Spexwavepy: an open-source Python package for X-ray wavefront sensing using speckle-based techniques.

In situ wavefront sensing plays a critical role in the delivery of high-quality beams for X-ray experiments. X-ray speckle-based techniques stand out among other in situ techniques for their easy experimental setup and various data acquisition modes. Although X-ray speckle-based techniques have been under development for more than a decade, there are still no user-friendly software packages for new researchers to begin with. Here, we present an open-source Python package, spexwavepy, for X-ray wavefront sensing using speckle-based techniques. This Python package covers a variety of X-ray speckle-based techniques, provides plenty of examples with real experimental data and offers detailed online documentation for users. We hope it can help new researchers learn and apply the speckle-based techniques for X-ray wavefront sensing to synchrotron radiation and X-ray free-electron laser beamlines.

Wavefront analysis and phase correctors design using SHADOW.

Knife-edge imaging is a successful method for determining the wavefront distortion of focusing optics such as Kirkpatrick-Baez mirrors or compound refractive lenses. In this study, the wavefront error of an imperfect elliptical mirror is predicted by developing a knife-edge program using the SHADOW/OASYS platform. It is shown that the focusing optics can be aligned perfectly by minimizing the parabolic and cubic coefficients of the wavefront error. The residual wavefront error provides precise information about the figure/height errors of the focusing optics suggesting it as an accurate method for in situ optical metrology. A Python program is developed to design a customized wavefront refractive corrector to minimize the residual wavefront error. Uniform beam at and out of focus and higher peak intensity are achieved by the wavefront correction in comparison with ideal focusing. The developed code provides a quick way for wavefront error analysis and corrector design for non-ideal optics especially for the new-generation diffraction-limited sources, and saves considerable experimental time and effort.

Modelling the power threshold and optimum thermal deformation of indirectly liquid-nitrogen cryo-cooled Si monochromators.

Maximizing the performance of crystal monochromators is a key aspect in the design of beamline optics for diffraction-limited synchrotron sources. Temperature and deformation of cryo-cooled crystals, illuminated by high-power beams of X-rays, can be estimated with a purely analytical model. The analysis is based on the thermal properties of cryo-cooled silicon crystals and the cooling geometry. Deformation amplitudes can be obtained, quickly and reliably. In this article the concept of threshold power conditions is introduced and defined analytically. The contribution of parameters such as liquid-nitrogen cooling efficiency, thermal contact conductance and interface contact area of the crystal with the cooling base is evaluated. The optimal crystal illumination and the base temperature are inferred, which help minimize the optics deformation. The model has been examined using finite-element analysis studies performed for several beamlines of the Diamond-II upgrade.

MLgrating: a program for simulating multilayer gratings for tender X-ray applications.

Multilayer gratings are increasingly popular optical elements at X-ray beamlines, as they can provide much higher photon flux in the tender X-ray range compared with traditional single-layer coated gratings. While there are several proprietary software tools that provide the functionality to simulate the efficiencies of such gratings, until now the X-ray community has lacked an open-source alternative. Here MLgrating is presented, a program for simulating the efficiencies of both multilayer gratings and single-layer coated gratings for X-ray applications. MLgrating is benchmarked by comparing its output with that of other software tools and plans are discussed for how the program could be extended in the future.

Development of an advanced in-line multilayer deposition system at Diamond Light Source.

A state-of-the-art multilayer deposition system with a 4200 mm-long linear substrate translator housed within an ultra-high vacuum chamber has been developed. This instrument is engineered to produce single and multilayer coatings, accommodating mirrors up to 2000 mm in length through the utilization of eight rectangular cathodes. To ensure the quality and reliability of the coatings, the system incorporates various diagnostic tools for in situ thickness uniformity and stress measurement. Furthermore, the system features an annealing process capable of heating up to 700°C within the load-lock chamber. The entire operation, including pump down, deposition and venting processes, is automated through user-friendly software. In addition, all essential log data, power of sputtering source, working pressure and motion positions are automatically stored for comprehensive data analysis. Preliminary commissioning results demonstrate excellent lateral film thickness uniformity, achieving 0.26% along the translation direction over 1500 mm in dynamic mode. The multilayer deposition system is poised for use in fabricating periodic, lateral-graded and depth-graded multilayers, specifically catering to the beamlines for diverse scientific applications at Diamond Light Source.

Ion beam figuring for X-ray mirrors: history, state-of-the-art and future prospects.

Synchrotron light sources require X-ray optics with extremely demanding accuracy for the surface profile, with less than 100 nrad slope errors and sub-nanometre height errors. Such errors are challenging to achieve for aspheres using traditional polishing methods. However, post-polishing error correction can be performed using techniques such as ion beam figuring (IBF) to improve optics to the desired quality. This work presents a brief overview of the history of IBF, introduces some of the challenges for obtaining such demanding figure errors, and highlights the work done at several in-house IBF facilities at synchrotron light sources worldwide to obtain state-of-the-art optical quality.

Sub-nanometre quality X-ray mirrors created using ion beam figuring.

Ion beam figuring (IBF) is a powerful technique for figure correction of X-ray mirrors to a high accuracy. Here, recent technical advancements in the IBF instrument developed at Diamond Light Source are presented and experimental results for figuring of X-ray mirrors are given. The IBF system is equipped with a stable DC gridded ion source (120 mm diameter), a four-axis motion stage to manipulate the optic, a Faraday cup to monitor the ion-beam current, and a camera for alignment. A novel laser speckle angular measurement instrument also provides on-board metrology. To demonstrate the IBF system's capabilities, two silicon X-ray mirrors were processed. For 1D correction, a height error of 0.08 nm r.m.s. and a slope error of 44 nrad r.m.s. were achieved. For 2D correction over a 67 mm × 17 mm clear aperture, a height error of 0.8 nm r.m.s. and a slope error of 230 nrad r.m.s. were obtained. For the 1D case, this optical quality is comparable with the highest-grade, commercially available, X-ray optics.

Hard X-ray omnidirectional differential phase and dark-field imaging.

Ever since the discovery of X-rays, tremendous efforts have been made to develop new imaging techniques for unlocking the hidden secrets of our world and enriching our understanding of it. X-ray differential phase contrast imaging, which measures the gradient of a sample's phase shift, can reveal more detail in a weakly absorbing sample than conventional absorption contrast. However, normally only the gradient's component in two mutually orthogonal directions is measurable. In this article, omnidirectional differential phase images, which record the gradient of phase shifts in all directions of the imaging plane, are efficiently generated by scanning an easily obtainable, randomly structured modulator along a spiral path. The retrieved amplitude and main orientation images for differential phase yield more information than the existing imaging methods. Importantly, the omnidirectional dark-field images can be simultaneously extracted to study strongly ordered scattering structures. The proposed method can open up new possibilities for studying a wide range of complicated samples composed of both heavy, strongly scattering atoms and light, weakly scattering atoms.

Research on the beam structures observed from X-ray optics in the far field.

For advanced X-ray sources such as synchrotron radiation facilities and X-ray free electron lasers, a smooth, structure-free beam on the far-field plane is usually strongly desired. The formation of the fine structures in far-field images downstream from imperfect optics must be understood. Although numerous studies have discussed the impacts on focused beams, there are still few quantitative theories for the impacts on beams in the far field. This article is an advance on our previous work, which discussed the uniformity of the intensity distribution in the far field. Here, a new theoretical approach is presented. It not only eases the assumptions needed to relate the fine structures to the wavefront curvature, but it also provides a quantitative estimation of the impacts of optical errors. The theoretical result is also verified by X-ray experiments.

Two-dimensional speckle technique for slope error measurements of weakly focusing reflective X-ray optics.

Speckle-based at-wavelength metrology techniques now play an important role in X-ray wavefront measurements. However, for reflective X-ray optics, the majority of existing speckle-based methods fail to provide reliable 2D information about the optical surface being characterized. Compared with the 1D information typically output from speckled-based methods, a 2D map is more informative for understanding the overall quality of the optic being tested. In this paper, we propose a method for in situ 2D absolute metrology of weakly focusing X-ray mirrors. Importantly, the angular misalignment of the mirror can be easily corrected with the proposed 2D processing procedure. We hope the speckle pattern data processing method presented here will help to extend this technique to wider applications in the synchrotron radiation and X-ray free-electron laser communities.

Cryo-cooled silicon crystal monochromators: a study of power load, temperature and deformation.

Crystal monochromators are often the primary optics in hard X-ray synchrotron beamlines. Management of power load is central to their design. Strict requirements on stability and deformation are to be met, as new-generation synchrotron sources deliver brighter beams of X-rays. This article sets out to illustrate an overall picture of the deformation caused by heat load in a cryo-cooled Si crystal monochromator using first principles. A theoretical model has been developed to predict the temperature distribution and surface deformation by applying intrinsic properties of Si material and the cooling system parameters. The model explains the universal behaviour of crystal slope error versus absorbed power; it has been benchmarked against experimental data and used to interpret finite-element analysis of cryogenically cooled crystals.

Fast wavefront sensing for X-ray optics with an alternating speckle tracking technique.

Advances in accelerator technologies have enabled the continuous development of synchrotron radiation and X-ray free electron laser (XFEL) sources. At the same time, it has been critical to perform in-situ wavefront sensing to aid delivery of high-quality X-ray beams to the end users of these facilities. The speckle-based scanning technique has obtained popularity due to its high spatial resolution and superior sensitivity compared to other wavefront sensing methods. However, these advantages often come at the expense of longer data acquisition times since multiple images have to be collected to derive the necessary wavefront information. Whereas initial speckle tracking techniques could obtain wavefront information relatively quickly, the installation of additional hardware was routinely required to do so. Here, we propose a novel speckle-based approach, termed Alternating Speckle Tracking (AST), to perform fast wavefront sensing within a conventional beamline setup. The wavefront information derived from the new technique has proven to be valuable for many applications that require temporal resolution. Importantly, both horizontal and vertical wavefront information can be simultaneously derived by moving the speckle generator along the diagonal direction. We expect this method will be widely used by the synchrotron radiation and XFEL community in the future.

Two-dimensional wavefront characterization of adaptable corrective optics and Kirkpatrick-Baez mirror system using ptychography.

Aberrations introduced during fabrication degrade the performance of X-ray optics and their ability to achieve diffraction limited focusing. Corrective optics can counteract these errors by introducing wavefront perturbations prior to the optic which cancel out the distortions. Here we demonstrate two-dimensional wavefront correction of an aberrated Kirkpatrick-Baez mirror pair using adaptable refractive structures. The resulting two-dimensional wavefront is measured using hard X-ray ptychography to recover the complex probe wavefield with high spatial resolution and model the optical performance under coherent conditions. The optical performance including the beam caustic, focal profile and wavefront error is examined before and after correction with both mirrors found to be diffraction limited after correcting. The results will be applicable to a wide variety of high numerical aperture X-ray optics aiming to achieve diffraction limited focussing using low emittance sources.

Investigation of the stripe patterns from X-ray reflection optics.

X-ray beams reflected from a single layer or multilayer coating are widely used for X-ray tomography, holography, and X-ray phase contrast imaging. However, the observed irregular stripe patterns from either unfocused or defocused beams often cause disturbing artifacts and seriously deteriorate the image quality. In this work, we investigate the origin of these irregular fine structures using the wave optics theory. The connection to similar results obtained by the geometric optics theory is also presented. The proposed relation between the second derivative of the wavefront and the irregular structures was then verified by conducting at-wavelength metrology with the speckle-based wavefront sensing technique. This work will not only help to understand the formation of these irregular structures but also provide the basis for manufacturing future 'stripe-free' refection optics.

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures.

A refractive phase corrector optics is proposed for the compensation of fabrication error of X-ray optical elements. Here, at-wavelength wavefront measurements of the focused X-ray beam by knife-edge imaging technique, the design of a three-dimensional corrector plate, its fabrication by 3D printing, and use of a corrector to compensate for X-ray lens figure errors are presented. A rotationally invariant corrector was manufactured in the polymer IP-STM using additive manufacturing based on the two-photon polymerization technique. The fabricated corrector was characterized at the B16 Test beamline, Diamond Light Source, UK, showing a reduction in r.m.s. wavefront error of a Be compound refractive Lens (CRL) by a factor of six. The r.m.s. wavefront error is a figure of merit for the wavefront quality but, for X-ray lenses, with significant X-ray absorption, a form of the r.m.s. error with weighting proportional to the transmitted X-ray intensity has been proposed. The knife-edge imaging wavefront-sensing technique was adapted to measure rotationally variant wavefront errors from two different sets of Be CRL consisting of 98 and 24 lenses. The optical aberrations were then quantified using a Zernike polynomial expansion of the 2D wavefront error. The compensation by a rotationally invariant corrector plate was partial as the Be CRL wavefront error distribution was found to vary with polar angle indicating the presence of non-spherical aberration terms. A wavefront correction plate with rotationally anisotropic thickness is proposed to compensate for anisotropy in order to achieve good focusing by CRLs at beamlines operating at diffraction-limited storage rings.

Hard X-ray ptychography for optics characterization using a partially coherent synchrotron source.

Ptychography is a scanning coherent diffraction imaging technique which provides high resolution imaging and complete spatial information of the complex electric field probe and sample transmission function. Its ability to accurately determine the illumination probe has led to its use at modern synchrotrons and free-electron lasers as a wavefront-sensing technique for optics alignment, monitoring and correction. Recent developments in the ptychography reconstruction process now incorporate a modal decomposition of the illuminating probe and relax the restriction of using sources with high spatial coherence. In this article a practical implementation of hard X-ray ptychography from a partially coherent X-ray source with a large number of modes is demonstrated experimentally. A strongly diffracting Siemens star test sample is imaged using the focused beam produced by either a Fresnel zone plate or beryllium compound refractive lens. The recovered probe from each optic is back propagated in order to plot the beam caustic and determine the precise focal size and position. The power distribution of the reconstructed probe modes also allows the quantification of the beams coherence and is compared with the values predicted by a Gaussian-Schell model and the optics exit intensity.

Room-temperature performance of 3 mm-thick cadmium-zinc-telluride pixel detectors with sub-millimetre pixelization.

Cadmium-zinc-telluride (CZT) pixel detectors represent a consolidated choice for the development of room-temperature spectroscopic X-ray imagers, finding important applications in medical imaging, often as detection modules of a variety of new SPECT and CT systems. Detectors with 3-5 mm thicknesses are able to efficiently detect X-rays up to 140 keV giving reasonable room-temperature energy resolution. In this work, the room-temperature performance of 3 mm-thick CZT pixel detectors, recently developed at IMEM/CNR of Parma (Italy), is presented. Sub-millimetre detector arrays with pixel pitch less than 500 µm were fabricated. The detectors are characterized by good room-temperature performance even at high bias voltage operation (6000 V cm-1), with energy resolutions (FWHM) of 3% (1.8 keV) and 1.6% (2 keV) at 59.5 keV and 122.1 keV, respectively. Charge-sharing investigations were performed with both uncollimated and collimated synchrotron X-ray beams with particular attention to recovering the charge losses at the inter-pixel gap region. High rate measurements demonstrated the absence of high-flux radiation-induced polarization phenomena up to 25 × 106 photons mm-2 s-1.

Room-temperature X-ray response of cadmium-zinc-telluride pixel detectors grown by the vertical Bridgman technique.

In this work, the spectroscopic performances of new cadmium-zinc-telluride (CZT) pixel detectors recently developed at IMEM-CNR of Parma (Italy) are presented. Sub-millimetre arrays with pixel pitch less than 500 µm, based on boron oxide encapsulated vertical Bridgman grown CZT crystals, were fabricated. Excellent room-temperature performance characterizes the detectors even at high-bias-voltage operation (9000 V cm-1), with energy resolutions (FWHM) of 4% (0.9 keV), 1.7% (1 keV) and 1.3% (1.6 keV) at 22.1, 59.5 and 122.1 keV, respectively. Charge-sharing investigations were performed with both uncollimated and collimated synchrotron X-ray beams with particular attention to the mitigation of the charge losses at the inter-pixel gap region. High-rate measurements demonstrated the absence of high-flux radiation-induced polarization phenomena up to 2 × 106 photons mm-2 s-1. These activities are in the framework of an international collaboration on the development of energy-resolved photon-counting systems for high-flux energy-resolved X-ray imaging.

Dynamic adaptive X-ray optics. Part I. Time-resolved optical metrology investigation of the bending behaviour of piezoelectric bimorph deformable X-ray mirrors.

Piezoelectric bimorph deformable mirrors (`bimorphs') are routinely used on many synchrotron and free-electron laser beamlines to provide active variation in the size and shape of the X-ray beam. However, the time-domain potential of such optics has never been fully exploited. For the first time, the fast dynamic bending response of bimorphs is investigated here using Fizeau interferometry. Automated scripts for acquisition and analysis were developed to collect Fizeau data at a rate of 0.1 Hz to record dynamic changes in the optical surface as voltages were applied to the electrodes of the piezoelectric actuators. It is demonstrated that residual drift in the tangential radius of curvature of a bimorph can be significantly reduced using enhanced opto-mechanical holders and a fast programmable high-voltage power supply. Further improvements are achieved by applying small opposing voltages to compensate for piezoelectric creep. The present study shows that bimorphs can truly be used as high-speed adaptive optics for the X-ray domain, even without closed-loop feedback correction. This opens the possibility for relatively simple real-time tuning of the profile of X-ray bimorphs. Part II of this study [Alcock, Nistea, Signorato, Owen, Axford, Sutter, Foster & Sawhney (2019), J. Synchrotron Rad. 26, 45-51] builds upon these results and demonstrates how bimorphs can rapidly provide customisable sizes and shapes of synchrotron X-ray beams, specifically tailored to suit the experimental samples being investigated.

Dynamic adaptive X-ray optics. Part II. High-speed piezoelectric bimorph deformable Kirkpatrick-Baez mirrors for rapid variation of the 2D size and shape of X-ray beams.

The tangential curvature of actively bent X-ray mirrors at synchrotron radiation and X-ray free-electron laser (XFEL) facilities is typically only changed every few hours or even days. This operation can take tens of minutes for active optics with multiple bending actuators and often requires expert guidance using in situ monitoring devices. Hence, the dynamic performance of active X-ray optics for synchrotron beamlines has historically not been exploited. This is in stark contrast to many other scientific fields. However, many areas of synchrotron radiation and XFEL science, including macromolecular crystallography, could greatly benefit from the ability to change the size and shape of the X-ray beam rapidly and continuously. The advantages of this innovative approach are twofold: a large reduction in the dead time required to change the size of the X-ray beam for different-sized samples and the possibility of making multiple changes to the beam during the measurement of a single sample. In the preceding paper [Part I; Alcock, Nistea, Signorato & Sawhney (2019), J. Synchrotron Rad. 26, 36-44], which accompanies this article, high-speed visible-light Fizeau interferometry was used to identify the factors which influence the dynamic bending behaviour of piezoelectric bimorph deformable X-ray mirrors. Building upon this ex situ metrology study, provided here is the first synchrotron radiation beamline implementation of high-speed adaptive X-ray optics using two bimorphs operating as a Kirkpatrick-Baez pair. With optimized substrates, novel opto-mechanical holders and a next-generation high-voltage power supply, the size of an X-ray beam was rapidly and repeatedly switched in <10 s. Of equal importance, it is also shown that compensation of piezoelectric creep ensures that the X-ray beam size remains stable for more than 1 h after making a major change. The era of high-speed adaptive X-ray optics for synchrotron radiation and XFEL beamlines has begun.