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.

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.

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.

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.

Alvarez varifocal X-ray lens.

Visible light optical elements such as lenses and mirrors have counterparts for X-rays. In the visible regime, a variable focusing power can be achieved by an Alvarez lens which consists of a pair of inline planar refractors with a cubic thickness profile. When the two refractors are laterally displaced in opposite directions, the parabolic component of the wavefront is changed resulting in a longitudinal displacement of the focus. This paper reports an implementation of this concept for X-rays using two planar microfabricated refractive elements. The Alvarez X-ray lens can vary the focal distance of an elliptical X-ray mirror or a planar compound X-ray lens over several millimetres. The study presents the first demonstration of an Alvarez X-ray lens which adaptively corrects defocus and astigmatism aberrations of X-ray optics. In addition, the Alvarez X-ray lens eliminates coma aberration in an elliptical mirror, to the lowest order, when combining the lens with an adjustment of the pitch angle of the mirror.

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.

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.

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.

Nano-precision metrology of X-ray mirrors with laser speckle angular measurement.

X-ray mirrors are widely used for synchrotron radiation, free-electron lasers, and astronomical telescopes. The short wavelength and grazing incidence impose strict limits on the permissible slope error. Advanced polishing techniques have already produced mirrors with slope errors below 50 nrad root mean square (rms), but existing metrology techniques struggle to measure them. Here, we describe a laser speckle angular measurement (SAM) approach to overcome such limitations. We also demonstrate that the angular precision of slope error measurements can be pushed down to 20nrad rms by utilizing an advanced sub-pixel tracking algorithm. Furthermore, SAM allows the measurement of mirrors in two dimensions with radii of curvature as low as a few hundred millimeters. Importantly, the instrument based on SAM is compact, low-cost, and easy to integrate with most other existing X-ray mirror metrology instruments, such as the long trace profiler (LTP) and nanometer optical metrology (NOM). The proposed nanometrology method represents an important milestone and potentially opens up new possibilities to develop next-generation super-polished X-ray mirrors, which will advance the development of X-ray nanoprobes, coherence preservation, and astronomical physics.

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.

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.

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.

Detection and imaging of gadolinium accumulation in human bone tissue by micro- and submicro-XRF.

Gadolinium-based contrast agents (GBCAs) are frequently used in patients undergoing magnetic resonance imaging. In GBCAs gadolinium (Gd) is present in a bound chelated form. Gadolinium is a rare-earth element, which is normally not present in human body. Though the blood elimination half-life of contrast agents is about 90 minutes, recent studies demonstrated that some tissues retain gadolinium, which might further pose a health threat due to toxic effects of free gadolinium. It is known that the bone tissue can serve as a gadolinium depot, but so far only bulk measurements were performed. Here we present a summary of experiments in which for the first time we mapped gadolinium in bone biopsy from a male patient with idiopathic osteoporosis (without indication of renal impairment), who received MRI 8 months prior to biopsy. In our studies performed by means of synchrotron radiation induced micro- and submicro-X-ray fluorescence spectroscopy (SR-XRF), gadolinium was detected in human cortical bone tissue. The distribution of gadolinium displays a specific accumulation pattern. Correlation of elemental maps obtained at ANKA synchrotron with qBEI images (quantitative backscattered electron imaging) allowed assignment of Gd structures to the histological bone structures. Follow-up beamtimes at ESRF and Diamond Light Source using submicro-SR-XRF allowed resolving thin Gd structures in cortical bone, as well as correlating them with calcium and zinc.

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.

Absolute metrology method of the x-ray mirror with speckle scanning technique.

As an important characterization method for beamline optics, at-wavelength metrology technology based on wavefront measurements has been developed for many years. However, the previous studies on at-wavelength metrology of reflective mirrors is limited to the indirect method. So, the accurate surface information of the mirror under test would normally be inaccessible because of lack of experimental deconvolution between the mirror and any backgrounds from upstream optics. In this study, an absolute metrology method is developed based on the speckle scanning technique. Using this method, the surface profile of the mirror can be extracted exactly from the mixed information of the entire upstream beamline. At the same time, data acquisition time can also be significantly reduced by the processing algorithm introduced in this study without sacrificing the angular sensitivity.