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.

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 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.

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.

Confinement generates single-crystal aragonite rods at room temperature.

The topic of calcite and aragonite polymorphism attracts enormous interest from fields including biomineralization and paleogeochemistry. While aragonite is only slightly less thermodynamically stable than calcite under ambient conditions, it typically only forms as a minor product in additive-free solutions at room temperature. However, aragonite is an abundant biomineral, and certain organisms can selectively generate calcite and aragonite. This fascinating behavior has been the focus of decades of research, where this has been driven by a search for specific organic macromolecules that can generate these polymorphs. However, despite these efforts, we still have a poor understanding of how organisms achieve such selectivity. In this work, we consider an alternative possibility and explore whether the confined volumes in which all biomineralization occurs could also influence polymorph. Calcium carbonate was precipitated within the cylindrical pores of track-etched membranes, where these enabled us to systematically investigate the relationship between the membrane pore diameter and polymorph formation. Aragonite was obtained in increasing quantities as the pore size was reduced, such that oriented single crystals of aragonite were the sole product from additive-free solutions in 25-nm pores and significant quantities of aragonite formed in pores as large as 200 nm in the presence of low concentrations of magnesium and sulfate ions. This effect can be attributed to the effect of the pore size on the ion distribution, which becomes of increasing importance in small pores. These intriguing results suggest that organisms may exploit confinement effects to gain control over crystal polymorph.

Using refractive optics to broaden the focus of an X-ray mirror.

X-ray mirrors are widely used at synchrotron radiation sources for focusing X-rays into focal spots of size less than 1 µm. The ability of the beamline optics to change the size of this spot over a range up to tens of micrometres can be an advantage for many experiments such as X-ray microprobe and X-ray diffraction from micrometre-scale crystals. It is a requirement that the beam size change should be reproducible and it is often essential that the change should be rapid, for example taking less than 1 s, in order to allow high data collection rates at modern X-ray sources. In order to provide a controlled broadening of the focused spot of an X-ray mirror, a series of refractive optical elements have been fabricated and installed immediately before the mirror. By translation, a new refractive element is moved into the X-ray beam allowing a variation in the size of the focal spot in the focusing direction. Measurements using a set of prefabricated refractive structures with a test mirror showed that the focused beam size could be varied from less than 1 µm to over 10 µm for X-rays in the energy range 10-20 keV. As the optics is in-line with the X-ray beam, there is no effect on the centroid position of the focus. Accurate positioning of the refractive optics ensures reproducibility in the focused beam profile and no additional re-alignment of the optics is required.

Two-dimensional in situ metrology of X-ray mirrors using the speckle scanning technique.

In situ metrology overcomes many of the limitations of existing metrology techniques and is capable of exceeding the performance of present-day optics. A novel technique for precisely characterizing an X-ray bimorph mirror and deducing its two-dimensional (2D) slope error map is presented. This technique has also been used to perform fast optimization of a bimorph mirror using the derived 2D piezo response functions. The measured focused beam size was significantly reduced after the optimization, and the slope error map was then verified by using geometrical optics to simulate the focused beam profile. This proposed technique is expected to be valuable for in situ metrology of X-ray mirrors at synchrotron radiation facilities and in astronomical telescopes.

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.

X-ray phase contrast tomography by tracking near field speckle.

X-ray imaging techniques that capture variations in the x-ray phase can yield higher contrast images with lower x-ray dose than is possible with conventional absorption radiography. However, the extraction of phase information is often more difficult than the extraction of absorption information and requires a more sophisticated experimental arrangement. We here report a method for three-dimensional (3D) X-ray phase contrast computed tomography (CT) which gives quantitative volumetric information on the real part of the refractive index. The method is based on the recently developed X-ray speckle tracking technique in which the displacement of near field speckle is tracked using a digital image correlation algorithm. In addition to differential phase contrast projection images, the method allows the dark-field images to be simultaneously extracted. After reconstruction, compared to conventional absorption CT images, the 3D phase CT images show greatly enhanced contrast. This new imaging method has advantages compared to other X-ray imaging methods in simplicity of experimental arrangement, speed of measurement and relative insensitivity to beam movements. These features make the technique an attractive candidate for material imaging such as in-vivo imaging of biological systems containing soft tissue.

Quadrupole transitions revealed by Borrmann spectroscopy.

The Borrmann effect-a dramatic increase in transparency to X-ray beams-is observed when X-rays satisfying Bragg's law diffract through a perfect crystal. The minimization of absorption seen in the Borrmann effect has been explained by noting that the electric field of the X-ray beam approaches zero amplitude at the crystal planes, thus avoiding the atoms. Here we show experimentally that under conditions of absorption suppression, the weaker electric quadrupole absorption transitions are effectively enhanced to such a degree that they can dominate the absorption spectrum. This effect can be exploited as an atomic spectroscopy technique; we show that quadrupole transitions give rise to additional structure at the L(1), L(2) and L(3) absorption edges of gadolinium in gadolinium gallium garnet, which mark the onset of excitations from 2s, 2p(1/2) and 2p(3/2) atomic core levels, respectively. Although the Borrmann effect served to underpin the development of the theory of X-ray diffraction, this is potentially the most important experimental application of the phenomenon since its first observation seven decades ago. Identifying quadrupole features in X-ray absorption spectroscopy is central to the interpretation of 'pre-edge' spectra, which are often taken to be indicators of local symmetry, valence and atomic environment. Quadrupolar absorption isolates states of different symmetries to that of the dominant dipole spectrum, and typically reveals orbitals that dominate the electronic ground-state properties of lanthanides and 3d transition metals, including magnetism. Results from our Borrmann spectroscopy technique feed into contemporary discussions regarding resonant X-ray diffraction and the nature of pre-edge lines identified by inelastic X-ray scattering. Furthermore, because the Borrmann effect has been observed in photonic materials, it seems likely that the quadrupole enhancement reported here will play an important role in modern optics.

A novel facility using a Laue focusing monochromator for high-pressure diffraction at the SRS, Daresbury, UK.

A novel Laue focusing monochromator has been developed to provide intense X-radiation for high-pressure diffraction experiments. A beamline using this monochromator has been successfully developed on station 9.5 at the SRS, Daresbury Laboratory. Contributions to resolution from monochromator bandpass and divergence due to focusing have been quantified and are used to assess experimental diffraction data from diamond-anvil cells recorded using image plates with X-rays at approximately 30 keV. This optical and beamline design could be readily adapted to use X-rays from a bending magnet on a third-generation synchrotron source.

A high-throughput structural biology/proteomics beamline at the SRS on a new multipole wiggler.

The North West Structural Genomics Centre's beamline, MAD10, at the SRS receives the central part of the radiation fan (0.5 mrad vertically, 4 mrad horizontally) produced by a new 2.46 T ten-pole wiggler. The optical arrangement of the beamline consists of a Rh-coated collimating Si mirror, a fixed-exit-beam double-crystal monochromator with sagittal bending for horizontal focusing and a second Rh-coated Si mirror for vertical focusing. The double-crystal Si (111) monochromator allows data collection in the 5-13.5 keV photon energy range with rapid (subsecond) tunability and high energy resolution. The monochromatic beam is optimized through a 200 microm collimator. The beamline end station has been designed around a Mar desktop beamline with high-throughput cryogenic sample changer, Mar225 CCD detector, liquid-N(2) autofill system and an ORTEC C-TRAIN-04 energy-resolving high-count-rate X-ray fluorescence detector. The instrument is optimized for MAD/SAD applications in protein crystallography with the additional mode of operation of online single-crystal EXAFS studies on the same crystals. Thus, screening of metals/Se in the crystal can be performed quickly prior to MAD/SAD data collection by exciting the crystal with X-rays of appropriate energy and recording an energy-dispersive fluorescence spectrum. In addition, this experimental set-up allows for parallel XAFS measurements on the same crystal to monitor 'radiation-induced' changes, if any, in e.g. the redox state of metal centres to be detected for a 'metallic' functional group during crystallographic data collection. Moreover, careful minimization of the thickness of the Be window maximizes the intensity performance for the 2.0-2.5 A softer wavelength range. This range also covers the K-edges of a number of important 3d transition metals as well as the L-edges of xenon and iodine and enhanced sulfur f ''.

Counting statistics of X-ray detectors at high counting rates.

Modern synchrotron radiation sources with insertion devices and focusing optics produce high fluxes of X-rays at the sample, which leads to a requirement for photon-counting detectors to operate at high counting rates. With high counting rates there can be significant non-linearity in the response of the detector to incident X-ray flux, where this non-linearity is caused by the overlap of the electronic pulses that are produced by each X-ray. A model that describes the overlap of detector pulses is developed in this paper. This model predicts that the correction to the counting rate for pulse overlap is the same as a conventional dead-time correction. The model is also used to calculate the statistical uncertainty of a measurement and predicts that the error associated with a measurement can be increased significantly over that predicted by Poisson (N(-1/2)) statistics. The error differs from that predicted by a conventional dead-time treatment.

Software for automatic calibration of synchrotron powder diffractometers.

An automatic procedure to calibrate angular-dispersive monochromatic diffraction instruments has been developed at the Daresbury Synchrotron Radiation Source. The procedure uses a macro Language to control the powder diffraction instruments to locate Bragg reflections and perform peak-centre refinement from a standard reference material. The information obtained is used to refine the wavelength of the radiation used and the angular offset of the detector arm. The concept and implementation of the new software are described with applications to demonstrate its viability. The results of a reliability and accuracy study are also presented.