Coherent Diffraction Patterns Research Articles

Hard X-ray polarizer to enable simultaneous three-dimensional nanoscale imaging of magnetic structure and lattice strain

Recent progress in the development of dichroic Bragg coherent diffractive imaging, a new technique for simultaneous three-dimensional imaging of strain and magnetization at the nanoscale, is reported. This progress includes the installation of a diamond X-ray phase retarder at beamline 34-ID-C of the Advanced Photon Source. The performance of the phase retarder for tuning X-ray polarization is demonstrated with temperature-dependent X-ray magnetic circular dichroism measurements on a gadolinium foil in transmission and on a Gd5Si2Ge2 crystal in diffraction geometry with a partially coherent, focused X-ray beam. Feasibility tests for dichroic Bragg coherent diffractive imaging are presented. These tests include (1) using conventional Bragg coherent diffractive imaging to determine whether the phase retarder introduces aberrations using a nonmagnetic gold nanocrystal as a control sample, and (2) collecting coherent diffraction patterns of a magnetic Gd5Si2Ge2 nanocrystal with left- and right-circularly polarized X-rays. Future applications of dichroic Bragg coherent diffractive imaging for the correlation of strain and lattice defects with magnetic ordering and inhomogeneities are considered.

Electrode-stress-induced nanoscale disorder in Si quantum electronic devices

Disorder in the potential-energy landscape presents a major obstacle to the more rapid development of semiconductor quantum device technologies. We report a large-magnitude source of disorder, beyond commonly considered unintentional background doping or fixed charge in oxide layers: nanoscale strain fields induced by residual stresses in nanopatterned metal gates. Quantitative analysis of synchrotron coherent hard x-ray nanobeam diffraction patterns reveals gate-induced curvature and strains up to 0.03% in a buried Si quantum well within a Si/SiGe heterostructure. Electrode stress presents both challenges to the design of devices and opportunities associated with the lateral manipulation of electronic energy levels.

Multiple defocused coherent diffraction imaging: method for simultaneously reconstructing objects and probe using X-ray free-electron lasers.

The sample size must be less than the diffraction-limited focal spot size of the incident beam in single-shot coherent X-ray diffraction imaging (CXDI) based on a diffract-before-destruction scheme using X-ray free electron lasers (XFELs). This is currently a major limitation preventing its wider applications. We here propose multiple defocused CXDI, in which isolated objects are sequentially illuminated with a divergent beam larger than the objects and the coherent diffraction pattern of each object is recorded. This method can simultaneously reconstruct both objects and a probe from the coherent X-ray diffraction patterns without any a priori knowledge. We performed a computer simulation of the prposed method and then successfully demonstrated it in a proof-of-principle experiment at SPring-8. The prposed method allows us to not only observe broad samples but also characterize focused XFEL beams.

X-ray Absorption Spectroscopy and Coherent X-ray Diffraction Imaging for Time-Resolved Investigation of the Biological Complexes: Computer Modelling towards the XFEL Experiment

The development of the next generation synchrotron radiation sources - free electron lasers - is approaching to become an effective tool for the time-resolved experiments aimed to solve actual problems in various fields such as chemistry’ biology’ medicine’ etc. In order to demonstrate’ how these experiments may be performed for the real systems to obtain information at the atomic and macromolecular levels’ we have performed a molecular dynamics computer simulation combined with quantum chemistry calculations for the human phosphoglycerate kinase enzyme with Mg containing substrate. The simulated structures were used to calculate coherent X-ray diffraction patterns’ reflecting the conformational state of the enzyme, and Mg K-edge X-ray absorption spectra, which depend on the local structure of the substrate. These two techniques give complementary information making such an approach highly effective for time-resolved investigation of various biological complexes, such as metalloproteins or enzymes with metal-containing substrate, to obtain information about both metal-containing active site or substrate and the atomic structure of each conformation.

Holography-guided ptychography with soft X-rays.

Ptychography is a lensless imaging technique that aims to reconstruct an object from a set of coherent diffraction patterns originating from different and partially overlapping sample illumination areas. For a successful convergence of the iterative algorithms used, the sample scan positions have to be known with very high accuracy. Here, we present a method that allows to directly encode this information in the diffraction patterns without the need of accurate position encoders. Our approach relies on combining ptychography with another coherent imaging method, namely Fourier-transform holography. We have imaged two different objects using coherent soft-X-ray illumination and investigate the influence of experimental and numerical position refinement on the reconstruction result. We demonstrate that holographically encoded positions significantly reduce the experimental and numerical requirements. Our ptychographic reconstructions cover a large field of view with diffraction-limited resolution and high sensitivity in the reconstructed phase shift and absorption of the objects.

Ptychographic iterative engine with partially coherent illumination for weakly scattering samples

As an expansion of coherent diffraction imaging, ptychographic iterative engine (PIE) not only inherits advantages such as ultra-high resolution and compact optical system, but also expands the field of view in quantitative imaging, thus PIE is widely used in short wavelength imaging such as X-ray and electron beam imaging, and then extended to visible light field. However, PIE requires coherent illumination for both phase and amplitude retrieval, while traditional X-ray or electron beam sources often cannot satisfy this strict coherent condition, which leads to poor-quality information retrieval with low signal-to-noise ratio. Though several proposed methods such as multiple wavelength and multi-mode algorithms can eliminate incoherency influence to some extent, various details such as quantitative spectrum of illuminating source should be obtained before information retrieval, which complicates computing procedures. In addition, it is hard to acquire the spectrum of the illuminating source in most cases. In order to acquire high-quality information based on PIE with partially coherent illumination, a newly designed enhanced phase retrieval method for weakly scattering samples in PIE with partially coherent illumination is presented in this paper, in which only the bright field of the diffraction patterns is used in the iterative procedures mimicking the coherent cases especially for weakly scattering samples without any prior illuminating details. The bright field area can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. While the dark-field area generated by interference of diffracted beams cannot satisfy the requirement for coherence, therefore, dark-field diffraction patterns should be excluded in sample information extraction and only the bright field is used for phase retrieval via iterative process. Compared with the proposed multiple wavelength and multi-mode algorithms, the proposed method can simplify sample reconstructing procedures due to needing no prior knowledge. Moreover, in order to enhance the information of weakly scattering samples in retrieval, high order iteration method is also introduced in the paper. Since the bright field can be regarded as purely coherent diffraction patterns composed of a strengthened zeroth order beam and a weakened diffracted beam. For weakly scattering sample, the weakened diffracted beam is much lower than zeroth order beam, thus it is difficult to acquire high-contrast information with classical PIE algorithms. Introducing high order iterative tactic, the contrast of weakly scattering sample is obviously improved and the details of weakly scattering sample can be retrieved clearly. Both theoretical analysis and numerical simulations are illustrated in detail, proving the robustness and availability of the designed method: high-contrast phase information can be obtained with the proposed method, while traditional phase retrieval algorithm almost loses all details of the sample. In order to mimic the real experimental situation, a 30 dB white noise is added into the simulation, the details of weakly scattering sample phase information can also be retrieved clearly by using the bright field of the diffraction patterns with high order iteration method. With the newly designed enhanced phase retrieval method for weakly scattering samples with partially coherent illumination, sample retrieval via PIE can not only use ordinary X-ray source or electron beam as illumination source, thereby avoiding the dependence on complete coherent source, but also obviously improve the retrieval quality of the sample characteristics, which widely expands the application fields of the PIE.

Low-kilovolt coherent electron diffractive imaging instrument based on a single-atom electron source

In this work, a transmission-type, low-kilovolt coherent electron diffractive imaging instrument was constructed. It comprised a single-atom field emitter, a triple-element electrostatic lens, a sample holder, and a retractable delay line detector to record the diffraction patterns at different positions behind the sample. It was designed to image materials thinner than 3 nm. The authors analyzed the asymmetric triple-element electrostatic lens for focusing the electron beams and achieved a focused beam spot of 87 nm on the sample plane at the electron energy of 2 kV. High-angle coherent diffraction patterns of a suspended graphene sample corresponding to (0.62 Å)−1 were recorded. This work demonstrated the potential of coherent diffractive imaging of thin two-dimensional materials, biological molecules, and nano-objects at a voltage between 1 and 10 kV. The ultimate goal of this instrument is to achieve atomic resolution of these materials with high contrast and little radiation damage.

Three-dimensional coherent diffraction imaging of Mie-scattering spheres by laser single-orientation measurement**Project supported by the Major State Basic Research Development Program of China (Grant No. 2014CB910401) and the National Natural Science Foundation of China (Grant Nos. 31430031, 21390414, and U1332118).

Three-dimensional imaging with single orientation is a potential and novel technique. We successfully demonstrate that three-dimensional (3D) structure can be determined by a single orientation diffraction measurement for a phase object of double-layer Mie-scattering silica spheres on a Si3N4 membrane. Coherent diffraction pattern at high numerical aperture was acquired with an optical laser, and the oversampled pattern was projected from a planar detector onto the Ewald sphere. The double-layered spheres are reconstructed from the spherical diffraction pattern and a 2D curvature-corrected pattern, which improve convergence speed and stability of reconstruction.

Efficient modeling of Bragg coherent x-ray nanobeam diffraction.

X-ray Bragg diffraction experiments that utilize tightly focused coherent beams produce complicated Bragg diffraction patterns that depend on scattering geometry, characteristics of the sample, and properties of the x-ray focusing optic. Here, we use a Fourier-transform-based method of modeling the 2D intensity distribution of a Bragg peak and apply it to the case of thin films illuminated with a Fresnel zone plate in three different Bragg scattering geometries. The calculations agree well with experimental coherent diffraction patterns, demonstrating that nanodiffraction patterns can be modeled at nonsymmetric Bragg conditions with this approach--a capability critical for advancing nanofocused x-ray diffraction microscopy.

Generalized eikonal approximation for strong-field ionization

We develop the eikonal perturbation theory to describe the strong-field ionization by finite laser pulses. This approach in the first order with respect to the binding potential (the so-called generalized eikonal approximation) avoids a singularity at the potential center. Thus, in contrast to the ordinary eikonal approximation, it allows to treat rescattering phenomena in terms of quantum trajectories. We demonstrate how the first Born approximation and its domain of validity follow from eikonal perturbation theory. Using this approach, we study the coherent diffraction patterns in photoelectron energy spectra and their modifications induced by the interaction of photoelectrons with the atomic potential. Along with these first results, we discuss the prospects of using the generalized eikonal approximation to study strong-field ionization from multi-centered atomic systems and to study other strong-field phenomena.

Signature of dislocations and stacking faults of face-centred cubic nanocrystals in coherent X-ray diffraction patterns: a numerical study.

Crystal defects induce strong distortions in diffraction patterns. A single defect alone can yield strong and fine features that are observed in high-resolution diffraction experiments such as coherent X-ray diffraction. The case of face-centred cubic nanocrystals is studied numerically and the signatures of typical defects close to Bragg positions are identified. Crystals of a few tens of nanometres are modelled with realistic atomic potentials and 'relaxed' after introduction of well defined defects such as pure screw or edge dislocations, or Frank or prismatic loops. Diffraction patterns calculated in the kinematic approximation reveal various signatures of the defects depending on the Miller indices. They are strongly modified by the dissociation of the dislocations. Selection rules on the Miller indices are provided, to observe the maximum effect of given crystal defects in the initial and relaxed configurations. The effect of several physical and geometrical parameters such as stacking fault energy, crystal shape and defect position are discussed. The method is illustrated on a complex structure resulting from the simulated nanoindentation of a gold nanocrystal.

Ptychographic x-ray imaging of surfaces on crystal truncation rod

Ptychography is a high-resolution imaging technique, which does not require lenses for image magnification and which provides phase contrast with high sensitivity. Here, we propose to use x-ray ptychography for the imaging of surface structure in crystalline samples. We show that ptychography can be used to image atomic step structures using coherent diffraction patterns recorded along the crystal truncation rod of a crystal surface. In a proof-of-concept experiment on a Pt (111) sample, we present ptychographic reconstructions showing features consistent with surface steps. Due to the penetration power of x-rays, this method could find interesting applications for the study of surface structures under buried interfaces or in harsh environments.

Evaluation of partial coherence correction in X-ray ptychography.

Coherent X-ray Diffraction Imaging (CDI) and X-ray ptychography both heavily rely on the high degree of spatial coherence of the X-ray illumination for sufficient experimental data quality for reconstruction convergence. Nevertheless, the majority of the available synchrotron undulator sources have a limited degree of partial coherence, leading to reduced data quality and a lower speckle contrast in the coherent diffraction patterns. It is still an open question whether experimentalists should compromise the coherence properties of an X-ray source in exchange for a higher flux density at a sample, especially when some materials of scientific interest are relatively weak scatterers. A previous study has suggested that in CDI, the best strategy for the study of strong phase objects is to maintain a high degree of coherence of the illuminating X-rays because of the broadening of solution space resulting from the strong phase structures. In this article, we demonstrate the first systematic analysis of the effectiveness of partial coherence correction in ptychography as a function of the coherence properties, degree of complexity of illumination (degree of phase diversity of the probe) and sample phase complexity. We have also performed analysis of how well ptychographic algorithms refine X-ray probe and complex coherence functions when those variables are unknown at the start of reconstructions, for noise-free simulated data, in the case of both real-valued and highly-complex objects.

Time-resolved coherent X-ray diffraction imaging of surface acoustic waves.

Time-resolved coherent X-ray diffraction experiments of standing surface acoustic waves, illuminated under grazing incidence by a nanofocused synchrotron beam, are reported. The data have been recorded in stroboscopic mode at controlled and varied phase between the acoustic frequency generator and the synchrotron bunch train. At each time delay (phase angle), the coherent far-field diffraction pattern in the small-angle regime is inverted by an iterative algorithm to yield the local instantaneous surface height profile along the optical axis. The results show that periodic nanoscale dynamics can be imaged at high temporal resolution in the range of 50 ps (pulse length).

Resolving high-speed colloidal dynamics beyond detector response time via two pulse speckle contrast correlation.

We report an alternate light scattering approach to measure intermediate scattering function and structures of colloidal suspension by using two-pulse speckle contrast correlation analysis. By systematically controlling time-delays between two laser pulses incident on the sample, we are able to monitor transient evolution of coherent diffraction pattern, from which particle dynamics at different length and time scales are obtained simultaneously. Our result demonstrates the feasibility of utilizing a megapixel detector to achieve sufficient data statistics in a short amount of time while enabling microsecond time-resolution. Ultimately, this method provides means to measure high-speed dynamics well beyond the time response limit of a large area two-dimensional (2D) detector.

Single-shot three-dimensional structure determination of nanocrystals with femtosecond X-ray free-electron laser pulses.

Conventional three-dimensional (3D) structure determination methods require either multiple measurements at different sample orientations or a collection of serial sections through a sample. Here we report the experimental demonstration of single-shot 3D structure determination of an object; in this case, individual gold nanocrystals at ~5.5 nm resolution using ~10 fs X-ray free-electron laser pulses. Coherent diffraction patterns are collected from high-index-faceted nanocrystals, each struck by an X-ray free-electron laser pulse. Taking advantage of the symmetry of the nanocrystal and the curvature of the Ewald sphere, we reconstruct the 3D structure of each nanocrystal from a single-shot diffraction pattern. By averaging a sufficient number of identical nanocrystals, this method may be used to determine the 3D structure of nanocrystals at atomic resolution. As symmetry exists in many virus particles, this method may also be applied to 3D structure studies of such particles at nanometer resolution on femtosecond time scales.

Retrieval of the atomic displacements in the crystal from the coherent X-ray diffraction pattern.

The retrieval of spatially resolved atomic displacements is investigated via the phases of the direct(real)-space image reconstructed from the strained crystal's coherent X-ray diffraction pattern. It is demonstrated that limiting the spatial variation of the first- and second-order spatial displacement derivatives improves convergence of the iterative phase-retrieval algorithm for displacements reconstructions to the true solution. This approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.

Coherent magnetic diffraction from the uranium M4 edge in the multi-k magnet, USb

The slow magnetic dynamics, from seconds to kiloseconds, of the canonical 3-k antiferromagnet USb have been probed, using X-ray photon correlation spectroscopy (XPCS). In this work, XPCS is combined with resonant X-ray diffraction to focus on scattering at an antiferromagnetic Bragg peak. High quality coherent magnetic diffraction patterns were recorded (speckle contrast of ~ 88%) and magnetic domains were observed; the number of domains increases on warming to T* ~ 160 K, where the spin waves soften to zero frequency, and again on warming to TN = 218 K. The intensity auto-correlation, g2(t), is primarily static over 1000 s, with a small dynamical process (change of ~ 0.4%) that increases in rate close to the transitions.

Coherent Bragg nanodiffraction at the hard X-ray Nanoprobe beamline

Bragg coherent diffraction with nanofocused hard X-ray beams provides unique opportunities for quantitative in situ studies of crystalline structure in nanoscale regions of complex materials and devices by a variety of diffraction-based techniques. In the case of coherent diffraction imaging, a major experimental challenge in using nanoscale coherent beams is maintaining a constant scattering volume such that coherent fringe visibility is maximized and maintained over the course of an exposure lasting several seconds. Here, we present coherent Bragg diffraction patterns measured from different nanostructured thin films at the Sector 26 Nanoprobe beamline at the Advanced Photon Source and demonstrate that with nanoscale positional control, coherent diffraction patterns can be measured with source-limited fringe visibilities more than 50% suitable for imaging by coherent Bragg ptychography techniques.

Ptychographic overlap constraint errors and the limits of their numerical recovery using conjugate gradient descent methods

Ptychographic coherent x-ray diffractive imaging is a form of scanning microscopy that does not require optics to image a sample. A series of scanned coherent diffraction patterns recorded from multiple overlapping illuminated regions on the sample are inverted numerically to retrieve its image. The technique recovers the phase lost by detecting the diffraction patterns by using experimentally known constraints, in this case the measured diffraction intensities and the assumed scan positions on the sample. The spatial resolution of the recovered image of the sample is limited by the angular extent over which the diffraction patterns are recorded and how well these constraints are known. Here, we explore how reconstruction quality degrades with uncertainties in the scan positions. We show experimentally that large errors in the assumed scan positions on the sample can be numerically determined and corrected using conjugate gradient descent methods. We also explore in simulations the limits, based on the signal to noise of the diffraction patterns and amount of overlap between adjacent scan positions, of just how large these errors can be and still be rendered tractable by this method.