Coherent X-ray Beam Research Articles

Impact of corner radius of the aperture on the accuracy of phase retrieval analysis in single-frame CDI for nanomaterials

Numerous efforts have been developed to advance the process of Ptychography, leading to the emergence of a phenomenon known as single-frame Coherent X-ray Diffraction Imaging (CDI). It represents an advanced form of Ptychography in which a well-defined coherent X-ray beam is directed onto the sample to generate a diffraction image that includes intensity information but lacks phase details. However, phase retrieval in single-frame CDI faces challenges like overlapping loss, inadequate samples, or phase ambiguity due to the characteristics of this method. The optimising effort has been conducted in the form of aperture implementation to address these problems, particularly in the iterative phase retrieval domain. This study explores non-point symmetrical apertures, specifically triangles, to enhance image reconstruction quality in iterative phase retrieval. We developed a simulation methodology to explore the impact of corner radius on the apertures in performing single-frame CDI. Our simulator generates diffraction images for each shape, which are processed through iterative algorithms and deep learning to reconstruct images. The effectiveness of each shape is assessed by visualising the loss function results, providing insights into optimal aperture designs for diffraction imaging, and contributing to the resolution of phase retrieval challenges in single-frame CDI.

Signal-to-noise and spatial resolution in in-line imaging. 1. Basic theory, numerical simulations and planar experimental images.

Signal-to-noise ratio and spatial resolution are quantitatively analysed in the context of in-line (propagation based) X-ray phase-contrast imaging. It is known that free-space propagation of a coherent X-ray beam from the imaged object to the detector plane, followed by phase retrieval in accordance with Paganin's method, can increase the signal-to-noise in the resultant images without deteriorating the spatial resolution. This results in violation of the noise-resolution uncertainty principle and demonstrates `unreasonable' effectiveness of the method. On the other hand, when the process of free-space propagation is performed in software, using the detected intensity distribution in the object plane, it cannot reproduce the same effectiveness, due to the amplification of photon shot noise. Here, it is shown that the performance of Paganin's method is determined by just two dimensionless parameters: the Fresnel number and the ratio of the real decrement to the imaginary part of the refractive index of the imaged object. The relevant theoretical analysis is performed first, followed by computer simulations and then by a brief test using experimental images collected at a synchrotron beamline. More extensive experimental tests will be presented in the second part of this paper.

Nanometer flat blazed x-ray gratings using ion beam figure correction.

With the development of nanometer accuracy stitching interferometry, ion beam figuring (IBF) of x-ray mirrors can now be achieved with unprecedented performance. However, the process of producing x-ray diffraction gratings on these surfaces may degrade the figure quality due to process errors introduced during the ruling of the grating grooves. To address this challenge, we have investigated the post-production correction of gratings using IBF, where stitching interferometry is used to provide in-process feedback. A concern with ion beam correction in this case is that ions will induce enough surface mobility of atoms to cause smoothing of the grating structure and degradation of diffraction efficiency. In this study we found however that it is possible to achieve a nanometer-level planarity of the global grating surface with IBF, while preserving the grating structure. The preservation was so good, that we could not detect a change in the diffraction efficiency after ion beam correction. This is of major importance in achieving ultra-high spectral resolution, and the preservation of brightness for coherent x-ray beams.

Focused and coherent X-ray beams for advanced microscopies

The use of focused X-ray beams in the micron and sub-micron range has fostered the progress of a wide range of scanning microscopy approaches that exploit the numerous interactions of X-rays with matter. These methods are becoming crucial for an increasing number of research fields, such as energy materials, electronic devices, biology, to cite a few. Nanobeams produced at 4th generation synchrotrons have coherence properties that make them ideal for a 3D diffraction-based microscopy with unique sensitivity to strain and defects in crystalline materials and allow delving into materials heterogeneities. We provide here a short overview on the use of nanobeams for diffraction experiments, and perspectives for their use in spectroscopy studies.

In situ compression of micropillars under coherent X-ray diffraction: a case study of experimental and data-analysis constraints.

Micropillar compression is a method of choice to understand mechanics at small scale. It is mainly studied with electron microscopy or white-beam micro-Laue X-ray diffraction. The aim of the present article is to show the possibilities of the use of diffraction with a coherent X-ray beam. InSb micropillars in epitaxy with their pedestals (i.e. their support) are studied in situ during compression. Firstly, an experiment using a collimated beam matching the pillar size allows determination of when the sample enters the plastic regime, independently of small defects induced by experimental artefacts. A second experiment deals with scanning X-ray diffraction maps with a nano-focused beam; despite the coherence of the beam, the contributions from the pedestal and from the micropillar in the diffraction patterns can be separated, making possible a spatially resolved study of the plastic strain fields. A quantitative measurement of the elastic strain field is nevertheless hampered by the fact that the pillar diffracts at the same angles as the pedestal. Finally, no image reconstructions were possible in these experiments, either in situ due to a blurring of the fringes during loading or post-mortem because the defect density after yielding was too high. However, it is shown how to determine the elastic bending of the pillar in the elastic regime. Bending angles of around 0.3° are found, and a method to estimate the sample's radius of curvature is suggested.

Experimental setup for high-resolution characterization of crystal optics for coherent X-ray beam applications.

Stanford Synchrotron Radiation Lightsource serves a wide scientific community with its variety of X-ray capabilities. Recently, a wiggler X-ray source located at beamline 10-2 has been employed to perform high-resolution rocking curve imaging (RCI) of diamond and silicon crystals. X-ray RCI is invaluable for the development of upcoming cavity-based X-ray sources at SLAC, including the cavity-based X-ray free-electron laser and X-ray laser oscillator. In this paper, the RCI apparatus is described and experimental results are provided to validate its design. Future improvements of the setup are also discussed.

Beam focus modifications by cropping partially coherent X-ray beams

We simulate the focusing of a partially coherent X-ray beam emitted by an undulator in a fourth-generation storage ring by performing a coherent mode decomposition and wave optics propagation. The focus position is shifted, and its size is enlarged when an entrance slit crops the beam. This is the usual case when a slit is used to select the coherent fraction. The pairing of two focusing elements (mirrors, lenses or transfocators) to ensure a fixed focal position is also analyzed. Our results show that the image of a partially coherent source, such an undulator in a low-emittance storage ring, is a non-trivial function of the aperture used to control the coherence fraction.

Simultaneous imaging and diffraction in the dynamic diamond anvil cell.

The ability to visualize a sample undergoing a pressure-induced phase transition allows for the determination of kinetic parameters, such as the nucleation and growth rates of the high-pressure phase. For samples that are opaque to visible light (such as metallic systems), it is necessary to rely on x-ray imaging methods for sample visualization. Here, we present an experimental platform developed at beamline P02.2 at the PETRA III synchrotron radiation source, which is capable of performing simultaneous x-ray imaging and diffraction of samples that are dynamically compressed in piezo-driven diamond anvil cells. This setup utilizes a partially coherent monochromatic x-ray beam to perform lensless phase contrast imaging, which can be carried out using either a parallel- or focused-beam configuration. The capabilities of this platform are illustrated by experiments on dynamically compressed Ga and Ar. Melting and solidification were identified based on the observation of solid/liquid phase boundaries in the x-ray images and corresponding changes in the x-ray diffraction patterns collected during the transition, with significant edge enhancement observed in the x-ray images collected using the focused-beam. These results highlight the suitability of this technique for a variety of purposes, including melt curve determination.

Coherent X-ray beam expander based on a multilens interferometer.

A coherent X-ray beam expander based on a multilens interferometer is proposed in this paper. The multilens interferometer allows efficient generation of a highly diverging coherent beam up to several milliradians in the hard X-ray energy range. The optical properties of the interferometer were experimentally demonstrated at the ESRF ID13 undulator beamline (Grenoble, France), using 12.4 keV X-rays. The beam expander allowed us to control the angular size and photon flux density of the formed beam and enabled operation in both coherent and incoherent modes. The experimental results were fully consistent with the theoretical concepts and appropriate computer simulations. Future design improvements and related applications are also discussed.

Shape memory effect in metallic glasses

Shape memory effect in metallic glasses

Generating X-rays with orbital angular momentum in a free-electron laser oscillator

Light with orbital angular momentum (OAM) provides new insights into a wide range of physical phenomena and has engendered advanced applications in various fields. Additionally, interest in X-ray OAM has been rapidly rising. We present a straightforward method to generate intense OAM beams from an X-ray free-electron laser oscillator (XFELO). The method leverages Bragg mirrors and longitudinal-transverse mode coupling to enable mode selection in a conventional XFELO configuration, thereby natively producing the fully coherent hard X-ray beams carrying OAM. Furthermore, simulation results demonstrate that fully coherent hard X-ray OAM beams at 1 MHz with a pulse energy of about 120 µJ can be generated without the optical mode converters. This simple approach could significantly advance the creation of X-ray OAM while stimulating the development of experimental methods.

Internal resistive heating of non-metallic samples to 3000K and >60GPa in the diamond anvil cell.

High pressure-temperature experiments provide information on the phase diagrams and physical characteristics of matter at extreme conditions and offer a synthesis pathway for novel materials with useful properties. Experiments recreating the conditions of planetary interiors provide important constraints on the physical properties of constituent phases and are key to developing models of planetary processes and interpreting geophysical observations. The laser-heated diamond anvil cell (DAC) is currently the only technique capable of routinely accessing the Earth's lower-mantle geotherm for experiments on non-metallic samples, but large temperature uncertainties and poor temperature stability limit the accuracy of measured data and prohibits analyses requiring long acquisition times. We have developed a novel internal resistive heating (IRH) technique for the DAC and demonstrate stable heating of non-metallic samples up to 3000K and 64GPa, as confirmed by in situ synchrotron x-ray diffraction and simultaneous spectroradiometric temperature measurement. The temperature generated in our IRH-DAC can be precisely controlled and is extremely stable, with less than 20K variation over several hours without any user intervention, resulting in temperature uncertainties an order of magnitude smaller than those in typical laser-heating experiments. Our IRH-DAC design, with its simple geometry, provides a new and highly accessible tool for investigating materials at extreme conditions. It is well suited for the rapid collection of high-resolution P-V-T data, precise demarcation of phase boundaries, and experiments requiring long acquisition times at high temperature. Our IRH technique is ideally placed to exploit the move toward coherent nano-focused x-ray beams at next-generation synchrotron sources.

High field X-ray laser physics

High field X-ray laser physics

X-Ray Phase-Contrast Image Reconstruction Based on the Chambolle-Pock Algorithm

The X-ray in-line phase-contrast imaging technique requires that the light source provides a spatially coherent X-ray beam typically generated by a microfocus X-ray tube in most laboratories. However, its small focal spot limits the lightness. An arrayed X-ray point source can overcome this drawback and provide an adequately bright spatial coherent light. However, the arrayed source will introduce artefacts to the phase-contrast image due to the point source spatial distribution. To eliminate these artefacts, an optimization-based algorithm is used to reconstruct the image as an optimization problem. An iterative method was developed to numerically solve the optimization problem by using the first-order primal-dual algorithm. The simulations demonstrate its convergence and reconstruction accuracy.

Three-Dimensional Coherent Bragg Imaging of Rotating Nanoparticles.

Bragg coherent diffraction imaging is a powerful strain imaging tool, often limited by beam-induced sample instability for small particles and high power densities. Here, we devise and validate an adapted diffraction volume assembly algorithm, capable of recovering three-dimensional datasets from particles undergoing uncontrolled and unknown rotations. We apply the method to gold nanoparticles which rotate under the influence of a focused coherent x-ray beam, retrieving their three-dimensional shapes and strain fields. The results show that the sample instability problem can be overcome, enabling the use of fourth generation synchrotron sources for Bragg coherent diffraction imaging to their full potential.

X-Ray Photon Correlation Spectroscopy with Coherent Nanobeams: A Numerical Study

X-ray photon correlation spectroscopy accesses a wide variety of dynamic phenomena at the nanoscale by studying the temporal correlations among photons that are scattered by a material in dynamical equilibrium when it is illuminated with a coherent X-ray beam. The information that is obtained is averaged over the illuminated area, which is generally of the order of several square microns. We propose here that more local information can be obtained by using nanobeams with great potential for the study of heterogeneous systems and show the feasibility of this approach with the support of numerical simulations.

Single-shot characterization of strongly focused coherent XUV and soft X-ray beams.

In this Letter, we present a novel, to the best of our knowledge, single-shot method for characterizing focused coherent beams. We utilize a dedicated amplitude-only mask, in combination with an iterative phase retrieval algorithm, to reconstruct the amplitude and phase of a focused beam from a single measured far-field diffraction pattern alone. In a proof-of-principle experiment at a wavelength of 13.5 nm, we demonstrate our new method and obtain an RMS phase error of better than λ/70. This method will find applications in the alignment of complex optical systems, real-time feedback to adaptive optics, and single-shot beam characterization, e.g., at free-electron lasers or high-order harmonic beamlines.

Ptychographic characterization of a coherent nanofocused X-ray beam.

The NanoMAX hard X-ray nanoprobe is the first beamline to take full advantage of the diffraction-limited storage ring at the MAX IV synchrotron and delivers a high coherent photon flux for applications in diffraction and imaging. Here, we characterize its coherent and focused beam using ptychographic analysis. We derive beam profiles in the energy range 6-22 keV and estimate the coherent flux based on a probe mode decomposition approach.

Khảo sát khả năng phục hồi ảnh của thuật toán tích chập trong phương pháp chụp ảnh nhiễu xạ sử dụng chùm tia X kết hợp không hoàn toàn

This research is aimed to investigate the ability of the convolutional algorithm to reconstruct the image of sample in coherent diffractive imaging using partially coherent X-ray beams. This work is performed using different degrees of coherence for the illuminating wavefield and different types of sample. The obtained results in this research allow to explore the ability to apply the convolutional algorithm in single-shot coherent diffractive imaging using partially coherent X-ray beams.

X-ray laser wakefield acceleration in a nanotube

Plasma-based accelerator technology enables compact particle accelerators. In Laser Wakefield Acceleration, with an ultrafast high-intensity optical laser driver, energy gain of electrons is greater if the electron density is reduced. This is because the energy gain of electrons is proportional to the ratio of laser’s critical density to electron density. However, an alternative path for higher energy electrons is increasing the critical density via going to shorter wavelengths. With the advent of Thin Film Compression, we now see a path to a single cycle coherent X-ray beam. Using this X-ray pulse allows us to increase the plasma density to solid density nanotube (carbon or porous alumina) regime and still be under-dense for a Laser Wakefield Acceleration technique. We will discuss some implications of this below.