Increased spatial coherence length from an asymmetric crystal reflection at grazing exit.

Coherent X-ray imaging is an active field at synchrotron sources. The images rely on the available coherent flux over a limited field of view. At many synchrotron beamlines a double-crystal monochromator (DCM) is employed in a standard nondispersive arrangement. For coherent diffraction imaging it is advantageous to increase the available field of view by increasing the spatial coherence length (SCL) of a beam exiting such a DCM. Here, Talbot interferometry data together with ray-tracing simulations for a (+ - - +) four-reflection experimental arrangement are presented, wherein the first two reflections are in the DCM and the final fourth reflection is asymmetric at grazing exit. Analyses of the interferometry data combined with the simulations show that compared with the beam exiting the DCM a gain of 76% in the SCL was achieved, albeit with a factor of 20 reduction in flux density, which may not be a severe penalty at a synchrotron beamline. Previous efforts reported in the literature to increase the SCL that employed asymmetric crystal diffraction at grazing incidence are also discussed. A much reduced SCL is found presently in simulations wherein the same asymmetric crystal is set for grazing incidence instead of grazing exit. In addition, the present study is compared and contrasted with two other means of increasing the SCL. These are (i) focusing the beam onto an aperture to act as a secondary source, and (ii) allowing the beam to propagate in vacuum an additional distance along the beamline.

AutoFocus: AI-driven alignment of nanofocusing X-ray mirror systems.

We describe the application of an AI-driven system to autonomously align complex x-ray-focusing mirror systems, including mirrors systems with variable focus spot sizes. The system has been developed and studied on a digital twin of nanofocusing X-ray beamlines, built using advanced optical simulation tools calibrated with wavefront sensing data collected at the beamline.We experimentally demonstrated that the system is reliably capable of positioning a focused beam on the sample, both by simulating the variation of a beamline with random perturbations due to typical changes in the light source and optical elements over time, and by conducting similar tests on an actual focusing mirror system.

Development of x-ray beam wavefront sensors for Advanced Photon Source upgrade.

Next-generation synchrotron radiation facilities, such as the Advanced Photon Source Upgrade (APS-U), bring significant advancements in scientific research capabilities, necessitating advanced diagnostic tools. Central to these diagnostics are x-ray wavefront sensors, crucial for preserving beam properties, including brightness, coherence, and stability. This paper presents two novel wavefront sensor prototypes developed at the APS using the coded-mask-based technique. The first is a compact design tailored for specific conditions and adaptability to diverse beamline configurations. The second, an adjustable zoom version, offers flexibility to accommodate a wide range of beam conditions. Both prototypes underwent rigorous testing at the APS 28-ID-B beamline and demonstrated their effectiveness in both absolute wavefront sensing and relative metrology modes. These results highlight their promise in beamline diagnostics, potentially enabling applications such as beamline auto-alignment and real-time wavefront manipulation.

At-wavelength characterization of X-ray wavefronts in Bragg diffraction from crystals.

The advent of next-generation synchrotron radiation sources and X-ray free-electron lasers calls for high-quality Bragg-diffraction crystal optics to preserve the X-ray beam coherence and wavefront. This requirement brings new challenges in characterizing crystals in Bragg diffraction in terms of Bragg-plane height errors and wavefront phase distortions. Here, a quantitative methodology to characterize crystal optics using a state-of-the-art at-wavelength wavefront sensing technique and statistical analysis is proposed. The method was tested at the 1-BM-B optics testing beamline at the Advanced Photon Source for measuring silicon and diamond crystals in a self-referencing single-crystal mode and an absolute double-crystal mode. The phase error sensitivity of the technique is demonstrated to be at the λ/100 level required by most applications, such as the characterization of diamond crystals for cavity-based X-ray free-electron lasers.

Real-time machine-learning-driven control system of a deformable mirror for achieving aberration-free X-ray wavefronts.

A neural-network machine learning model is developed to control a bimorph adaptive mirror to achieve and preserve aberration-free coherent X-ray wavefronts at synchrotron radiation and free electron laser beamlines. The controller is trained on a mirror actuator response directly measured at a beamline with a real-time single-shot wavefront sensor, which uses a coded mask and wavelet-transform analysis. The system has been successfully tested on a bimorph deformable mirror at the 28-ID IDEA beamline of the Advanced Photon Source at Argonne National Laboratory. It achieved a response time of a few seconds and maintained desired wavefront shapes (e.g., a spherical wavefront) with sub-wavelength accuracy at 20 keV of X-ray energy. This result is significantly better than what can be obtained using a linear model of the mirror's response. The developed system has not been tailored to a specific mirror and can be applied, in principle, to different kinds of bending mechanisms and actuators.

Data-driven modeling and control of an X-ray bimorph adaptive mirror.

Adaptive X-ray mirrors are being adopted on high-coherent-flux synchrotron and X-ray free-electron laser beamlines where dynamic phase control and aberration compensation are necessary to preserve wavefront quality from source to sample, yet challenging to achieve. Additional difficulties arise from the inability to continuously probe the wavefront in this context, which demands methods of control that require little to no feedback. In this work, a data-driven approach to the control of adaptive X-ray optics with piezo-bimorph actuators is demonstrated. This approach approximates the non-linear system dynamics with a discrete-time model using random mirror shapes and interferometric measurements as training data. For mirrors of this type, prior states and voltage inputs affect the shape-change trajectory, and therefore must be included in the model. Without the need for assumed physical models of the mirror's behavior, the generality of the neural network structure accommodates drift, creep and hysteresis, and enables a control algorithm that achieves shape control and stability below 2 nm RMS. Using a prototype mirror and ex situ metrology, it is shown that the accuracy of our trained model enables open-loop shape control across a diverse set of states and that the control algorithm achieves shape error magnitudes that fall within diffraction-limited performance.

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation.

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ2 = (2)2 and (71)2 Å2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of qz = 0.05 and 0.10 Å-1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both qz values simultaneously, that is, identical fitting parameters were applied at both values of qz. The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for qz = 0.04, 0.05, and 0.06 Å-1. Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of qz. Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

X-ray beam monitoring and wavelength calibration using four-beam diffraction.

Rigorous dynamical theory calculations show that four-beam diffraction (4BD) can be activated only by a unique photon energy and a unique incidence direction. Thus, 4BD may be used to precisely calibrate X-ray photon energies and beam positions. Based on the principles that the forbidden-reflection 4BD pattern, which is typically an X-shaped cross, can be generated by instant imaging using the divergent beam from a point source without rocking the crystal, a detailed real-time high-resolution beam (and source) position monitoring scheme is illustrated for monitoring two-dimensional beam positions and directions of modern synchrotron light sources, X-ray free-electron lasers and nano-focused X-ray sources.

High-Resolution Scanning Coded-Mask-Based X-ray Multi-Contrast Imaging and Tomography.

Near-field X-ray speckle tracking has been used in phase-contrast imaging and tomography as an emerging technique, providing higher contrast images than traditional absorption radiography. Most reported methods use sandpaper or membrane filters as speckle generators and digital image cross-correlation for phase reconstruction, which has either limited resolution or requires a large number of position scanning steps. Recently, we have proposed a novel coded-mask-based multi-contrast imaging (CMMI) technique for single-shot measurement with superior performance in efficiency and resolution compared with other single-shot methods. We present here a scanning CMMI method for the ultimate imaging resolution and phase sensitivity by using a coded mask as a high-contrast speckle generator, the flexible scanning mode, the adaption of advanced maximum-likelihood optimization to scanning data, and the multi-resolution analysis. Scanning CMMI can outperform other speckle-based imaging methods, such as X-ray speckle vector tracking, providing higher quality absorption, phase, and dark-field images with fewer scanning steps. Scanning CMMI is also successfully demonstrated in multi-contrast tomography, showing great potentials in high-resolution full-field imaging applications, such as in vivo biomedical imaging.

Optimal deformation procedure for hybrid adaptive x-ray mirror based on mechanical and piezo-driven bending system.

A hybrid deformable x-ray mirror consisting of a mechanical bender and a bimorph deformable mirror has been developed to realize adaptive optical systems, such as zoom condenser optics, for synchrotron-radiation-based x-ray microscopy. In the developed system, both bending mechanisms comprehensively contribute to the formation of the target mirror shape and can narrow the role of piezoelectric actuators, thereby enabling a more stable operation. In this study, the behavior of the bimorph mirror under the clamped condition was investigated, and the sharing of the deformation amount for each bending mechanism was optimized to minimize the amplitude of the voltage distribution of the bimorph mirror.

A large field-of-view high-resolution hard x-ray microscope using polymer optics.

We present an effective approach using a matched pair of polymer-based condenser-objective lenses to build a compact full-field x-ray microscope with a high spatial resolution. A unique condenser comprising arrays of high-aspect-ratio prisms with equilateral cross section is used for uniformly illuminating samples over a large field of view (FOV) from all angles, which match the acceptance of an objective made of interdigitated orthogonal rows of one-dimensional lenses. State-of-the-art Talbot grating interferometry used to characterize these lenses for the first time revealed excellent focusing properties and minimal wavefront distortions. Using a specific lens pair designed for 20 keV x rays, short-exposure times, and image registration with a cross-correlation technique, we circumvent vibrational instabilities to obtain distortion-free images with a uniform resolution of 240 nm (smallest resolvable line pair) over a large FOV, 80 × 80 µm2 in extent. The results were contrasted with those collected using commercial two-dimensional parabolic lenses with a smaller FOV. This approach implemented on a diffractometer would enable diffraction-contrast or dark-field microscopy for fast observations of "mesoscopic" phenomena in real space complementing reciprocal-space studies using diffraction on the same instrument.

Small Bragg-plane slope errors revealed in synthetic diamond crystals.

Wavefront-preserving X-ray diamond crystal optics are essential for numerous applications in X-ray science. Perfect crystals with flat Bragg planes are a prerequisite for wavefront preservation in Bragg diffraction. However, this condition is difficult to realize in practice because of inevitable crystal imperfections. Here, X-ray rocking curve imaging is used to study the smallest achievable Bragg-plane slope errors in the best presently available synthetic diamond crystals and how they compare with those of perfect silicon crystals. It is shown that the smallest specific slope errors in the best diamond crystals are about 0.08 (3) µrad mm-2. These errors are only 50% larger than the 0.05 (2) µrad mm-2 specific slope errors measured in perfect silicon crystals. High-temperature annealing at 1450°C of almost flawless diamond crystals reduces the slope errors very close to those of silicon. Further investigations are in progress to establish the wavefront-preservation properties of these crystals.

Wavelet-transform-based speckle vector tracking method for X-ray phase imaging.

We introduce a new X-ray speckle-vector tracking method for phase imaging, which is based on the wavelet transform. Theoretical and experimental results show that this method, which is called wavelet-transform-based speckle-vector tracking (WSVT), has stronger noise robustness and higher efficiency compared with the cross-correlation-based method. In addition, the WSVT method has the controllable noise reduction and can be applied with fewer scan steps. These unique features make the WSVT method suitable for measurements of large image sizes and phase shifts, possibly under low-flux conditions, and has the potential to broaden the applications of speckle tracking to new areas requiring faster phase imaging and real-time wavefront sensing, diagnostics, and characterization.

Adaptive shape control of wavefront-preserving X-ray mirrors with active cooling and heating.

This article describes the development and testing of a novel, water-cooled, active optic mirror system (called "REAL: Resistive Element Adjustable Length") that combines cooling with applied auxiliary heating, tailored to the spatial distribution of the thermal load generated by the incident beam. This technique is theoretically capable of sub-nanometer surface figure error control even at high power density. Tests conducted in an optical metrology laboratory and at synchrotron X-ray beamlines showed the ability to maintain the mirror profile to the level needed for the next generation storage rings and FEL mirrors.

Effects of surface undulations on asymmetric X-ray diffraction: a rocking-curve topography study.

The results are reported of an X-ray diffraction study of an Si crystal designed and fabricated for very asymmetric diffraction from the 333 reflection for X-ray energies of 8.100 and 8.200 keV. A crystal with an asymmetry angle of 46 ±â€…0.1° between the surface and the (111) planes was studied. The grazing angles of incidence were near 1.08 and 0.33° for these two energies, respectively. Features arising from surface undulations were not observed at 8.100 keV, but were observed at 8.200 keV. The results at 8.100 keV allow an alternative explanation based on strain near the surface to be ruled out. Topographic images were obtained as a function of rocking angle, and in the case of 8.200 keV the surface morphology is evident. The results are found to be in agreement with dynamical X-ray diffraction calculations made with the Takagi-Taupin equations specialized to a surface having convex or concave features, as reported in the accompanying paper [Macrander (2020). J. Appl. Cryst. 53, 793-799].

X-ray free-electron laser wavefront sensing using the fractional Talbot effect.

Wavefront sensing at X-ray free-electron lasers is important for quantitatively understanding the fundamental properties of the laser, for aligning X-ray instruments and for conducting scientific experimental analysis. A fractional Talbot wavefront sensor has been developed. This wavefront sensor enables measurements over a wide range of energies, as is common on X-ray instruments, with simplified mechanical requirements and is compatible with the high average power pulses expected in upcoming X-ray free-electron laser upgrades. Single-shot measurements were performed at 500 eV, 1000 eV and 1500 eV at the Linac Coherent Light Source. These measurements were applied to study both mirror alignment and the effects of undulator tapering schemes on source properties. The beamline focal plane position was tracked to an uncertainty of 0.12 mm, and the source location for various undulator tapering schemes to an uncertainty of 1 m, demonstrating excellent sensitivity. These findings pave the way to use the fractional Talbot wavefront sensor as a routine, robust and sensitive tool at X-ray free-electron lasers as well as other high-brightness X-ray sources.

Micro-focused MHz pink beam for time-resolved X-ray emission spectroscopy.

The full radiation from the first harmonic of a synchrotron undulator (between 5 and 12 keV) at the Advanced Photon Source is microfocused using a stack of beryllium compound refractive lenses onto a fast-moving liquid jet and overlapped with a high-repetition-rate optical laser. This micro-focused geometry is used to perform efficient nonresonant X-ray emission spectroscopy on transient species using a dispersive spectrometer geometry. The overall usable flux achieved on target is above 1015 photons s-1 at 8 keV, enabling photoexcited systems in the liquid phase to be tracked with time resolutions from tens of picoseconds to microseconds, and using the full emission spectrum, including the weak valence-to-core signal that is sensitive to chemically relevant electronic properties.

In-plane wavevector distribution in partially coherent X-ray propagation.

The MOI (Mutual Optical Intensity) code for propagating partially coherent radiation through beamline optics is updated by including the in-plane wavevector in the wavefield calculation. The in-plane wavevector is a local function and accurately describes the average phase distribution in a partially coherent wavefield. The improved MOI code is demonstrated by beam propagation through free space and non-ideal mirrors. The improved MOI code can provide more accurate results with lower numbers of elements, and thus has a higher calculation efficiency. Knowledge of the in-plane wavevector also enables detailed studies of wavefield information under different coherence conditions. The improved MOI code is available at http://www.moixray.cn.