Diffractive–refractive optics: X‐ray splitter

The possibility of splitting a thin (e.g. undulator) X‐ray beam based on diffraction–refraction effects is discussed. The beam is diffracted from a crystal whose diffracting surface has the shape of a roof with the ridge lying in the plane of diffraction. The crystal is cut asymmetrically. One half of the beam impinges on the left‐hand part of the roof and the other half impinges on the right‐hand side of the roof. Owing to refraction the left part of the beam is deviated to the left whereas the right part is deviated to the right. The device proposed consists of two channel‐cut crystals with roof‐like diffraction surfaces; the crystals are set in a dispersive position. The separation of the beams after splitting is calculated at a distance of 10 m from the crystals for various asymmetry and inclination angles. It is shown that such a splitting may be utilized for long beamlines. Advantages and disadvantages of this method are discussed.     

Particle Size Distribution of Nanospheres by Monte Carlo Fitting of Small Angle X‐Ray Scattering Curves

A method for recovering the size distribution of spherical particles from small angle scattering data by using a Monte Carlo interference function fitting algorithm is presented. The method is based on the direct simulation of the small angle scattering data upon the assumption of non‐interacting hard sphere ensembles (“dilute” solution approximation). The algorithm for retrieving the particle size distribution does not require any additional parameters apart from the input of the scattering data. The fitting strategy necessarily implies positive particle size distributions, while preserving the advantage of the indirect transformation method for data desmearing. Furthermore, the present approach does not use any regularisation procedures of the best fit solution and favours smooth particle size distributions. The Monte Carlo procedure has been tested against several simulated cases with various types of mono‐ and bi‐modal size distributions and different noise levels. In the special case of non‐interacting spheres, the Monte Carlo fitting algorithm had the same retrieving ability as the well assessed indirect transformation, structure interference and maximum entropy methods. Finally, the algorithm was applied to retrieve the distribution of spherical nanopowders produced by gas‐to‐particle conversion both as free powder and as reinforcing second‐phase agent in polymer nanocomposites.     

Characterization of Pd/Y multilayers with B4C barrier layers using GIXR and X‐ray standing wave enhanced HAXPES

Pd/Y multilayers are high‐reflectance mirrors designed to work in the 7.5–11 nm wavelength range. Samples, prepared by magnetron sputtering, are deposited with or without B₄C barrier layers located at the interfaces of the Pd and Y layers to reduce interdiffusion, which is expected from calculating the mixing enthalpy of Pd and Y. Grazing‐incident X‐ray reflectometry is used to characterize these multilayers. B₄C barrier layers are found to be effective in reducing Pd–Y interdiffusion. Details of the composition of the multilayers are revealed by hard X‐ray photoemission spectroscopy with X‐ray standing wave effects. This consists of measuring the photoemission intensity from the samples by performing an angular scan in the region corresponding to the multilayer period and an incident photon energy according to Bragg's law. The experimental results indicate that Pd does not chemically react with B nor C at the Pd–B₄C interface while Y does react at the Y–B₄C interface. The formation of Y–B or Y–C chemical compounds could be the reason why the interfaces are stabilized. By comparing the experimentally obtained angular variation of the characteristic photoemission with theoretical calculations, the depth distribution of each component element can be interpreted.     

The Munich Compact Light Source: initial performance measures

While large‐scale synchrotron sources provide a highly brilliant monochromatic X‐ray beam, these X‐ray sources are expensive in terms of installation and maintenance, and require large amounts of space due to the size of storage rings for GeV electrons. On the other hand, laboratory X‐ray tube sources can easily be implemented in laboratories or hospitals with comparatively little cost, but their performance features a lower brilliance and a polychromatic spectrum creates problems with beam hardening artifacts for imaging experiments. Over the last decade, compact synchrotron sources based on inverse Compton scattering have evolved as one of the most promising types of laboratory‐scale X‐ray sources: they provide a performance and brilliance that lie in between those of large‐scale synchrotron sources and X‐ray tube sources, with significantly reduced financial and spatial requirements. These sources produce X‐rays through the collision of relativistic electrons with infrared laser photons. In this study, an analysis of the performance, such as X‐ray flux, source size and spectra, of the first commercially sold compact light source, the Munich Compact Light Source, is presented.     

Object image correction using an X‐ray dynamical diffraction Fraunhofer hologram

Taking into account background correction and using Fourier analysis, a numerical method of an object image correction using an X‐ray dynamical diffraction Fraunhofer hologram is presented. An example of the image correction of a cylindrical beryllium wire is considered. A background correction of second‐order iteration leads to an almost precise reconstruction of the real part of the amplitude transmission coefficient and improves the imaginary part compared with that without a background correction. Using Fourier analysis of the reconstructed transmission coefficient, non‐physical oscillations can be avoided. This method can be applied for the determination of the complex amplitude transmission coefficient of amplitude as well as phase objects, and can be used in X‐ray microscopy.     

X‐ray focusing by the system of refractive lens(es) placed inside asymmetric channel‐cut crystals

An X‐ray one‐dimensionally focusing system, a refracting–diffracting lens (RDL), composed of Bragg double‐asymmetric‐reflecting two‐crystal plane parallel plates and a double‐concave cylindrical parabolic lens placed in the gap between the plates is described. It is shown that the focal length of the RDL is equal to the focal distance of the separate lens multiplied by the square of the asymmetry factor. One can obtain RDLs with different focal lengths for certain applications. Using the point‐source function of dynamic diffraction, as well as the Green function in a vacuum with parabolic approximation, an expression for the double‐diffracted beam amplitude for an arbitrary incident wave is presented. Focusing of the plane incident wave and imaging of a point source are studied. The cases of non‐absorptive and absorptive lenses are discussed. The intensity distribution in the focusing plane and on the focusing line, and its dependence on wavelength, deviation from the Bragg angle and magnification is studied. Geometrical optical considerations are also given. RDLs can be applied to focus radiation from both laboratory and synchrotron X‐ray sources, for X‐ray imaging of objects, and for obtaining high‐intensity beams. RDLs can also be applied in X‐ray astronomy.     

Obtaining local reciprocal lattice vectors from finite‐element analysis

Finite‐element analysis is frequently used by engineers at synchrotron beamlines to calculate the elastic deformation of a single crystal undergoing mechanical bending or thermal load. ANSYS^® Workbench? software is widely used for such simulations. However, although ANSYS^® Workbench? software provides useful information on the displacements, strains and stresses within the crystal, it does not yield the local reciprocal lattice vectors that would be required for X‐ray diffraction calculations. To bridge this gap, a method based on the shape functions and interpolation procedures of the software itself has been developed. An application to the double‐crystal bent Laue monochromator being designed for the I12 (JEEP) wiggler beamline at the Diamond Light Source is presented.     

Feasibility of in‐line instruments for high‐resolution inelastic X‐ray scattering

Inelastic X‐ray scattering instruments in operation at third‐generation synchrotron radiation facilities are based on backreflections from perfect silicon crystals. This concept reaches back to the very beginnings of high‐energy‐resolution X‐ray spectroscopy and has several advantages but also some inherent drawbacks. In this paper an alternate path is investigated using a different concept, the `M⁴ instrument'. It consists of a combination of two in‐line high‐resolution monochromators, focusing mirrors and collimating mirrors. Design choices and performance estimates in comparison with existing conventional inelastic X‐ray scattering instruments are presented.     

Comparative study of multilayers used in monochromators for synchrotron‐based coherent hard X‐ray imaging

A systematic study is presented in which multilayers of different composition (W/Si, Mo/Si, Pd/B₄C), periodicity (from 2.5 to 5.5 nm) and number of layers have been characterized. In particular, the intrinsic quality (roughness and reflectivity) as well as the performance (homogeneity and coherence of the outgoing beam) as a monochromator for synchrotron radiation hard X‐ray micro‐imaging are investigated. The results indicate that the material composition is the dominating factor for the performance. By helping scientists and engineers specify the design parameters of multilayer monochromators, these results can contribute to a better exploitation of the advantages of multilayer monochromators over crystal‐based devices; i.e. larger spectral bandwidth and high photon flux density, which are particularly useful for synchrotron‐based micro‐radiography and ‐tomography.     

X‐ray harmonics rejection on third‐generation synchrotron sources using compound refractive lenses

A new method of harmonics rejection based on X‐ray refractive optics has been proposed. Taking into account the fact that the focal distance of the refractive lens is energy‐dependent, the use of an off‐axis illumination of the lens immediately leads to spatial separation of the energy spectrum by focusing the fundamental harmonic at the focal point and suppressing the unfocused high‐energy radiation with a screen absorber or slit. The experiment was performed at the ESRF ID06 beamline in the in‐line geometry using an X‐ray transfocator with compound refractive lenses. Using this technique the presence of the third harmonic has been reduced to 10^?3. In total, our method enabled suppression of all higher‐order harmonics to five orders of magnitude using monochromator detuning. The method is well suited to third‐generation synchrotron radiation sources and is very promising for the future ultimate storage rings.     

Quantitative performance measurements of bent crystal Laue analyzers for X‐ray fluorescence spectroscopy

Third‐generation synchrotron radiation sources pose difficult challenges for energy‐dispersive detectors for XAFS because of their count rate limitations. One solution to this problem is the bent crystal Laue analyzer (BCLA), which removes most of the undesired scatter and fluorescence before it reaches the detector, effectively eliminating detector saturation due to background. In this paper experimental measurements of BCLA performance in conjunction with a 13‐element germanium detector, and a quantitative analysis of the signal‐to‐noise improvement of BCLAs are presented. The performance of BCLAs are compared with filters and slits.     

Alignment of low‐dose X‐ray fluorescence tomography images using differential phase contrast

X‐ray fluorescence nanotomography provides unprecedented sensitivity for studies of trace metal distributions in whole biological cells. Dose fractionation, in which one acquires very low dose individual projections and then obtains high statistics reconstructions as signal from a voxel is brought together (Hegerl & Hoppe, 1976), requires accurate alignment of these individual projections so as to correct for rotation stage runout. It is shown here that differential phase contrast at 10.2 keV beam energy offers the potential for accurate cross‐correlation alignment of successive projections, by demonstrating that successive low dose, 3 ms per pixel, images acquired at the same specimen position and rotation angle have a narrower and smoother cross‐correlation function (1.5 pixels FWHM at 300 nm pixel size) than that obtained from zinc fluorescence images (25 pixels FWHM). The differential phase contrast alignment resolution is thus well below the 700 nm × 500 nm beam spot size used in this demonstration, so that dose fractionation should be possible for reduced‐dose, more rapidly acquired, fluorescence nanotomography experiments.     

X‐ray‐Raman‐scattering‐based EXAFS beyond the dipole limit

X‐ray Raman scattering (XRS) provides a bulk‐sensitive method of measuring the extended X‐ray absorption fine structure (EXAFS) of soft X‐ray absorption edges. Accurate measurements and data analysis procedures for the determination of XRS‐EXAFS of polycrystalline diamond are described. The contributions of various angular‐momentum components beyond the dipole limit to the atomic background and the EXAFS oscillations are incorporated using self‐consistent real‐space multiple‐scattering calculations. The properly extracted XRS‐EXAFS oscillations are in good agreement with calculations and earlier soft X‐ray EXAFS results. It is shown, however, that under certain conditions multiple‐scattering contributions to XRS‐EXAFS deviate from those in standard EXAFS, leading to noticeable changes in the real‐space signal at higher momentum transfers owing to non‐dipole contributions. These results pave the way for the accurate application of XRS‐EXAFS to previously inaccessible light‐element systems.     

Ratio-contrast imaging of dual-energy absorption for element mapping with a scanning transmission X-ray microscope

The detection of chemical mapping with a spatial resolution of 30 nm has been achieved with a scanning transmission X‐ray microscope at the Shanghai Synchrotron Radiation Facility. For each specimen, two absorption images were scanned separately with energies E₁ and E₂: E₁ was focused on the absorption edge of the chosen element and E₂ was focused below the edge. A K‐edge division method is proposed and applied to obtain the element mapping. Compared with the frequently used K‐edge subtraction method, this ratio‐contrast method is shown to be more accurate and sensitive in identifying the elements of interest, where the definition of the contrast threshold is simple and clear in physics. Several examples are presented to illustrate the effectiveness of the method.     

Numerical reconstruction of an object image using an X‐ray dynamical diffraction Fraunhofer hologram

A numerical method of reconstruction of an object image using an X‐ray dynamical diffraction Fraunhofer hologram is presented. Analytical approximation methods and numerical methods of iteration are discussed. An example of a reconstruction of an image of a cylindrical beryllium wire is considered. The results of analytical approximation and zero‐order iteration coincide with exact values of the amplitude complex transmission coefficient of the object as predicted by the resolution limit of the scheme, except near the edges of the object. Calculations of the first‐ and second‐order iterations improve the result at the edges of the object. This method can be applied for determination of the complex amplitude transmission coefficient of amplitude as well as phase objects. It can be used in X‐ray microscopy.     

Hard X‐ray phase‐contrast tomography of non‐homogeneous specimens: grating interferometry versus propagation‐based imaging

X‐ray phase‐contrast imaging is an effective approach to drastically increase the contrast and sensitivity of microtomographic techniques. Numerous approaches to depict the real part of the complex‐valued refractive index of a specimen are nowadays available. A comparative study using experimental data from grating‐based interferometry and propagation‐based phase contrast combined with single‐distance phase retrieval applied to a non‐homogeneous sample is presented (acquired at beamline ID19‐ESRF). It is shown that grating‐based interferometry can handle density gradients in a superior manner. The study underlines the complementarity of the two techniques for practical applications.     

X‐ray photon correlation spectroscopy in systems without long‐range order: existence of an intermediate‐field regime

Successful X‐ray photon correlation spectroscopy studies often require that signals be optimized while minimizing power density in the sample to decrease radiation damage and, at free‐electron laser sources, thermal impact. This suggests exploration of scattering outside the Fraunhofer far‐field diffraction limit d²/λR, where d is the incident beam size, λ is the photon wavelength and R is the sample‐to‐detector distance. Here it is shown that, in an intermediate regime d²/λ > Rdξ/λ, where ξ is the structural correlation length in the material, the ensemble averages of the scattered intensity and of the structure factor are equal. Similarly, in the regime d²/λ > Rdξ(τ)/λ, where ξ(τ) is a time‐dependent dynamics length scale of interest, the ensemble‐averaged correlation functions g₁(τ) and g₂(τ) of the scattered electric field are also equal to their values in the far‐field limit. This broadens the parameter space for X‐ray photon correlation spectroscopy experiments, but detectors with smaller pixel size and variable focusing are required to more fully exploit the potential for such studies.     

An attempt at kidney stone analysis with the application of synchrotron radiation

X‐ray absorption near‐edge spectroscopy (XANES) is a spectroscopic technique using synchrotron light to determine the valence state of excited atoms as well as the electronegativity of their neighbouring atoms. XANES spectra can provide information about the chemical bond in the second coordination shell of the excited atom. In this study, XANES spectra of unknown compounds from human kidney stones were recorded around the K‐edges of sulfur, phosphorus and calcium. The XANES results agree well with the diffractogram data of the same stones obtained through an X‐ray powder diffraction (XRPD) technique. By comparing the measurement techniques presented here, it is shown that XANES requires a smaller amount of each sample than XRPD for analysis.