Hard X-ray nanofocusing at low-emittance synchrotron radiation sources

X-ray lens figure errors retrieved by deep learning from several beam intensity images

The phase problem in the context of focusing synchrotron beams with X-ray lenses is addressed. The feasibility of retrieving the surface error of a lens system by using only the intensity of the propagated beam at several distances is demonstrated. A neural network, trained with a few thousand simulations using random errors, can predict accurately the lens error profile that accounts for all aberrations. It demonstrates the feasibility of routinely measuring the aberrations induced by an X-ray lens, or another optical system, using only a few intensity images.

FOCUS: fast Monte Carlo approach to coherence of undulator sources

FOCUS (Fast Monte CarlO approach to Coherence of Undulator Sources) is a new GPU-based simulation code to compute the transverse coherence of undulator radiation from ultra-relativistic electrons. The core structure of the code, which is written in the language C++ accelerated with CUDA, combines an analytical description of the emitted electric fields and massively parallel computations on GPUs. The combination is rigorously justified by a statistical description of synchrotron radiation based on a Fourier optics approach. FOCUS is validated by direct comparison with multi-electron Synchrotron Radiation Workshop (SRW) simulations, evidencing a reduction in computation times by up to five orders of magnitude on a consumer laptop. FOCUS is then applied to systematically study the transverse coherence in typical third- and fourth-generation facilities, highlighting peculiar features of undulator sources close to the diffraction limit. FOCUS is aimed at fast evaluation of the transverse coherence of undulator radiation as a function of the electron beam parameters, to support and help prepare more advanced and detailed numerical simulations with traditional codes like SRW.

Multi-beam X-ray ptychography using coded probes for rapid non-destructive high resolution imaging of extended samples

Imaging large areas of a sample non-destructively and with high resolution is of great interest for both science and industry. For scanning coherent X-ray diffraction microscopy, i. e., ptychography, the achievable scan area at a given spatial resolution is limited by the coherent photon flux of modern X-ray sources. Multibeam X-ray ptychography can improve the scanning speed by scanning the sample with several parallel mutually incoherent beams, e. g., generated by illuminating multiple focusing optics in parallel by a partially coherent beam. The main difficulty with this scheme is the robust separation of the superimposed signals from the different beams, especially when the beams and the illuminated sample areas are quite similar. We overcome this difficulty by encoding each of the probing beams with its own X-ray phase plate. This helps the algorithm to robustly reconstruct the multibeam data. We compare the coded multibeam scans to uncoded multibeam and single beam scans, demonstrating the enhanced performance on a microchip sample with regular and repeating structures.

X-ray-Based Techniques to Study the Nano-Bio Interface

X-ray-based analytics are routinely applied in many fields, including physics, chemistry, materials science, and engineering. The full potential of such techniques in the life sciences and medicine, however, has not yet been fully exploited. We highlight current and upcoming advances in this direction. We describe different X-ray-based methodologies (including those performed at synchrotron light sources and X-ray free-electron lasers) and their potentials for application to investigate the nano-bio interface. The discussion is predominantly guided by asking how such methods could better help to understand and to improve nanoparticle-based drug delivery, though the concepts also apply to nano-bio interactions in general. We discuss current limitations and how they might be overcome, particularly for future use in vivo.

Fast convolution-based performance estimation method for diffraction-limited source with imperfect X-ray optics

Although optical element error analysis is always an important part of beamline design for highly coherent synchrotron radiation or free-electron laser sources, the usual wave optics simulation can be very time-consuming, which limits its application at the early stage of the beamline design. In this work, a new theoretical approach has been proposed for quick evaluations of the optical performance degradation due to optical element error. In this way, time-consuming detailed simulations can be applied only when truly necessary. This approach treats the imperfections as perturbations that convolve with the ideal performance. For simplicity, but not by necessity, the Gaussian Schell-model has been used to show the application of this theoretical approach. The influences of the finite aperture size and height error of a focusing mirror are analysed using the proposed theory. The physical explanation of the performance degradation acquired from the presented approach helps to give a better definition of the critical range of error spatial frequencies that most affect the performance of a mirror. An example comparing two mirror surface errors with identical power spectral density functions is given. These two types of mirror surface errors result in very different intensity profiles. The approach presented in this work could help beamline designers specify the error tolerances on general optical elements more accurately.

Focusing a round coherent beam by spatial filtering the horizontal source

This paper illustrates the use of spatial filtering with a horizontal slit near the source to enlarge the horizontal coherence in an experimental station and produce a diffraction-limited round focus at an insertion device beamline for X-ray photon correlation spectroscopy experiments. Simple expressions are provided to guide the optical layout, and wave propagation simulations confirm their applicability. The two-dimensional focusing performance of Be compound refractive lenses to produce a round diffraction-limited focus at 11 keV capable of generating a high-contrast speckle pattern of an aerogel sample is demonstrated. The coherent scattering patterns have comparable speckle sizes in both horizontal and vertical directions. The focal spot sizes are consistent with hybrid ray-tracing calculations. Producing a two-dimensional focus on the sample can be helpful to resolve speckle patterns with modern pixel array detectors with high visibility. This scheme has now been in use since 2019 for the 8-ID beamline at the Advanced Photon Source, sharing the undulator beam with two separate beamlines, 8-ID-E and 8-ID-I at 7.35 keV, with increased partially coherent flux, reduced horizontal spot sizes on samples, and good speckle contrast.

Hard X-ray wavefront correction via refractive phase plates made by additive and subtractive fabrication techniques

Modern subtractive and additive manufacturing techniques present new avenues for X-ray optics with complex shapes and patterns. Refractive phase plates acting as glasses for X-ray optics have been fabricated, and spherical aberration in refractive X-ray lenses made from beryllium has been successfully corrected. A diamond phase plate made by femtosecond laser ablation was found to improve the Strehl ratio of a lens stack with a numerical aperture (NA) of 0.88 × 10-3 at 8.2 keV from 0.1 to 0.7. A polymer phase plate made by additive printing achieved an increase in the Strehl ratio of a lens stack at 35 keV with NA of 0.18 × 10-3 from 0.15 to 0.89, demonstrating diffraction-limited nanofocusing at high X-ray energies.

PtyNAMi: ptychographic nano-analytical microscope

Ptychographic X-ray imaging at the highest spatial resolution requires an optimal experimental environment, providing a high coherent flux, excellent mechanical stability and a low background in the measured data. This requires, for example, a stable performance of all optical components along the entire beam path, high temperature stability, a robust sample and optics tracking system, and a scatter-free environment. This contribution summarizes the efforts along these lines to transform the nanoprobe station on beamline P06 (PETRA III) into the ptychographic nano-analytical microscope (PtyNAMi).

Modelling phase imperfections in compound refractive lenses

A framework based on physical optics for simulating the effect of imperfect compound refractive lenses (CRLs) upon an X-ray beam is described, taking into account measured phase errors obtained from at-wavelength metrology. A CRL stack is modelled, with increasing complexity, as a single thin phase element, then as a more realistic compound element including absorption and thickness effects, and finally adding realistic optical imperfections to the CRL. Coherent and partially coherent simulations using Synchrotron Radiation Workshop (SRW) are used to evaluate the different models, the effects of the phase errors and to check the validity of the design equations and suitability of the figures of merit.

Coherence properties of the high-energy fourth-generation X-ray synchrotron sources

An analysis of the coherence properties of the fourth-generation high-energy storage rings with emittance values of 10 pm rad is performed. It is presently expected that a storage ring with these low emittance values will reach diffraction limit at hard X-rays. Simulations of coherence properties were performed with the XRT software and an analytical approach for different photon energies from 500 eV to 50 keV. It was demonstrated that a minimum photon emittance (diffraction limit) reached at such storage rings is λ/2π. Using mode decomposition it is shown that, for the parameters of the storage ring considered in this work, the diffraction limit will be reached for soft X-ray energies of 500 eV. About ten modes will contribute to the radiation field at 12 keV photon energy and even more modes give a contribution at higher photon energies. Energy spread effects of the electron beam in a low-emittance storage ring were analysed in detail. Simulations were performed at different relative energy spread values from zero to 2 × 10^-3. A decrease of the degree of coherence with an increase of the relative energy spread value was observed. This analysis shows that, to reach the diffraction limit for high photon energies, electron beam emittance should go down to 1 pm rad and below.

Methods for Determining and Understanding Serpin Structure and Function: X-Ray Crystallography

Deciphering the X-ray crystal structures of serine protease inhibitors (serpins) and serpin complexes has been an integral part of understanding serpin function and inhibitory mechanisms. In addition, high-resolution structural information of serpins derived from the three domains of life (bacteria, archaea, and eukaryotic) and viruses has provided valuable insights into the hereditary and evolutionary history of this unique superfamily of proteins. This chapter will provide an overview of the predominant biophysical method that has yielded this information, X-ray crystallography. In addition, details of up-and-coming methods, such as neutron crystallography, cryo-electron microscopy, and small- and wide-angle solution scattering, and their potential applications to serpin structural biology will be briefly discussed. As serpins remain important both biologically and medicinally, the information provided in this chapter will aid in future experiments to expand our knowledge of this family of proteins.

PETRA IV: the ultralow-emittance source project at DESY

The PETRA IV project aims at upgrading the present synchrotron radiation source PETRA III at DESY into an ultralow-emittance source. Being diffraction limited up to X-rays of about 10 keV, PETRA IV will be ideal for three-dimensional X-ray microscopy of biological, chemical and physical processes under realistic conditions at length scales from atomic dimensions to millimetres and time scales down to the sub-nanosecond regime. In this way, it will enable groundbreaking studies in many fields of science and industry, such as health, energy, earth and environment, mobility and information technology. The science case is reviewed and the current state of the conceptual design is summarized, discussing a reference lattice, a hybrid multi-bend achromat with an interleaved sextupole configuration based on the ESRF-EBS design, in more detail as well as alternative lattice concepts.

Incoherent Nuclear Resonant Scattering from a Standing Spin Wave

We introduce a method to study the spatial profiles of standing spin waves in ferromagnetic microstructures. The method relies on Nuclear Resonant Scattering of ⁵⁷Fe using a microfocused beam of synchrotron radiation, the transverse coherence length of which is smaller than the length scale of lateral variations in the magnetization dynamics. Using this experimental method, the nuclear resonant scattering signal due to a confined spin wave is determined on the basis of an incoherent superposition model. From the fits of the Nuclear Resonant Scattering time spectra, the precessional amplitude profile across the stripe predicted by an analytical model is reconstructed. Our results pave the way for studying non-homogeneous dynamic spin configurations in microstructured magnetic systems using nuclear resonant scattering of synchrotron light.

The Influence of Photoelectron Escape in Radiation Damage Simulations of Protein Micro-Crystallography

Radiation damage represents a fundamental limit in the determination of protein structures via macromolecular crystallography (MX) at third-generation synchrotron sources. Over the past decade, improvements in both source and detector technology have led to MX experiments being performed with smaller and smaller crystals (on the order of a few microns), often using microfocus beams. Under these conditions, photoelectrons (PEs), the primary agents of radiation-damage in MX, may escape the diffraction volume prior to depositing all of their energy. The impact of PE escape is more significant at higher beam energies (>20 keV) as the electron inelastic mean free path (IMFP) is longer, allowing the electrons to deposit their energy over a larger area, extending further from their point of origin. Software such as RADDOSE-3D has been used extensively to predict the dose (energy absorbed per unit mass) that a crystal will absorb under a given set of experimental parameters and is an important component in planning a successful MX experiment. At the time this study was undertaken, dose predictions made using RADDOSE-3D were spatially-resolved, but did not yet account for the propagation of PEs through the diffraction volume. Hence, in the case of microfocus crystallography, it is anticipated that deviations may occur between the predicted and actual dose absorbed due to the influence of PEs. To explore this effect, we conducted a series of simulations of the dose absorbed by micron-sized crystals during microfocus MX experiments. Our simulations spanned beam and crystal sizes ranging from 1μm to 5μm for beam energies between 9 keV and 30 keV. Our simulations were spatially and temporarily resolved and accounted for the escape of PEs from the diffraction volume. The spatially-resolved dose maps produced by these simulations were used to predict the rate of intensity loss in a Bragg spot, a key metric for tracking global radiation damage. Our results were compared to predictions obtained using a recent version of RADDOSE-3D that did not account for PE escape; the predicted crystal lifetimes are shown to differ significantly for the smallest crystals and for high-energy beams, when PE escape is included in the simulations.

The coherent radiation fraction of low-emittance synchrotrons

In this work the coherence properties of the synchrotron radiation beam from an X-ray undulator in a fourth-generation storage ring are analyzed. A slightly focused X-ray beam is simulated using a wavefront propagation through a non-redundant array of slits and the mutual coherence function is directly obtained and compared with the Gaussian-Schell approximation. The numerical wave propagation and the approximate analytical approaches are shown to agree qualitatively, and it is also shown that, when the coherent fraction is selected by a finite aperture before the focusing element, even achromatic focusing systems like total reflection mirrors become slightly chromatic. This effect is also well accounted for in the Gaussian-Schell model. The wavefront propagation simulation through the non-redundant array was repeated with an imperfect mirror demonstrating that, although the wavefront is distorted, its coherent length is practically unchanged.

Actin bundles cross-linked with α-actinin studied by nanobeam X-ray diffraction

We have performed scanning nano-beam small-angle X-ray scattering (nano-SAXS) experiments on in vitro-formed actin filaments cross-linked with [Formula: see text]-actinin. The experimental method combines a high resolution in reciprocal space with a real space resolution as given by the spot-size of the nano-focused X-ray beam, and opens up new opportunities to study local super-molecular structures of actin filaments. In this first proof-of-concept, we show that the local orientation of actin bundles formed by the cross-linking can be visualized by the X-ray darkfield maps. The filament bundles give rise to highly anisotropic diffraction patterns showing distinct streaks perpendicular to the bundle axes. Interestingly, some diffraction patterns exhibit a fine structure in the form of intensity modulations allowing for a more detailed analysis of the order within the bundles. A first empirical quantification of these modulations is included in the present work.

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.

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.

The potential of future light sources to explore the structure and function of matter

Structural studies in general, and crystallography in particular, have benefited and still do benefit dramatically from the use of synchrotron radiation. Low-emittance storage rings of the third generation provide focused beams down to the micrometre range that are sufficiently intense for the investigation of weakly scattering crystals down to the size of several micrometres. Even though the coherent fraction of these sources is below 1%, a number of new imaging techniques have been developed to exploit the partially coherent radiation. However, many techniques in nanoscience are limited by this rather small coherent fraction. On the one hand, this restriction limits the ability to study the structure and dynamics of non-crystalline materials by methods that depend on the coherence properties of the beam, like coherent diffractive imaging and X-ray correlation spectroscopy. On the other hand, the flux in an ultra-small diffraction-limited focus is limited as well for the same reason. Meanwhile, new storage rings with more advanced lattice designs are under construction or under consideration, which will have significantly smaller emittances. These sources are targeted towards the diffraction limit in the X-ray regime and will provide roughly one to two orders of magnitude higher spectral brightness and coherence. They will be especially suited to experiments exploiting the coherence properties of the beams and to ultra-small focal spot sizes in the regime of several nanometres. Although the length of individual X-ray pulses at a storage-ring source is of the order of 100 ps, which is sufficiently short to track structural changes of larger groups, faster processes as they occur during vision or photosynthesis, for example, are not accessible in all details under these conditions. Linear accelerator (linac) driven free-electron laser (FEL) sources with extremely short and intense pulses of very high coherence circumvent some of the limitations of present-day storage-ring sources. It has been demonstrated that their individual pulses are short enough to outrun radiation damage for single-pulse exposures. These ultra-short pulses also enable time-resolved studies 1000 times faster than at standard storage-ring sources. Developments are ongoing at various places for a totally new type of X-ray source combining a linac with a storage ring. These energy-recovery linacs promise to provide pulses almost as short as a FEL, with brilliances and multi-user capabilities comparable with a diffraction-limited storage ring. Altogether, these new X-ray source developments will provide smaller and more intense X-ray beams with a considerably higher coherent fraction, enabling a broad spectrum of new techniques for studying the structure of crystalline and non-crystalline states of matter at atomic length scales. In addition, the short X-ray pulses of FELs will enable the study of fast atomic dynamics and non-equilibrium states of matter.

Diffraction-limited storage rings - a window to the science of tomorrow

This article summarizes the contributions in this special issue on Diffraction-Limited Storage Rings. It analyses the progress in accelerator technology enabling a significant increase in brightness and coherent fraction of the X-ray light provided by storage rings. With MAX IV and Sirius there are two facilities under construction that already exploit these advantages. Several other projects are in the design stage and these will probably enhance the performance further. To translate the progress in light source quality into new science requires similar progress in aspects such as optics, beamline technology, detectors and data analysis. The quality of new science will be limited by the weakest component in this value chain. Breakthroughs can be expected in high-resolution imaging, microscopy and spectroscopy. These techniques are relevant for many fields of science; for example, for the fundamental understanding of the properties of correlated electron materials, the development and characterization of materials for data and energy storage, environmental applications and bio-medicine.

Spectromicroscopy and coherent diffraction imaging: focus on energy materials applications

Current and future capabilities of X-ray spectromicroscopy are discussed based on coherence-limited imaging methods which will benefit from the dramatic increase in brightness expected from a diffraction-limited storage ring (DLSR). The methods discussed include advanced coherent diffraction techniques and nanoprobe-based real-space imaging using Fresnel zone plates or other diffractive optics whose performance is affected by the degree of coherence. The capabilities of current systems, improvements which can be expected, and some of the important scientific themes which will be impacted are described, with focus on energy materials applications. Potential performance improvements of these techniques based on anticipated DLSR performance are estimated. Several examples of energy sciences research problems which are out of reach of current instrumentation, but which might be solved with the enhanced DLSR performance, are discussed.