X-ray Optical Elements Research Articles

X-ray scattering tensor tomography based finite element modelling of heterogeneous materials

Among micro-scale imaging technologies of materials, X-ray micro-computed tomography has evolved as most popular choice, even though it is restricted to limited field-of-views and long acquisition times. With recent progress in small-angle X-ray scattering these downsides of conventional absorption-based computed tomography have been overcome, allowing complete analysis of the micro-architecture for samples in the dimension of centimetres in a matter of minutes. These advances have been triggered through improved X-ray optical elements and acquisition methods. However, it has not yet been shown how to effectively transfer this small-angle X-ray scattering data into a numerical model capable of accurately predicting the actual material properties. Here, a method is presented to numerically predict mechanical properties of a carbon fibre-reinforced polymer based on imaging data with a voxel-size of 100 μm corresponding to approximately fifteen times the fibre diameter. This extremely low resolution requires a completely new way of constructing the material’s constitutive law based on the fibre orientation, the X-ray scattering anisotropy, and the X-ray scattering intensity. The proposed method combining the advances in X-ray imaging and the presented material model opens for an accurate tensile modulus prediction for volumes of interest between three to six orders of magnitude larger than those conventional carbon fibre orientation image-based models can cover.

A versatile beamline for soft x-ray reflectivity, absorption, and fluorescence measurements at Indus-2 synchrotron source.

A versatile beamline for performing reflectivity, fluorescence, and absorption experiments in the soft x-ray region of 100-1500eV is commissioned on a bending magnet port of the Indus-2 synchrotron source. A high vacuum 2-axis reflectometer with x, y, and z sample scanning stages is installed. This reflectometer is used to measure the reflectivity of large samples up to 300mm in length and 5kg in weight. This feature is useful for characterizing x-ray optical elements, such as mirrors, gratings, and multilayers. A flange mounted silicon drift detector is installed in the downstream of the reflectometer for soft x-ray fluorescence measurements. The soft x-ray absorption measurements are carried out in the total electron yield and partial fluorescence yield modes. Integration of three different experimental techniques in the experimental station makes the beamline versatile for materials science applications as it provides structural, chemical, and electronic state information by performing the required experiments in an identical environment. The beamline uses a varied line spacing plane grating monochromator and gives a high flux (∼109 to 1011 photon/s) with a moderate resolution (λ/Δλ ~1000-5000). A three-mirror-based higher harmonic setup is incorporated to get rid of harmonics and to get a high spectral purity monochromatic beam with less than 0.1% harmonic content. In the present article, the beamline optical scheme, mechanical configuration, and details of the experimental setups are presented, along with a few representative results of each experimental mode.

Ultrashort X-ray Free Electron Laser Pulse Manipulation by Optical Matrix

Free electron laser (FEL) is capable of producing ultra-short X-ray pulses. The estimation of X-ray pulse propagation is the key process of X-ray FEL beamline design. By using the Kostenbauder matrix approach, the evolution of an ultra-short pulse in a beamline system can be calculated. Therefore, it is of significant importance to investigate the Kostenbauder matrices of different kinds of X-ray optics. In this work, we derive a unified 6 × 6 optical matrix to describe various kinds of X-ray optical elements, including varied-line-spacing (VLS) toroidal grating, VLS spherical grating, VLS cylindrical grating, VLS plane grating, toroidal grating, spherical grating, cylindrical grating, plane grating, toroidal mirror, spherical mirror, cylindrical mirror, and plane mirror. These optics are usually adopted in soft X-ray regime. We apply this method to describe the transverse focusing, pulse front tilt, and pulse stretching after an X-ray pulse going through a VLS plane grating monochromator (VLS-PGM). We also use this approach to simulate a grating compressor which can be used to compress chirped soft X-ray pulse. This work is helpful in the design and optimization of X-ray beamline systems.

Refractive axicon for X-ray microscopy applications: design, optimization, and experiment.

In a full-field transmission X-ray microscopy (TXM) setup, a condenser X-ray optical element is used to illuminate the sample by condensing the X-ray beam delivered by the synchrotron storage ring. On-going and future upgrades of synchrotron facilities to diffraction-limited storage rings will pose new challenges to these TXM setups, such as much smaller X-ray beams on the condenser. Here, we demonstrate that a refractive axicon can be used as an X-ray beam shaper to match the ring-shaped aperture of the condenser. Aiming at more efficient use of the incoming X-ray intensity, we explore several axicon designs both analytically and with numerical simulations. The axicons were produced by two-photon polymerization 3D printing on thin silicon nitride membrane substrates. The first characterization of the axicon was carried out at the TOMCAT beamline of the Swiss Light Source (Switzerland).

Использование морфометрических величин при изучении рельефа поверхности рентгенооптических элементов

We studied the use of morphometric variables (maximal curvature, minimal curvature, mean curvature, topographic index, etc.) for study of the surface of X-ray optical elements. We performed calculations on digital elevation models of a spherical concave substrates: primordial and smoothed digital elevation models, before and after technological operations (mechanical lapping, axisymmetric surface shape correction, ion beam figuring). We have demonstrated a visual display of weakly expressed topography inhomogeneities, incl. which are not displayed on the maps of the original digital elevation models. The consideration included the study of both the measured samples and the errors in the formation of the digital elevation model (artifacts from the recording system and from the inhomogeneity of the medium), as well as the features of scale decomposition when using the universal spectral-analytical method.

Adaptive X-Ray Optical Elements Based on Bending Piezoactuators: Possibilities and Prospects of Practical Application

Adaptive X-Ray Optical Elements Based on Bending Piezoactuators: Possibilities and Prospects of Practical Application

Precise wavefront characterization of x-ray optical elements using a laboratory source.

Improvements in x-ray optics critically depend on the measurement of their optical performance. The knowledge of wavefront aberrations, for example, can be used to improve the fabrication of optical elements or to design phase correctors to compensate for these errors. At present, the characterization of such optics is made using intense x-ray sources, such as synchrotrons. However, the limited access to these facilities can substantially slow down the development process. Improvements in the brightness of lab-based x-ray micro-sources in combination with the development of new metrology methods, particularly ptychographic x-ray speckle tracking, enable characterization of x-ray optics in the lab with a precision and sensitivity not possible before. Here, we present a laboratory setup that utilizes a commercially available x-ray source and can be used to characterize different types of x-ray optics. The setup is used in our laboratory on a routine basis to characterize multilayer Laue lenses of high numerical aperture and other optical elements. This typically includes measurements of the wavefront distortions, optimum operating photon energy, and focal length of the lens. To check the sensitivity and accuracy of this laboratory setup, we compared the results to those obtained at the synchrotron and saw no significant difference. To illustrate the feedback of measurements on performance, we demonstrated the correction of the phase errors of a particular multilayer Laue lens using a 3D printed compound refractive phase plate.

Rapid non-mechanical reciprocal space mapping using LiNbO3-based bimorph piezoactuator

A new approach is proposed for fast recording Reciprocal Space Maps (RSM) of crystals without using mechanical systems. It is based on the simultaneous use of two Adaptive Bending X-ray Optics (ABXO) elements made of lithium niobate crystals located on a laboratory X-ray diffractometer at the positions of the monochromator and analyzer. The technique has been tested on a model silicon crystal. It was shown that the proposed technique allows fast and precision measurements of the RSM, providing significant progress both in speed (up to 30 times) and accuracy of the data (up to 3 times) obtained. It opens up opportunities for studying the evolution of the defective structure of various prospective crystalline materials under external loading.

X-ray wavefront sensing and optics metrology using a microfocus x-ray grating interferometer with electromagnetic phase stepping

A metrology method of x-ray optical elements based on an electromagnetic phase stepping x-ray grating interferometer with high slope accuracy is presented in this study. The device consists of an x-ray tube, a phase grating G1 for modulating the incoming wavefront, and an absorption grating G2 as a transmission mask to produce a broader moiré pattern for the x-ray camera. The focal spot of the microfocus x-ray source is shifted by a magnetic field from a solenoid coil. Electromagnetic phase stepping analysis is used to obtain a pixel-wise map of the wavefront phase distortion to replace the traditional precision mechanical scanning system, improving stability, speed, accuracy, and flexibility. The x-ray grating interferometer can be used as a feedback tool for evaluating the quality of optical elements and detecting defects caused by the x-ray beam or the x-ray optical elements in ordinary laboratories and mirror-processing centers without the need of scheduling synchrotron beam time.

Using diffraction losses of X-rays in a single crystal for determination of its lattice parameters as well as for monochromator calibration.

A way has been developed to measure the unit-cell parameters of a single crystal just from an energy scan with X-rays, even when the exact energy of the X-rays is not well defined due to an error in the pitch angle of the monochromator. The precision of this measurement reaches da/a ∼ 1 × 10-5. The method is based on the analysis of diffraction losses of the beam, transmitted through a single crystal (the so-called `glitch effect'). This method can be easily applied to any transmissive X-ray optical element made of single crystals (for example, X-ray lenses). The only requirements are the possibility to change the energy of the generated X-ray beam and some intensity monitor to measure the transmitted intensity. The method is agnostic to the error in the monochromator tuning and it can even be used for determination of the absolute pitch (or 2θ) angle of the monochromator. Applying the same method to a crystal with well known lattice parameters allows determination of the exact cell parameters of the monochromator at any energy.

Improved Micro-X-ray Fluorescence Confocal Imaging of Two-Dimensional Distribution of Arsenic Concentration in Cucumber Hypocotyls Using Synchrotron Radiation.

An optimized micro-X-ray fluorescence confocal imaging (μXRF-CI) analytical method has been developed to determine the 2D distribution of elemental composition in small (1–3 mm) biological objects at a 10–20 μm spatial resolution. Plants take up chemical elements from soil, and the vascular system transports them toward shoots. In order to obtain biochemical information related to this biological process, 2D distributions of chemical elements in roots and in hypocotyls of cucumber plants were analyzed by synchrotron radiation based on micro-X-ray fluorescence computer tomography and μXRF-CI techniques. The experiments were carried out at HASYLAB Beamline L of the DORIS-III storage ring in Hamburg, a facility that provided optimal physical conditions for developing and performing these unique analyses: high flux monochromatic synchrotron beam, X-ray optical elements, precision moving stages, and silicon drift detectors. New methodological improvements and experimental studies were carried out for applicability of lyophilized samples and cryo-cooling. Experimental parameters were optimized to maximize the excitation yield of arsenic Kα radiation and improvement of the spatial resolution of the μXRF-CI analytical method.

Studies of the functional characteristics of adaptive X-ray optical elements based on combination of longitudinal and transverse acoustic waves in wide frequency ranges

Studies of the functional characteristics of adaptive X-ray optical elements based on combination of longitudinal and transverse acoustic waves in wide frequency ranges

Properties of polycapillary optics dedicated to low-energy parallel-beam wavelength-dispersive spectrometers for synchrotron-based X-ray fluorescence study.

The main advantage of wavelength-dispersive spectrometers applied in X-ray study is their high energy resolution. The design and construction of spectrometer, usually dedicated to the specific experimental systems, for example synchrotron based setups, need information about the characteristics of the main elements of the spectrometer such as X-ray optics elements, crystals and detectors. Such information can be obtained using Monte-Carlo simulations. In this paper, the Monte-Carlo simulations of X-ray tracing in parallel-beam wavelength-dispersive spectrometer (PBWDS), equipped with polycapillary optics, are presented and discussed. The study concentrates on the description of the polycapillary model, simulations of the properties of X-ray polycapillary optics and, finally, on the simulations of X-ray track in the spectrometer designed and installed at the ID21 beamline at the European Synchrotron Radiation Facility (ESRF, Grenoble, France). The results of simulations were compared with experimental data obtained for different registered X-ray energies and spectrometer crystals, showing good agreement. The obtained results showed that the X-ray transmission in the tested polycapillary optics is at the level of 15%, while the divergence of the outgoing beam changes from 8 mrad to 3 mrad with an increase of photon energy from 2 keV to 10 keV. The spectrometer provides an energy resolution of 5 eV and 33 eV in the energy range of 1.4 keV - 6.5 keV. The developed simulation program can be successfully used for the construction of spectrometers dedicated to the different experimental conditions.

Optics metrology and at-wavelength wavefront characterization by a microfocus X-ray grating interferometer

A microfocus X-ray grating interferometer (MFXGI) is proposed to measure the profile of the X-ray wavefront and slope error of X-ray optical elements. This device consists of a phase grating G1 to modulate the incoming wavefront and an absorption grating G2 as a transmission mask for the position-sensitive detector. The wavefront distortions caused by the deformable mirror were analyzed under operating conditions for in situ investigation of X-ray optical elements. The MFXGI can obtain direct and reflected beams in one recorded image at the same time through a microfocus X-ray source. The direct beam can be used to calculate the parameter errors and spherical shape for error compensation and retrieve the aspherical shape of the height profile. This instrument is expected to be a valuable tool for further technical progress in X-ray adaptive optics and X-ray mirror manufacturing and mounting.

Miniature source of accelerated ions with focusing ion-optical system

The paper describes a small-sized accelerated ion source developed on the basis of the KLAN-10M technological source. Record values of the ion current density (j ≈ 95 mA/cm2) were obtained, which made it possible to use this source for problems of deep correction of the shape of X-ray optical elements. Formation of small beam (FWHM ∼ 1.5 mm) with a Gaussian distribution of the ion current along the output aperture without cut-off diaphragms is the main feature of this source. A focusing ion-optical system makes it possible to change the beam size depending on the distance and the value of the accelerating voltage. Thus, this source allows deep final correction of the shape errors of the surfaces of optical elements and bringing it to subnanometer accuracy in terms of the RMS parameter in the range of spatial frequencies up to 1.3∗10−3μm−1 for the case of conductive and up to 9.5∗10−4μm−1 for the case of dielectric materials. The special design of the neutralizing unit allows to fully compensate for the positive ion flux, avoiding heating the sample to 50 degrees Celsius at a distance of 10 mm from the source, which is a necessary condition in a number of tasks. The influence of the thermal cathode-neutralizer on the ion density distribution of the beam is shown and explained.

Optical design and optimization study of metrology sector at high energy photon source

X-ray metrology, including the metrological calibration of X-ray detectors, optical elements and sources, is important for many frontier science, such as X-ray astronomy, EUV-lithography, plasma physics. Among many types of X-ray sources, synchrotron-radiation is considered perfect for X-ray metrology, mainly due to that arbitrarily X-rays specifications can be tailored to meet the demands of metrological calibration of X-ray detectors and optical elements. As a consequence, many metrology beamlines around the world are built, upgrading or to be constructed, including the metrology sector to be constructed at High Energy Photon Source (HEPS). One reasonable way to access good metrological data is using a stable X-ray beam, which means that beam position as well as flux should be as constant as possible and the beamline configuration should be simple and robust to reduce the uncertainty from beamline itself. In addition, the spectral purity of monochromatic X-rays is another crucial factor for X-ray metrology, which means stray X-rays and harmonic X-rays must be as low as possible. Many measures are taken to satisfy these requirements. An optical design of the metrology sector optimized for synchrotron-radiation-based- metrology is described here. The metrology sector, ranging from 50 eV to 20 keV, will be set up to meet the growing needs of X-ray metrology in China. All beamlines’ configurations are simple and easy to use, with an acceptable ratio of high-order harmonics and stray X-rays, which can be under 1% in the entire energy range.

Finite-element simulation for X-ray volume diffractive optics based on the wave optical theory.

We developed a novel numerical simulation method for volume diffractive optics based on the Takagi-Taupin (TT) dynamical theory of diffraction. A general integral system of equations with a powerful and convenient distortion function was developed for finite-element analysis (FEA). The proposed framework is promising with regard to flexibility, robustness, and stability and has potential for solving dynamical X-ray diffraction problems related to diffractive optical elements of arbitrary shape and deformation. This FEA method was used for evaluating laterally graded multilayer (LGML) mirrors, and a general coordinate system was introduced to make the geometric optimization simple and effective. Moreover, the easily implemented boundary conditions inherent in FEA, combined with the analysis of the energy resolution derived from the TT theory, can make the simulation of volume diffractive optics, including LGML mirrors, more accurate. Thus, a comprehensive and highly efficient computation of LGML mirror diffraction problems was performed. The evaluation of the effects of the figure errors can provide practical guidance for the fabrication of X-ray optical elements.

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.

Speckle-tracking: a software suite for ptychographic X-ray speckle tracking.

In recent years, X-ray speckle-tracking techniques have emerged as viable tools for wavefront metrology and sample imaging applications. These methods are based on the measurement of near-field images. Thanks to their simple experimental setup, high angular sensitivity and compatibility with low-coherence sources, these methods have been actively developed for use with synchrotron and laboratory light sources. Not only do speckle-tracking techniques give the potential for high-resolution imaging, but they also provide rapid and robust characterization of aberrations of X-ray optical elements, focal spot profiles, and sample position and transmission properties. In order to realize these capabilities, software implementations are required that are equally rapid and robust. To address this need, a software suite has been developed for the ptychographic X-ray speckle-tracking technique, an X-ray speckle-based method suitable for highly divergent wavefields. The software suite is written in Python 3, with an OpenCL back end for GPU and multi-CPU core processing. It is accessible as a Python module, through the command line or through a graphical user interface, and is available as source code under Version 3 or later of the GNU General Public License.

Multifocus off-axis zone plates for x-ray free-electron laser experiments

X-ray free-electron lasers (XFELs) are paving the way towards new experiments in many scientific fields, such as ultrafast science, nonlinear spectroscopy, and coherent imaging. However, the strong intensity fluctuations inherent to the lasing process in these sources often lead to problems in signal normalization. In order to address this challenge, we designed, fabricated, and characterized diffractive x-ray optics that combine the focusing properties of a Fresnel zone plate with the beam-splitting capability of a grating in a single diffractive optical element. The possibility to split the incident beam into identical copies allows for direct shot-to-shot normalization of the sample signal, thereby greatly enhancing the signal-to-noise ratio in experiments with XFEL radiation. Here we propose two schemes for the design of such diffractive x-ray optical elements for splitting and focusing an incoming beam into up to three foci by merging a grating with a focusing zone plate. By varying the duty cycle of the grating or the relative shift of the Fresnel zone plate structure, we are able to tune the relative intensities of the different diffraction orders to achieve the desired splitting ratios. Experimental confirmation of the design is provided with soft x-ray light (540 eV) and shows a good agreement with calculations, confirming the suitability of this approach for XFEL experiments.