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.

X-ray optics for the cavity-based X-ray free-electron laser.

A cavity-based X-ray free-electron laser (CBXFEL) is a possible future direction in the development of fully coherent X-ray sources. CBXFELs consist of a low-emittance electron source, a magnet system with several undulators and chicanes, and an X-ray cavity. The X-ray cavity stores and circulates X-ray pulses for repeated FEL interactions with electron pulses until the FEL reaches saturation. CBXFEL cavities require low-loss wavefront-preserving optical components: near-100%-reflectivity X-ray diamond Bragg-reflecting crystals, outcoupling devices such as thin diamond membranes or X-ray gratings, and aberration-free focusing elements. In the framework of the collaborative CBXFEL research and development project of Argonne National Laboratory, SLAC National Accelerator Laboratory and SPring-8, we report here the design, manufacturing and characterization of X-ray optical components for the CBXFEL cavity, which include high-reflectivity diamond crystal mirrors, a diamond drumhead crystal with thin membranes, beryllium refractive lenses and channel-cut Si monochromators. All the designed optical components have been fully characterized at the Advanced Photon Source to demonstrate their suitability for the CBXFEL cavity application.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Influence of optics vibration on synchrotron beam coherence.

Vibration of optics is one of the major limiting factors of the performance of state-of-the-art beamlines at low-emittance synchrotron facilities. We present a theoretical model with experimental data describing vibration-induced effects on x-ray beam coherence. Owing to the incoherent nature of vibration, the decrease in the beam spatial coherence perturbed by optics vibrations can be characterized by modeling the effective source profile of the vibrating beam. The measurements were carried out by using grating interferometry and a refractive lens with controlled vibration as test optics. The experimental results confirm the model and reveal the dependency of the measured beam spatial coherence on the acquisition time. The proposed method can be used to identify the eigenfrequency of the optical system as well as to optimize beamline operation and experimental conditions for coherence-related techniques.

Efficiency and coherence preservation studies of Be refractive lenses for XFELO application.

Performance tests of parabolic beryllium refractive lenses, considered as X-ray focusing elements in the future X-ray free-electron laser oscillator (XFELO), are reported. Single and double refractive lenses were subject to X-ray tests, which included: surface profile, transmissivity measurements, imaging capabilities and wavefront distortion with grating interferometry. Optical metrology revealed that surface profiles were close to the design specification in terms of the figure and roughness. The transmissivity of the lenses is >94% at 8 keV and >98% at 14.4 and 18 keV. These values are close to the theoretical values of ideal lenses. Images of the bending-magnet source obtained with the lenses were close to the expected ones and did not show any significant distortion. Grating interferometry revealed that the possible wavefront distortions produced by surface and bulk lens imperfections were on the level of ∼λ/60 for 8 keV photons. Thus the Be lenses can be succesfully used as focusing and beam collimating elements in the XFELO.

Mutual optical intensity propagation through non-ideal mirrors.

The mutual optical intensity (MOI) model is extended to include the propagation of partially coherent radiation through non-ideal mirrors. The propagation of the MOI from the incident to the exit plane of the mirror is realised by local ray tracing. The effects of figure errors can be expressed as phase shifts obtained by either the phase projection approach or the direct path length method. Using the MOI model, the effects of figure errors are studied for diffraction-limited cases using elliptical cylinder mirrors. Figure errors with low spatial frequencies can vary the intensity distribution, redistribute the local coherence function and distort the wavefront, but have no effect on the global degree of coherence. The MOI model is benchmarked against HYBRID and the multi-electron Synchrotron Radiation Workshop (SRW) code. The results show that the MOI model gives accurate results under different coherence conditions of the beam. Other than intensity profiles, the MOI model can also provide the wavefront and the local coherence function at any location along the beamline. The capability of tuning the trade-off between accuracy and efficiency makes the MOI model an ideal tool for beamline design and optimization.

Characterization of a bent Laue double-crystal beam-expanding monochromator.

A bent Laue double-crystal monochromator system has been designed for vertically expanding the X-ray beam at the Canadian Light Source's BioMedical Imaging and Therapy beamlines. Expansion by a factor of 12 has been achieved without deteriorating the transverse coherence of the beam, allowing phase-based imaging techniques to be performed with high flux and a large field of view. However, preliminary studies revealed a lack of uniformity in the beam, presumed to be caused by imperfect bending of the silicon crystal wafers used in the system. Results from finite-element analysis of the system predicted that the second crystal would be most severely affected and has been shown experimentally. It has been determined that the majority of the distortion occurs in the second crystal and is likely caused by an imperfection in the surface of the bending frame. Measurements were then taken to characterize the bending of the crystal using both mechanical and diffraction techniques. In particular, two techniques commonly used to map dislocations in crystal structures have been adapted to map local curvature of the bent crystals. One of these, a variation of Berg-Berrett topography, has been used to quantify the diffraction effects caused by the distortion of the crystal wafer. This technique produces a global mapping of the deviation of the diffraction angle relative to a perfect cylinder. This information is critical for improving bending and measuring tolerances of imperfections by correlating this mapping to areas of missing intensity in the beam.

Hard x-ray spectroscopy and imaging by a reflection zone plate in the presence of astigmatism.

The feasibility of an off-axis x-ray reflection zone plate to perform wavelength-dispersive spectroscopy, on-axis point focusing, and two-dimensional imaging is demonstrated by means of one and the same diffractive optical element (DOE) at a synchrotron radiation facility. The resolving power varies between 3×101 and 4×102 in the range of 7.6 keV to 9.0 keV, with its maximum at the design energy of 8.3 keV. This result is verified using an adjustable entrance slit, by which horizontal (H) and vertical (V) focusing to 0.85 µm(H) and 1.29 µm(V) is obtained near the sagittal focal plane of the astigmatic configuration. An angular and axial scan proves an accessible field of view of at least 0.6 arcmin × 0.8 arcmin and a focal depth of ±0.86 mm. Supported by the grating efficiency of around 17.5% and a very short pulse elongation, future precision x-ray fluorescence and absorption studies of transition metals at their K-edge on an ultrashort timescale could benefit from our findings.

Profile etching for prefiguring X-ray mirrors.

A method to pre-shape mirror substrates through etching with a broad-beam ion source and a contoured mask is presented. A 100 mm-long elliptical cylinder substrate was obtained from a super-polished flat Si substrate with a 48 nm root-mean-square (r.m.s.) figure error and a 1.5 Šr.m.s. roughness after one profile-etching process at a beam voltage of 600 V without iteration. A follow-up profile coating can be used to achieve a final mirror. Profile etching and profile coating combined provide an economic way to make X-ray optics, such as nested Kirkpatrick-Baez mirrors.