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.

Extending synchrotron SAXS instrument ranges through addition of a portable, inexpensive USAXS module with vertical rotation axes.

Ultra-SAXS can enhance the capabilities of existing synchrotron SAXS/WAXS beamlines. A compact ultra-SAXS module has been developed, which extends the measurable q-range with 0.0015 ≤ q (nm-1) ≤ 0.2, allowing structural dimensions in the range 30 ≤ D (nm) ≤ 4000 to be probed in addition to the range covered by a high-end SAXS/WAXS instrument. By shifting the module components in and out on their respective motor stages, SAXS/WAXS measurements can be easily and rapidly interleaved with USAXS measurements. The use of vertical crystal rotation axes (horizontal diffraction) greatly simplifies the construction, at minimal cost to efficiency. In this paper, the design considerations, realization and synchrotron findings are presented. Measurements of silica spheres, an alumina membrane, and a porous carbon catalyst are provided as application examples.

Beamline K11 DIAD: a new instrument for dual imaging and diffraction at Diamond Light Source.

The Dual Imaging and Diffraction (DIAD) beamline at Diamond Light Source is a new dual-beam instrument for full-field imaging/tomography and powder diffraction. This instrument provides the user community with the capability to dynamically image 2D and 3D complex structures and perform phase identification and/or strain mapping using micro-diffraction. The aim is to enable in situ and in operando experiments that require spatially correlated results from both techniques, by providing measurements from the same specimen location quasi-simultaneously. Using an unusual optical layout, DIAD has two independent beams originating from one source that operate in the medium energy range (7-38 keV) and are combined at one sample position. Here, either radiography or tomography can be performed using monochromatic or pink beam, with a 1.4 mm × 1.2 mm field of view and a feature resolution of 1.2 µm. Micro-diffraction is possible with a variable beam size between 13 µm × 4 µm and 50 µm × 50 µm. One key functionality of the beamline is image-guided diffraction, a setup in which the micro-diffraction beam can be scanned over the complete area of the imaging field-of-view. This moving beam setup enables the collection of location-specific information about the phase composition and/or strains at any given position within the image/tomography field of view. The dual beam design allows fast switching between imaging and diffraction mode without the need of complicated and time-consuming mode switches. Real-time selection of areas of interest for diffraction measurements as well as the simultaneous collection of both imaging and diffraction data of (irreversible) in situ and in operando experiments are possible.

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.

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.

Beamline B21: high-throughput small-angle X-ray scattering at Diamond Light Source.

B21 is a small-angle X-ray scattering (SAXS) beamline with a bending magnet source in the 3 GeV storage ring at the Diamond Light Source Ltd synchrotron in the UK. The beamline utilizes a double multi-layer monochromator and a toroidal focusing optic to deliver 2 × 1012 photons per second to a 34 × 40 µm (FWHM) focal spot at the in-vacuum Eiger 4M (Dectris) detector. A high-performance liquid chromatography system and a liquid-handling robot make it possible to load solution samples into a temperature-controlled in-vacuum sample cell with a high level of automation. Alternatively, a range of viscous or solid materials may be loaded manually using a range of custom sample cells. A default scattering vector range from 0.0026 to 0.34 Å-1 and low instrument background make B21 convenient for measuring a wide range of biological macromolecules. The beamline has run a full user programme since 2013.

Application of interference fits on cylindrical monochromator crystals to overcome clamping and cooling deformations.

In order to provide adequate cryogenic cooling of both existing and next-generation crystal monochromators, a new approach to produce an optimum thermal interface between the first crystal and its copper heat exchanger is proposed. This will ensure that the increased heat load deposited by higher X-ray powers can be properly dissipated. Utilizing a cylindrical silicon crystal, a tubular copper heat exchanger and by exploiting the differing thermal and mechanical properties of the two, a very good thermal interface was achieved at liquid-nitrogen temperatures. The surface flatness of the diffracting plane at one end of the cylindrical crystal was measured at room temperature while unconstrained. The crystal was then placed into the copper heat exchanger, a slide fit at room temperature, and then cooled to liquid-nitrogen temperature. At -200°C the slide fit became an interference fit. This room-temperature `loose' fit was modelled using finite-element analysis to obtain the desired fit at cryogenic temperatures by prescribing the fit at room temperature. Under these conditions, the diffraction surface was measured for distortion due to thermal and mechanical clamping forces. The total deformation was measured to be 30 nm, an order of magnitude improvement over deformation caused by cooling alone with the original side-clamped design this concept method is set to replace. This new methodology also has the advantage that it is repeatable and does not require macro-scale tools to acquire a nanometre-accuracy mounting.

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.

1 m long multilayer-coated deformable piezoelectric bimorph mirror for adjustable focusing of high-energy X-rays.

The Diamond Light Source (DLS) beamline I15-1 measures atomic pair distribution functions (PDF) using scattering of 40-80 keV X-rays. A unique focusing element was needed to condense these X-rays from an initial large cross section (11.0 mm H × 4.2 mm V) into a required spot size of FWHM ≈680 µm (H) × 20 µm (V) at a variable position between the sample and the detector. The large numerical aperture is achieved by coating a silicon substrate over 1 m long with three multilayer stripes of Bragg angle 4.2 mrad. One stripe selects X-rays of each energy 40.0, 65.4, and 76.6 keV. Sixteen piezoelectric bimorph actuators attached to the sides of the mirror substrate adjusted the reflecting surface's shape. Focal spots of vertical width < 15 µm were obtained at three positions over a 0.92 m range, with fast, easy switching from one focal position to another. Minimized root mean square slope errors were close to 0.5 µrad after subtraction of a uniform curvature. Reflectivity curves taken along each stripe showed consistent high peaks with generally small angular variation of peak positions. This is the first application of a 1 m long multilayer-coated bimorph mirror at a synchrotron beamline. Data collected with its help on a slice of a lithium ion battery's cathode are presented.

The scanning four-bounce monochromator for beamline I20 at the Diamond Light Source.

A description of the technical and design details of a scanning four-bounce crystal monochromator that has recently been commissioned for the Versatile X-ray Absorption Spectroscopy (XAS) beamline at Diamond Light Source is presented. This device consists of two independent rotary axes of unique design which are synchronized using a multiple read-head encoder system. This monochromator is shown to be capable of maintaining the flux throughput of the Bragg axes without the need of any external feedback mechanism from 4 to 20 keV. The monochromator is currently equipped with cryogenically cooled crystals with the upstream axis consisting of two independent Si(111) crystals and a pair of channel-cut crystals in the downstream axis. The possibility of installing an additional Si(311) crystal-set to extend the energy range to 34 keV is incorporated into the preliminary design of the device. Experimental data are presented showing the exceptional mechanical stability and repeatability of the monochromator axes.

In situ beamline analysis and correction of active optics. Erratum.

A correction to one of the equations in the paper by Sutter et al. (2012). [J. Synchrotron Rad. 19, 960-968] is made.

Aberration-free aspherical lens shape for shortening the focal distance of an already convergent beam.

The shapes of single lens surfaces capable of focusing divergent and collimated beams without aberration have already been calculated. However, nanofocusing compound refractive lenses (CRLs) require many consecutive lens surfaces. Here a theoretical example of an X-ray nanofocusing CRL with 48 consecutive surfaces is studied. The surfaces on the downstream end of this CRL accept X-rays that are already converging toward a focus, and refract them toward a new focal point that is closer to the surface. This case, so far missing from the literature, is treated here. The ideal surface for aberration-free focusing of a convergent incident beam is found by analytical computation and by ray tracing to be one sheet of a Cartesian oval. An `X-ray approximation' of the Cartesian oval is worked out for the case of small change in index of refraction across the lens surface. The paraxial approximation of this surface is described. These results will assist the development of large-aperture CRLs for nanofocusing.

Creating flat-top X-ray beams by applying surface profiles of alternating curvature to deformable piezo bimorph mirrors.

Beam shaping is becoming increasingly important for synchrotron X-ray applications. Although routine for visible light lasers, this is challenging for X-rays due to the limited source coherence and extreme optical tolerances required for the shaping mirrors. In deliberate defocusing, even surface errors <5 nm r.m.s. introduce damagingly large striations into the reflected beam. To counteract such problems, surface modifications with alternating concave and convex curvature on equal segments were polished onto the surface of non-active mirrors of fixed curvature. Such optics are useful for providing a fixed size of X-ray beam, but do not provide the adaptability required by many experiments. In contrast, deformable piezo bimorph mirrors permit a continuous range of X-ray beam sizes and shapes. A new theory is developed for applying non-periodic modifications of alternating curvature to optical surfaces. The position and length of the segments may be freely chosen. For the first time, surface modifications of alternating curvature are applied to bimorph mirrors to generate non-Gaussian X-ray beam profiles of specified width. The new theory's freedom is exploited to choose the segments to match the polishing errors of medium wavelength (>10 mm) and the piezos' influence on the mirror's figure. Five- and seven-segment modifications of alternating curvature are calculated and verified by visible light and X-ray metrology. The latter yields beam profiles with less striation than those made by defocusing. Remaining beam striations are explained by applying geometrical optics to the deviations from the ideal surface modifications of alternating curvature.

Ultra-high-resolution inelastic X-ray scattering at high-repetition-rate self-seeded X-ray free-electron lasers.

Inelastic X-ray scattering (IXS) is an important tool for studies of equilibrium dynamics in condensed matter. A new spectrometer recently proposed for ultra-high-resolution IXS (UHRIX) has achieved 0.6 meV and 0.25 nm(-1) spectral and momentum-transfer resolutions, respectively. However, further improvements down to 0.1 meV and 0.02 nm(-1) are required to close the gap in energy-momentum space between high- and low-frequency probes. It is shown that this goal can be achieved by further optimizing the X-ray optics and by increasing the spectral flux of the incident X-ray pulses. UHRIX performs best at energies from 5 to 10 keV, where a combination of self-seeding and undulator tapering at the SASE-2 beamline of the European XFEL promises up to a 100-fold increase in average spectral flux compared with nominal SASE pulses at saturation, or three orders of magnitude more than what is possible with storage-ring-based radiation sources. Wave-optics calculations show that about 7 × 10(12) photons s(-1) in a 90 µeV bandwidth can be achieved on the sample. This will provide unique new possibilities for dynamics studies by IXS.

Characterization of a next-generation piezo bimorph X-ray mirror for synchrotron beamlines.

Piezo bimorph mirrors are versatile active optics used on many synchrotron beamlines. However, many bimorphs suffer from the `junction effect': a periodic deformation of the optical surface which causes major aberrations to the reflected X-ray beam. This effect is linked to the construction of such mirrors, where piezo ceramics are glued directly below the thin optical substrate. In order to address this problem, a next-generation bimorph with piezos bonded to the side faces of a monolithic substrate was developed at Thales-SESO and optimized at Diamond Light Source. Using metrology feedback from the Diamond-NOM, the optical slope error was reduced to ∼ 0.5 µrad r.m.s. for a range of ellipses. To maximize usability, a novel holder was built to accommodate the substrate in any orientation. When replacing a first-generation bimorph on a synchrotron beamline, the new mirror significantly improved the size and shape of the reflected X-ray beam. Most importantly, there was no evidence of the junction effect even after eight months of continuous beamline usage. It is hoped that this new design will reinvigorate the use of active bimorph optics at synchrotron and free-electron laser facilities to manipulate and correct X-ray wavefronts.

Advanced in situ metrology for x-ray beam shaping with super precision.

We report a novel method for in situ metrology of an X-ray bimorph mirror by using the speckle scanning technique. Both the focusing beam and the "tophat" defocussed beam have been generated by optimizing the bimorph mirror in a single iteration. Importantly, we have demonstrated that the angular sensitivity for measuring the slope error of an optical surface can reach accuracy in the range of two nanoradians. When compared with conventional ex-situ metrology techniques, the method enables a substantial increase of around two orders of magnitude in the angular sensitivity and opens the way to a previously inaccessible region of slope error measurement. Such a super precision metrology technique will be beneficial for both the manufacture of polished mirrors and the optimization of beam shaping.

Surface profiling of X-ray mirrors for shaping focused beams.

Grazing incidence mirrors are a standard optic for focusing X-rays. Active mirrors, whose surface profile can be finely adjusted, allow control of beam shape and size at the sample. However, progress towards their routine use for beam shaping has been hampered by the strong striations in reflected beams away from the focal plane. Re-entrant (partly concave and partly convex) surface modifications are proposed for shaping X-ray beams to a top-hat in the focal plane while reducing the striations caused by unavoidable polishing errors. A method for constructing such surfaces with continuous height and slope (but only piecewise continuous curvature) will be provided. Ray tracing and wave propagation calculations confirm its effectiveness. A mirror system is proposed allowing vertical beam sizes in the range 0.5 to 10µm. A prototype will be fabricated and is expected to have applications on many synchrotron X-ray beamlines.

Fast optimization of a bimorph mirror using x-ray grating interferometry.

An x-ray grating interferometer was employed for in situ optimization of an x-ray bimorph mirror. Unlike many other at-wavelength techniques, only a single interferogram image, captured out of the focal plane, is required, enabling the optical surface to be quickly optimized. Moiré fringe analysis was used to calculate the wavefront slope error, which is proportional to the mirror's slope error. Using feedback from grating interferometry, the slope error of a bimorph mirror was reduced to <200 nrad (rms) in only two iterations. This technique has the potential to create photon beams with spatially homogeneous intensities for use in synchrotron and free electron laser beam lines.

In situ beamline analysis and correction of active optics.

At the Diamond Light Source, pencil-beam measurements have enabled long-wavelength slope errors on X-ray mirror surfaces to be examined under ultra-high vacuum and beamline mounting without the need to remove the mirror from the beamline. For an active mirror an automated procedure has been implemented to calculate the actuator settings that optimize its figure. More recently, this in situ pencil-beam method has been applied to additional uses for which ex situ measurements would be inconvenient or simply impossible. First, it has been used to check the stability of the slope errors of several bimorph mirrors at intervals of several weeks or months. Then, it also proved useful for the adjustment of bender and sag compensation actuators on mechanically bent mirrors. Fits to the bending of ideal beams have been performed on the slope errors of a mechanically bent mirror in order to distinguish curvatures introduced by the bending actuators from gravitational distortion. Application of the optimization procedure to another mechanically bent mirror led to an improvement of its sag compensation mechanism.

Implementation of a beam deflection system for studies of liquid interfaces on beamline I07 at Diamond.

X-ray optics, based on a double-crystal deflection scheme, that enable reflectivity measurements from liquid surfaces/interfaces have been designed, built and commissioned on beamline I07 at Diamond Light Source. This system is able to deflect the beam onto a fixed sample position located at the centre of a five-circle diffractometer. Thus the incident angle can be easily varied without moving the sample, and the reflected beam is tracked either by a moving Pilatus 100K detector mounted on the diffractometer arm or by a stationary Pilatus 2M detector positioned appropriately for small-angle scattering. Thus the system can easily combine measurements of the reflectivity from liquid interfaces (Q(z) > 1 Å(-1)) with off-specular data collection, both in the form of grazing-incidence small-angle X-ray scattering (GISAXS) or wider-angle grazing-incidence X-ray diffraction (GIXD). The device allows operation over the energy range 10-28 keV.