.

Single-view phase retrieval of an extended sample by exploiting edge detection and sparsity

We propose a new approach to robustly retrieve the exit wave of an extended sample from its coherent diffraction pattern by exploiting sparsity of the sample's edges. This approach enables imaging of an extended sample with a single view, without ptychography. We introduce nonlinear optimization methods that promote sparsity, and we derive update rules to robustly recover the sample's exit wave. We test these methods on simulated samples by varying the sparsity of the edge-detected representation of the exit wave. Our tests illustrate the strengths and limitations of the proposed method in imaging extended samples.

Imaging Shock Waves in Diamond with Both High Temporal and Spatial Resolution at an XFEL

The advent of hard x-ray free-electron lasers (XFELs) has opened up a variety of scientific opportunities in areas as diverse as atomic physics, plasma physics, nonlinear optics in the x-ray range, and protein crystallography. In this article, we access a new field of science by measuring quantitatively the local bulk properties and dynamics of matter under extreme conditions, in this case by using the short XFEL pulse to image an elastic compression wave in diamond. The elastic wave was initiated by an intense optical laser pulse and was imaged at different delay times after the optical pump pulse using magnified x-ray phase-contrast imaging. The temporal evolution of the shock wave can be monitored, yielding detailed information on shock dynamics, such as the shock velocity, the shock front width, and the local compression of the material. The method provides a quantitative perspective on the state of matter in extreme conditions.

Mass density and water content of saturated never-dried calcium silicate hydrates

Calcium silicate hydrates (C-S-H) are the most abundant hydration products in ordinary Portland cement paste. Yet, despite the critical role they play in determining mechanical and transport properties, there is still a debate about their density and exact composition. Here, the site-specific mass density and composition of C-S-H in hydrated cement paste are determined with nanoscale resolution in a nondestructive approach. We used ptychographic X-ray computed tomography in order to determine spatially resolved mass density and water content of the C-S-H within the microstructure of the cement paste. Our findings indicate that the C-S-H at the border of hydrated alite particles possibly have a higher density than the apparent inner-product C-S-H, which is contrary to the common expectations from previous works on hydrated cement paste.

Coherent imaging at the diffraction limit

X-ray ptychography, a scanning coherent diffractive imaging technique, holds promise for imaging with dose-limited resolution and sensitivity. If the foreseen increase of coherent flux by orders of magnitude can be matched by additional technological and analytical advances, ptychography may approach imaging speeds familiar from full-field methods while retaining its inherently quantitative nature and metrological versatility. Beyond promises of high throughput, spectroscopic applications in three dimensions become feasible, as do measurements of sample dynamics through time-resolved imaging or careful characterization of decoherence effects.

Reconstruction of wave front and object for inline holography from a set of detection planes

We illustrate the errors inherent in the conventional empty beam correction of full field X-ray propagation imaging, i.e. the division of intensities in the detection plane measured with an object in the beam by the intensity pattern measured without the object, i.e. the empty beam intensity pattern. The error of this conventional approximation is controlled by the ratio of the source size to the smallest feature in the object, as is shown by numerical simulation. In a second step, we investigate how to overcome the flawed empty beam division by simultaneous reconstruction of the probing wavefront (probe) and of the object, based on measurements in several detection planes (multi-projection approach). The algorithmic scheme is demonstrated numerically and experimentally, using the defocus wavefront of the hard X-ray nanoprobe setup at the European Synchrotron Radiation Facility (ESRF).

Dynamic imaging using ptychography

We demonstrate through experiment an example of "mixed state" reconstruction using x-ray ptychography. We demonstrate successful imaging of a vibrating sample that has dynamics that are of one order magnitude faster than the measurement times. We show how increased vibrational amplitude leads to an increased population of illumination modes, a characteristic of partial coherence. Implications of a vibrating sample are explored, with its possible use in manipulating coherent wave field mode shapes and coherence properties.

Fresnel coherent diffractive imaging of elemental distributions in nanoscale binary compounds

We report quantitative determination of elemental distribution in binary compounds with nano meter scale spatial resolution using x-ray Fresnel coherent diffractive imaging (FCDI). We show that the quantitative magnitude and phase values of the x-ray wave exiting an object determined by FCDI can be utilized to obtain full-field atomic density maps of each element independently. The proposed method was demonstrated by reconstructing the density maps of Pt and NiO in a Pt-NiO binary compound with about 18 nm spatial resolution.

Whole-cell phase contrast imaging at the nanoscale using Fresnel coherent diffractive imaging tomography

X-ray tomography can provide structural information of whole cells in close to their native state. Radiation-induced damage, however, imposes a practical limit to image resolution, and as such, a choice between damage, image contrast, and image resolution must be made. New coherent diffractive imaging techniques, such Fresnel Coherent Diffractive Imaging (FCDI), allows quantitative phase information with exceptional dose efficiency, high contrast, and nano-scale resolution. Here we present three-dimensional quantitative images of a whole eukaryotic cell by FCDI at a spatial resolution below 70 nm with sufficient phase contrast to distinguish major cellular components. From our data, we estimate that the minimum dose required for a similar resolution is close to that predicted by the Rose criterion, considerably below accepted estimates of the maximum dose a frozen-hydrated cell can tolerate. Based on the dose efficiency, contrast, and resolution achieved, we expect this technique will find immediate applications in tomographic cellular characterisation.

Phase-diverse Fresnel coherent diffractive imaging of malaria parasite-infected red blood cells in the water window

Phase-diverse Fresnel coherent diffractive imaging has been shown to reveal the structure and composition of biological specimens with high sensitivity at nanoscale resolution. However, the method has yet to be applied using X-ray illumination with energy in the so-called 'water-window' that lies between the carbon and oxygen K edges. In this range, differences in the strength of the X-ray interaction for protein based biological materials and water is increased. Here we demonstrate a proof-of-principle application of FCDI at an X-ray energy within the water-window to a dehydrated cellular sample composed of red blood cells infected with the trophozoite stage of the malaria parasite, Plasmodium falciparum. Comparison of the results to both optical and electron microscopy shows that the correlative imaging methods that include water-window FCDI will find utility in studying cellular architecture.

Application of a complex constraint for biological samples in coherent diffractive imaging

We demonstrate the application of a complex constraint in the reconstruction of images from phase-diverse Fresnel coherent diffraction data for heterogeneous biological objects. The application of this constraint is shown to improve the quality of the reconstruction of both the phase and the magnitude of the complex object transmission function.

Holographically aided iterative phase retrieval

Fourier transform holography (FTH) is a noise-resistant imaging technique which allows for nanometer spatial resolution x-ray imaging, where the inclusion of a small reference scattering object provides the otherwise missing phase information. With FTH, one normally requires a considerable distance between the sample and the reference to ensure spatial separation of the reconstruction and its autocorrelation. We demonstrate however that this requirement can be omitted at the small cost of iteratively separating the reconstruction and autocorrelation. In doing so, the photon efficiency of FTH can be increased due to a smaller illumination area, and we show how the presence of the reference prevents the non-uniqueness problems often encountered with plane-wave iterative phase retrieval. The method was tested on a cobalt/platinum multilayer exhibiting out of plane magnetized domains, where the magnetic circular dichroism effect was used to image the magnetic domains at the cobalt L₃-edge at 780eV.

An in-vacuum x-ray diffraction microscope for use in the 0.7-2.9 keV range

A dedicated in-vacuum coherent x-ray diffraction microscope was installed at the 2-ID-B beamline of the Advanced Photon Source for use with 0.7-2.9 keV x-rays. The instrument can accommodate three common implementations of diffractive imaging; plane wave illumination; defocused-probe (Fresnel diffractive imaging) and scanning (ptychography) using either a pinhole, focused or defocused probe. The microscope design includes active feedback to limit motion of the optics with respect to the sample. Upper bounds on the relative optics-to-sample displacement have been measured to be 5.8 nm(v) and 4.4 nm(h) rms/h using capacitance micrometry and 27 nm/h using x-ray point projection imaging. The stability of the measurement platform and in-vacuum operation allows for long exposure times, high signal-to-noise and large dynamic range two-dimensional intensity measurements to be acquired. Finally, we illustrate the microscope's stability with a recent experimental result.

Dichroic coherent diffractive imaging

Understanding electronic structure at the nanoscale is crucial to untangling fundamental physics puzzles such as phase separation and emergent behavior in complex magnetic oxides. Probes with the ability to see beyond surfaces on nanometer length and subpicosecond time scales can greatly enhance our understanding of these systems and will undoubtedly impact development of future information technologies. Polarized X-rays are an appealing choice of probe due to their penetrating power, elemental and magnetic specificity, and high spatial resolution. The resolution of traditional X-ray microscopes is limited by the nanometer precision required to fabricate X-ray optics. Here we present a novel approach to lensless imaging of an extended magnetic nanostructure, in which a scanned series of dichroic coherent diffraction patterns is recorded and numerically inverted to map its magnetic domain configuration. Unlike holographic methods, it does not require a reference wave or precision optics. In addition, it enables the imaging of samples with arbitrarily large spatial dimensions, at a spatial resolution limited solely by the coherent X-ray flux, wavelength, and stability of the sample with respect to the beam. It can readily be extended to nonmagnetic systems that exhibit circular or linear dichroism. We demonstrate this approach by imaging ferrimagnetic labyrinthine domains in a Gd/Fe multilayer with perpendicular anisotropy and follow the evolution of the domain structure through part of its magnetization hysteresis loop. This approach is scalable to imaging with diffraction-limited resolution, a prospect rapidly becoming a reality in view of the new generation of phenomenally brilliant X-ray sources.

Dynamic sample imaging in coherent diffractive imaging

As the resolution in coherent diffractive imaging improves, interexposure and intraexposure sample dynamics, such as motion, degrade the quality of the reconstructed image. Selecting data sets that include only exposures where tolerably little motion has occurred is an inefficient use of time and flux, especially when detector readout time is significant. We provide an experimental demonstration of an approach in which all images of a data set exhibiting sample motion are combined to improve the quality of a reconstruction. This approach is applicable to more general sample dynamics (including sample damage) that occur during measurement.

Phase-diverse coherent diffractive imaging: high sensitivity with low dose

This Letter demonstrates that coherent diffractive imaging (CDI), in combination with phase-diversity methods, provides reliable and artefact free high-resolution images. Here, using x rays, experimental results show a threefold improvement in the available image contrast. Furthermore, in conditions requiring low imaging dose, it is demonstrated that phase-diverse CDI provides a factor of 2 improvement in comparison to previous CDI techniques.

Fresnel coherent diffraction tomography

Tomographic coherent imaging requires the reconstruction of a series of two-dimensional projections of the object. We show that using the solution for the image of one projection as the starting point for the reconstruction of the next projection offers a reliable and rapid approach to the image reconstruction. The method is demonstrated on simulated and experimental data. This technique also simplifies reconstructions using data with curved incident wavefronts.