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

High-resolution and high-sensitivity X-ray ptychographic coherent diffraction imaging using the CITIUS detector

Ptychographic coherent diffraction imaging (PCDI) is a synchrotron X-ray microscopy technique that provides high spatial resolution and a wide field of view. To improve the performance of PCDI, the performance of the synchrotron radiation source and imaging detector should be improved. In this study, ptychographic diffraction pattern measurements using the CITIUS high-speed X-ray image detector and the corresponding image reconstruction are reported. X-rays with an energy of 6.5 keV were focused by total reflection focusing mirrors, and a flux of ∼2.6 × 1010 photons s-1 was obtained at the sample plane. Diffraction intensity data were collected at up to ∼250 Mcounts s-1 pixel-1 without saturation of the detector. Measurements of tantalum test charts and silica particles and the reconstruction of phase images were performed. A resolution of ∼10 nm and a phase sensitivity of ∼0.01 rad were obtained. The CITIUS detector can be applied to the PCDI observation of various samples using low-emittance synchrotron radiation sources and to the stability evaluation of light sources.

Towards optimized illumination for high-resolution ptychography

We present a systematic study, where effects of the illumination probe design on ptychography reconstruction quality are evaluated under well-controlled conditions. The illumination probe was created using Fresnel zone-plate (FZP) optics with locally displaced zones to provide a fine control over perturbations of the illumination wavefront. We show that optimally designed wavefront modulations not only reduce bias and variance in the reconstruction of the lowest spatial frequencies but also lead to improved imaging resolution and reduction of artefacts compared to a conventional FZP. Both these factors are important for quantitative accuracy and resolution of ptychographic tomography. Our work furthers the understanding of the important characteristics of an optimal illumination for high-resolution X-ray ptychography and how to design optimal FZP wavefront modulations for different applications of ptychographic imaging. These findings are applicable and relevant for ptychography using optical, EUV, and X-ray photons as well as electrons.

Enhancement of phase retrieval capability in ptychography by using strongly scattering property of the probe-generating device

In common ptychographic coherent diffractive imaging (PCDI) systems, the probe-generating devices typically exhibit strong scattering, which is not fully used. Here, we report the reasonableness of using the diffraction pattern of the probe-generating device as the frequency-domain information of the scanning probe located in the sample plane, and we propose a method introducing this frequency-domain information into an iterative process to improve the imaging quality of PCDI. The new method was demonstrated using both a visible laser source and a synchrotron radiation X-ray source; the proposed method significantly improved the imaging quality in both demonstrations.

In situ coherent diffractive imaging

Coherent diffractive imaging (CDI) has been widely applied in the physical and biological sciences using synchrotron radiation, X-ray free-electron laser, high harmonic generation, electrons, and optical lasers. One of CDI’s important applications is to probe dynamic phenomena with high spatiotemporal resolution. Here, we report the development of a general in situ CDI method for real-time imaging of dynamic processes in solution. By introducing a time-invariant overlapping region as real-space constraint, we simultaneously reconstructed a time series of complex exit wave of dynamic processes with robust and fast convergence. We validated this method using optical laser experiments and numerical simulations with coherent X-rays. Our numerical simulations further indicated that in situ CDI can potentially reduce radiation dose by more than an order of magnitude relative to conventional CDI. With further development, we envision in situ CDI could be applied to probe a range of dynamic phenomena in the future.

Coherent diffractive imaging (CDI) allows for high resolution imaging without lenses. Here, Lo et al. develop in situ CDI with real-time imaging and a corresponding low-dose requirement, with expected applications in the physical and life sciences.

Robust X-ray angular correlations for the study of meso-structures

As self-assembling nanomaterials become more sophisticated, it is becoming increasingly important to measure the structural order of finite-sized assemblies of nano-objects. These mesoscale clusters represent an acute challenge to conventional structural probes, owing to the range of implicated size scales (10 nm to several micrometres), the weak scattering signal and the dynamic nature of meso-clusters in native solution environments. The high X-ray flux and coherence of modern synchrotrons present an opportunity to extract structural information from these challenging systems, but conventional ensemble X-ray scattering averages out crucial information about local particle configurations. Conversely, a single meso-cluster scatters too weakly to recover the full diffraction pattern. Using X-ray angular cross-correlation analysis, it is possible to combine multiple noisy measurements to obtain robust structural information. This paper explores the key theoretical limits and experimental challenges that constrain the application of these methods to probing structural order in real nanomaterials. A metric is presented to quantify the signal-to-noise ratio of angular correlations, and it is used to identify several experimental artifacts that arise. In particular, it is found that background scattering, data masking and inter-cluster interference profoundly affect the quality of correlation analyses. A robust workflow is demonstrated for mitigating these effects and extracting reliable angular correlations from realistic experimental data.

Holographic imaging with a hard x-ray nanoprobe: ptychographic versus conventional phase retrieval

We have performed near-field x-ray imaging with simultaneous object and probe reconstruction. By an advanced ptychographic algorithm based on longitudinal and lateral translations, full-field images of nanoscale objects are reconstructed with quantitative contrast values, along with the extended wavefronts used to illuminate the objects. The imaging scheme makes idealizing assumptions on the probe obsolete, and efficiently disentangles phase shifts related to the object from the imperfections in the illumination. We validate this approach by comparison to the conventional reconstruction scheme without simultaneous probe retrieval, based on the contrast transfer function algorithm. To this end, a set of semiconductor nanowires with controlled chemical composition (InP core, insulating SiO₂ layer, and indium tin oxide cover) is imaged using the quasi-point source illumination realized by the hard x-ray nanofocus (26  nm×39  nm spot size) of the ID16A Nano-Imaging beamline at the European Synchrotron Radiation Facility.

Probe-diverse ptychography

We propose an extension of ptychography where the target sample is scanned separately through several probes with distinct amplitude and phase profiles and a diffraction image is recorded for each probe and each sample translation. The resulting probe-diverse dataset is used to iteratively retrieve high-resolution images of the sample and all probes simultaneously. The method is shown to yield significant improvement in the reconstructed sample image compared to the image obtained using the standard single-probe ptychographic phase-retrieval scheme.

Molar concentration from sequential 2-D water-window X-ray ptychography and X-ray fluorescence in hydrated cells

Recent developments in biological X-ray microscopy have allowed structural information and elemental distribution to be simultaneously obtained by combining X-ray ptychography and X-ray fluorescence microscopy. Experimentally, these methods can be performed simultaneously; however, the optimal conditions for each measurement may not be compatible. Here, we combine two distinct measurements of ultrastructure and elemental distribution, with each measurement performed under optimised conditions. By combining optimised ptychography and fluorescence information we are able to determine molar concentrations from two-dimensional images, allowing an investigation into the interactions between the environment sensing filopodia in fibroblasts and extracellular calcium. Furthermore, the biological ptychography results we present illustrate a point of maturity where the technique can be applied to solve significant problems in structural biology.

Compound focusing mirror and X-ray waveguide optics for coherent imaging and nano-diffraction

A compound optical system for coherent focusing and imaging at the nanoscale is reported, realised by high-gain fixed-curvature elliptical mirrors in combination with X-ray waveguide optics or different cleaning apertures. The key optical concepts are illustrated, as implemented at the Göttingen Instrument for Nano-Imaging with X-rays (GINIX), installed at the P10 coherence beamline of the PETRA III storage ring at DESY, Hamburg, and examples for typical applications in biological imaging are given. Characteristic beam configurations with the recently achieved values are also described, meeting the different requirements of the applications, such as spot size, coherence or bandwidth. The emphasis of this work is on the different beam shaping, filtering and characterization methods.

Quantitative X-ray phase contrast waveguide imaging of bacterial endospores

Quantitative X-ray phase contrast imaging uniquely offers quantitative imaging information in terms of electron density maps allowing for mass and mass density determinations of soft biological samples (‘weighing with light’). Here, it was carried out using coherent X-ray waveguide illumination, yielding values of the mass and mass density of freeze-dried bacterial endospores (Bacillus spp.).

Quantitative waveguide-based X-ray phase contrast imaging has been carried out on the level of single, unstained, unsliced and freeze-dried bacterial cells of Bacillus thuringiensis and Bacillus subtilis using hard X-rays of 7.9 keV photon energy. The cells have been prepared in the metabolically dormant state of an endospore. The quantitative phase maps obtained by iterative phase retrieval using a modified hybrid input–output algorithm allow for mass and mass density determinations on the level of single individual endospores but include also large field of view investigations. Additionally, a direct reconstruction based on the contrast transfer function is investigated, and the two approaches are compared. Depending on the field of view and method, a resolution down to 65 nm was achieved at a maximum applied dose of below 5 × 10⁵ Gy. Masses in the range of about ∼110–190 (20) fg for isolated endospores have been obtained.

Mapping biological composition through quantitative phase and absorption X-ray ptychography

Isolating compositional information in biological X-ray imaging can be problematic as such information is conflated with thickness and density variations when viewing in projection through a sample. We demonstrate an effective method for identifying variations in material composition by simultaneously using the quantitative phase and magnitude images provided through soft X-ray ptychography. Using this approach we show significantly increased contrast and improved reliability of the identification of intracellular features from uncharacterised samples. While demonstrated for X-ray ptychography, this method is immediately applicable to electron and optical microscopy methods where the complex transmission function of the sample is recovered.

High-dynamic-range coherent diffractive imaging: ptychography using the mixed-mode pixel array detector

Coherent (X-ray) diffractive imaging (CDI) is an increasingly popular form of X-ray microscopy, mainly due to its potential to produce high-resolution images and the lack of an objective lens between the sample and its corresponding imaging detector. One challenge, however, is that very high dynamic range diffraction data must be collected to produce both quantitative and high-resolution images. In this work, hard X-ray ptychographic coherent diffractive imaging has been performed at the P10 beamline of the PETRA III synchrotron to demonstrate the potential of a very wide dynamic range imaging X-ray detector (the Mixed-Mode Pixel Array Detector, or MM-PAD). The detector is capable of single photon detection, detecting fluxes exceeding 1 × 10(8) 8-keV photons pixel(-1) s(-1), and framing at 1 kHz. A ptychographic reconstruction was performed using a peak focal intensity on the order of 1 × 10(10) photons µm(-2) s(-1) within an area of approximately 325 nm × 603 nm. This was done without need of a beam stop and with a very modest attenuation, while `still' images of the empty beam far-field intensity were recorded without any attenuation. The treatment of the detector frames and CDI methodology for reconstruction of non-sensitive detector regions, partially also extending the active detector area, are described.

Fast deterministic ptychographic imaging using X-rays

We present a deterministic approach to the ptychographic retrieval of the wave at the exit surface of a specimen of condensed matter illuminated by X-rays. The method is based on the solution of an overdetermined set of linear equations, and is robust to measurement noise. The set of linear equations is efficiently solved using the conjugate gradient least-squares method implemented using fast Fourier transforms. The method is demonstrated using a data set obtained from a gold-chromium nanostructured test object. It is shown that the transmission function retrieved by this linear method is quantitatively comparable with established methods of ptychography, with a large decrease in computational time, and is thus a good candidate for real-time reconstruction.

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.

High-resolution multislice x-ray ptychography of extended thick objects

We report the first demonstration of hard x-ray ptychography using a multislice approach, which can solve the problem of the limited spatial resolution under the projection approximation. We measured ptychographic diffraction patterns of a two-layered object with a 105  μm gap using 7 keV focused coherent x rays. We successfully reconstructed the phase map of each layer at ∼50  nm resolution using a multislice approach, while the resolution was worse than ∼192  nm under the projection approximation. The present method has the potential to enable the three-dimensional high-resolution observation of extended thick specimens in materials science and biology.

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.

Using coherent X-ray ptychography to probe medium-range order

Characterization of microscopic structural order and in particular medium range order (MRO) in amorphous materials is challenging. A new technique is demonstrated that allows analysis of MRO using X-rays. Diffraction data were collected from a sample consisting of densely packed polystyrene-latex micro-spheres. Ptychography is used to reconstruct the sample transmission function and fluctuation microscopy applied to characterize structural order producing a detailed `fluctuation map' allowing analysis of the sample at two distinct length scales. Independent verification is provided via X-ray diffractometry. Simulations of dense random packing of spheres have also been used to explore the origin of the structural order measured.

Quantitative phase imaging via Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently developed imaging modality that uses angularly varying illumination to extend a system's performance beyond the limit defined by its optical components. The FPM technique applies a novel phase-retrieval procedure to achieve resolution enhancement and complex image recovery. In this Letter, we compare FPM data to theoretical prediction and phase-shifting digital holography measurement to show that its acquired phase maps are quantitative and artifact-free. We additionally explore the relationship between the achievable spatial and optical thickness resolution offered by a reconstructed FPM phase image. We conclude by demonstrating enhanced visualization and the collection of otherwise unobservable sample information using FPM's quantitative phase.

Phase retrieval for object and probe using a series of defocus near-field images

Full field x-ray propagation imaging can be severely deteriorated by wave front aberrations. Here we present an extension of ptychographic phase retrieval with simultaneous probe and object reconstruction suitable for the near-field diffractive imaging setting. Update equations used to iteratively solve the phase problem from a set of near-field images in view of reconstruction both object and probe are derived. The algorithm is tested based on numerical simulations including photon shot noise. The results indicate that the approach provides an efficient way to overcome restrictive idealizations of the illumination wave in the near-field (propagation) imaging.

Versatility of a hard X-ray Kirkpatrick-Baez focus characterized by ptychography

In the past decade Kirkpatrick-Baez (KB) mirrors have been established as powerful focusing systems in hard X-ray microscopy applications. Here a ptychographic characterization of the KB focus in the dedicated nano-imaging setup GINIX (Göttingen Instrument for Nano-Imaging with X-rays) at the P10 coherence beamline of the PETRA III synchrotron at HASLYLAB/DESY, Germany, is reported. More specifically, it is shown how aberrations in the KB beam, caused by imperfections in the height profile of the focusing mirrors, can be eliminated using a pinhole as a spatial filter near the focal plane. A combination of different pinhole sizes and illumination conditions of the KB setup makes the prepared optical setup well suited not only for high-resolution ptychographic coherent X-ray diffractive imaging but also for moderate-resolution/large-field-of-view propagation imaging in the divergent KB beam.

Effects of missing low-frequency information on ptychographic and plane-wave coherent diffraction imaging

In coherent diffractive imaging (CDI) experiments, a beamstop (BS) is commonly used to extend the exposure time of the charge-coupled detector and obtain high-angle diffraction signals. However, the negative effect of a large BS is also evident, causing low-frequency signals to be missed and making CDI reconstruction unstable or causing it to fail. We performed a systematic simulation investigation of the effects of BSs on the quality of reconstructed images from both plane-wave and ptychographic CDI (PCDI). For the same imaging quality, we found that ptychography can tolerate BSs that are at least 20 times larger than those for plane-wave CDI. For PCDI, a larger overlap ratio and a smaller illumination spot can significantly increase the imaging robustness to the negative influence of BSs. Our results provide guidelines for the usage of BSs in CDI, especially in PCDI experiments, which can help to further improve the spatial resolution of PCDI.

In-Line Phase-Contrast X-ray Imaging and Tomography for Materials Science

X-ray phase-contrast imaging and tomography make use of the refraction of X-rays by the sample in image formation. This provides considerable additional information in the image compared to conventional X-ray imaging methods, which rely solely on X-ray absorption by the sample. Phase-contrast imaging highlights edges and internal boundaries of a sample and is thus complementary to absorption contrast, which is more sensitive to the bulk of the sample. Phase-contrast can also be used to image low-density materials, which do not absorb X-rays sufficiently to form a conventional X-ray image. In the context of materials science, X-ray phase-contrast imaging and tomography have particular value in the 2D and 3D characterization of low-density materials, the detection of cracks and voids and the analysis of composites and multiphase materials where the different components have similar X-ray attenuation coefficients. Here we review the use of phase-contrast imaging and tomography for a wide variety of materials science characterization problems using both synchrotron and laboratory sources and further demonstrate the particular benefits of phase contrast in the laboratory setting with a series of case studies.

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.

Atom-scale ptychographic electron diffractive imaging of boron nitride cones

Ptychographic coherent diffractive imaging (CDI) has been extensively applied using both x rays and electrons. The extension to atomic resolution has been elusive. This Letter demonstrates ptychographic electron diffractive imaging at atomic resolution, permitting identification of structure in a boron nitride helical cone at a resolution of order 1 Å, beyond that of comparative Z-contrast images. A scanning transmission electron microscope is used to create a diverging illumination in a defocused Fresnel CDI geometry, providing a robust strategy leading to a unique solution.

Multi-wavelength elemental contrast absorption imaging

We report experimental demonstrations of a quantitative technique for elemental mapping. The technique operates in full-field imaging mode and uses three intensity measurements at energies across an absorption edge of an element of interest to obtain its elemental distribution. The experimental results show that the technique can overcome some limitations in the conventional Absorption Edge Contrast Imaging. The technique allows for an accurate determination of the elemental distribution in a compound sample even at a low level of percentage composition. It is also robust to the choice of energy intervals.

Phase tomography from x-ray coherent diffractive imaging projections

Coherent diffractive imaging provides accurate phase projections that can be tomographically combined to yield detailed quantitative 3D reconstructions with a resolution that is not limited by imaging optics. We present robust algorithms for post-processing and alignment of these tomographic phase projections. A simple method to remove undesired constant and linear phase terms on the reconstructions is given. Also, we provide an algorithm for automatic alignment of projections that has good performance even for samples with no fiducial markers. Currently applied to phase projections, this alignment algorithm has proven to be robust and should also be useful for lens-based tomography techniques that pursue nanoscale 3D imaging. Lastly, we provide a method for tomographic reconstruction that works on phase projections that are known modulo 2π, such that the phase unwrapping step is avoided. We demonstrate the performance of these algorithms by 3D imaging of bacteria population in legume root-nodule cells.

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.