Performance of a collimating L‐shaped laterally graded multilayer mirror for the IXS analyzer system at NSLS‐II

The L‐shaped laterally graded multilayer mirror is a vital part of the ultrahigh‐energy and momentum‐resolution inelastic X‐ray scattering spectrometer at the National Synchrotron Light Source II. This mirror was designed and implemented as a two‐dimensional collimating optic for the analyzer system. Its performance was characterized using a secondary large‐divergence source at the 30‐ID beamline of the Advanced Photon Source, which yielded an integrated reflectivity of 47% and a collimated beam divergence of 78 µrad with a source size of 10 µm. Numerical simulations of the mirror performance in tandem with the analyzer crystal optics provided details on the acceptance sample volume in forward scattering and defined the technical requirements on the mirror stability and positioning precision. It was shown that the mirror spatial and angular stability must be in the range <8.4 µm and <21.4 µrad, respectively, for reliable operation of the analyzer.     

Synchrotron X‐ray tests of an L‐shaped laterally graded multilayer mirror for the analyzer system of the ultra‐high‐resolution IXS spectrometer at NSLS‐II

Characterization and testing of an L‐shaped laterally graded multilayer mirror are presented. This mirror is designed as a two‐dimensional collimating optics for the analyzer system of the ultra‐high‐resolution inelastic X‐ray scattering (IXS) spectrometer at National Synchrotron Light Source II (NSLS‐II). The characterization includes point‐to‐point reflectivity measurements, lattice parameter determination and mirror metrology (figure, slope error and roughness). The synchrotron X‐ray test of the mirror was carried out reversely as a focusing device. The results show that the L‐shaped laterally graded multilayer mirror is suitable to be used, with high efficiency, for the analyzer system of the IXS spectrometer at NSLS‐II.     

Collimating Montel mirror as part of a multi‐crystal analyzer system for resonant inelastic X‐ray scattering

Advances in resonant inelastic X‐ray scattering (RIXS) have come in lockstep with improvements in energy resolution. Currently, the best energy resolution at the Ir L₃‐edge stands at ～25 meV, which is achieved using a diced Si(844) spherical crystal analyzer. However, spherical analyzers are limited by their intrinsic reflection width. A novel analyzer system using multiple flat crystals provides a promising way to overcome this limitation. For the present design, an energy resolution at or below 10 meV was selected. Recognizing that the angular acceptance of flat crystals is severely limited, a collimating element is essential to achieve the necessary solid‐angle acceptance. For this purpose, a laterally graded, parabolic, multilayer Montel mirror was designed for use at the Ir L₃‐absorption edge. It provides an acceptance larger than 10 mrad, collimating the reflected X‐ray beam to smaller than 100 µrad, in both vertical and horizontal directions. The performance of this mirror was studied at beamline 27‐ID at the Advanced Photon Source. X‐rays from a diamond (111) monochromator illuminated a scattering source of diameter 5 µm, generating an incident beam on the mirror with a well determined divergence of 40 mrad. A flat Si(111) crystal after the mirror served as the divergence analyzer. From X‐ray measurements, ray‐tracing simulations and optical metrology results, it was established that the Montel mirror satisfied the specifications of angular acceptance and collimation quality necessary for a high‐resolution RIXS multi‐crystal analyzer system.     

GROIN: a fast optical adjustment of a Kirkpatrick–Baez set‐up

A very simple and compact optical device aimed at the fast adjustment, alignment and bending of the mirrors of a Kirpatrick–Baez system used in the X‐ray domain is described.     

磁控溅射制备横向梯度分布的Mo/Si周期多层膜

采用磁控溅射方法在Si基板上镀制了横向梯度分布的Mo/Si周期多层膜。以X射线掠入射反射测量了横向梯度多层膜的膜系结构,在基板65 mm长度范围内,多层膜周期从8.21 nm线性减小到6.57 nm,周期梯度为0.03 nm/mm。国家同步辐射实验室反射率计的反射率测试结果表明：该横向梯度分布周期多层膜上不同位置,能反射在13.3~15.9 nm波段范围内不同波长的极紫外光,反射率为60%~65%。     

Phase‐space analysis and experimental results for secondary focusing at X‐ray beamlines

Micro‐focusing optical devices at synchrotron beamlines usually have a limited acceptance, but more flux can be intercepted if such optics are used to focus secondary sources created by the primary optics. Flux throughput can be maximized by placing the secondary focusing optics close to or exactly at the secondary source position. However, standard methods of beamline optics analysis, such as the lens equation or matching the mirror surface to an ellipse, work poorly when the source‐to‐optics distance is very short. In this paper the general characteristics of the focusing of beams with Gaussian profiles by a `thin lens' are analysed under the paraxial approximation in phase space, concluding that the focusing of a beam with a short source‐to‐optics distance is distinct from imaging the source; slope errors are successfully included in all the formulas so that they can be used to calculate beamline focusing with good accuracy. A method is also introduced to use the thin‐lens result to analyse the micro‐focusing produced by an elliptically bent trapezoid‐shaped Kirkpatrick–Baez mirror. The results of this analysis are in good agreement with ray‐tracing simulations and are confirmed by the experimental results of the secondary focusing at the 18‐ID Bio‐CAT beamline (at the APS). The result of secondary focusing carried out at 18‐ID using a single‐bounce capillary can also be explained using this phase‐space analysis. A discussion of the secondary focusing results is presented at the end of this paper.     

磁控溅射制备横向梯度分布的Mo/Si周期多层膜

 采用磁控溅射方法在Si基板上镀制了横向梯度分布的Mo/Si周期多层膜。以X射线掠入射反射测量了横向梯度多层膜的膜系结构,在基板65 mm长度范围内,多层膜周期从8.21 nm线性减小到6.57 nm,周期梯度为0.03 nm/mm。国家同步辐射实验室反射率计的反射率测试结果表明：该横向梯度分布周期多层膜上不同位置,能反射在13.3~15.9 nm波段范围内不同波长的极紫外光,反射率为60%~65%。     

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.     

Characterization of an X‐ray mirror mechanical bender for the European XFEL

One of the classical devices used to tune a mirror on an X‐ray optical setup is a mechanical bender. This is often designed in such a way that the mirror is held with clamps on both ends; a motor is then used to put a torque on the clamps, inducing a cylindrical shape of the mirror surface. A mechanical bender with this design was recently characterized, to bend a 950 mm‐long mirror up to a radius of curvature of 10 km. The characterization was performed using a large‐aperture Fizeau interferometer with an angled incidence setup. Some particular and critical effects were investigated, such as calibration, hysteresis, twisting and long‐term stability.     

A sagittally focusing double‐multilayer monochromator for ultrafast X‐ray imaging applications

The development of a sagittally focusing double‐multilayer monochromator is reported, which produces a spatially extended wide‐bandpass X‐ray beam from an intense synchrotron bending‐magnet source at the Advanced Photon Source, for ultrafast X‐ray radiography and tomography applications. This monochromator consists of two W/B₄C multilayers with a 25 Å period coated on Si single‐crystal substrates. The second multilayer is mounted on a sagittally focusing bender, which can dynamically change the bending radius of the multilayer in order to condense and focus the beam to various points along the beamline. With this new apparatus, it becomes possible to adjust the X‐ray beam size to best match the area detector size and the object size to facilitate more efficient data collection using ultrafast X‐ray radiography and tomography.     

Investigation of multilayer X‐ray optics for the 6 keV to 20 keV energy range

The X‐ray optics group at the Swiss Light Source in co‐operation with RIT (Rigaku Innovative Technologies) have investigated seven different multilayer samples. The goal was to find an ideal multilayer structure for the energy range between 6 keV and 20 keV in terms of energy resolution and reflectivity. Such multilayer structures deposited on substrates can be used as X‐ray monochromators or reflecting synchrotron mirrors. The measured reflectivities agree with the simulated ones. They cover a reflectivity range from 45% to 80% for energies between 6 keV and 10 keV, and 80% to 90% for energies between 10 keV and 20 keV. The experimentally measured energy resolution of the samples lies between 0.3% and 3.5%.     

The inverse problem of bimorph mirror tuning on a beamline

One of the challenges of tuning bimorph mirrors with many electrodes is that the calculated focusing voltages can be different by more than the safety limit (such as 500 V for the mirrors used at 17‐ID at the Advanced Photon Source) between adjacent electrodes. A study of this problem at 17‐ID revealed that the inverse problem of the tuning in situ, using X‐rays, became ill‐conditioned when the number of electrodes was large and the calculated focusing voltages were contaminated with measurement errors. Increasing the number of beamlets during the tuning could reduce the matrix condition number in the problem, but obtaining voltages with variation below the safety limit was still not always guaranteed and multiple iterations of tuning were often required. Applying Tikhonov regularization and using the L‐curve criterion for the determination of the regularization parameter made it straightforward to obtain focusing voltages with well behaved variations. Some characteristics of the tuning results obtained using Tikhonov regularization are given in this paper.     

Microfocusing options for the inelastic X‐ray scattering beamline at sector 3 of the Advanced Photon Source

Synchrotron radiation from third‐generation high‐brilliance storage rings is an ideal source for X‐ray microbeams. The aim of this paper is to describe a microfocusing scheme that combines both a toroidal mirror and Kirkpatrick–Baez (KB) mirrors for upgrading the existing optical system for inelastic X‐ray scattering experiments at sector 3 of the Advanced Photon Source. SHADOW ray‐tracing simulations without considering slope errors of both the toroidal mirror and KB mirrors show that this combination can provide a beam size of 4.5 µm (H) × 0.6 µm (V) (FWHM) at the end of the existing D‐station (66 m from the source) with use of full beam transmission of up to 59%, and a beam size of 3.7 µm (H) × 0.46 µm (V) (FWHM) at the front‐end of the proposed E‐station (68 m from the source) with a transmission of up to 52%. A beam size of about 5 µm (H) × 1 µm (V) can be obtained, which is close to the ideal case, by using high‐quality mirrors (with slope errors of less than 0.5 µrad r.m.s.). Considering the slope errors of the existing toroidal and KB mirrors (5 and 2.9 µrad r.m.s., respectively), the beam size grows to about 13.5 µm (H) × 6.3 µm (V) at the end of the D‐station and to 12.0 µm (H) × 6.0 µm (V) at the front‐end of the proposed E‐station. The simulations presented here are compared with the experimental measurements that are significantly larger than the theoretical values even when slope error is included in the simulations. This is because of the experimental set‐up that could not yet be optimized.     

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.     

Concept of a spectrometer for resonant inelastic X‐ray scattering with parallel detection in incoming and outgoing photon energies

A spectrometer for resonant inelastic X‐ray scattering (RIXS) is proposed where imaging and dispersion actions in two orthogonal planes are combined to deliver a full two‐dimensional map of RIXS intensity in one shot with parallel detection at incoming hv_in and outgoing hv_out photon energies. Preliminary ray‐tracing simulations with a typical undulator beamline demonstrate a resolving power well above 11000 with both hv_in and hv_out near 930 eV, with a vast potential for improvement. Combining this instrument – nicknamed hv² spectrometer – with an X‐ray free‐electron laser source simplifies its technical implementation and enables efficient time‐resolved RIXS experiments.     

Point focusing with flat and wedged crossed multilayer Laue lenses

Point focusing measurements using pairs of directly bonded crossed multilayer Laue lenses (MLLs) are reported. Several flat and wedged MLLs have been fabricated out of a single deposition and assembled to realise point focusing devices. The wedged lenses have been manufactured by adding a stress layer onto flat lenses. Subsequent bending of the structure changes the relative orientation of the layer interfaces towards the stress‐wedged geometry. The characterization at ESRF beamline ID13 at a photon energy of 10.5 keV demonstrated a nearly diffraction‐limited focusing to a clean spot of 43 nm × 44 nm without significant side lobes with two wedged crossed MLLs using an illuminated aperture of approximately 17 µm × 17 µm to eliminate aberrations originating from layer placement errors in the full 52.7 µm × 52.7 µm aperture. These MLLs have an average individual diffraction efficiency of 44.5%. Scanning transmission X‐ray microscopy measurements with convenient working distances were performed to demonstrate that the lenses are suitable for user experiments. Also discussed are the diffraction and focusing properties of crossed flat lenses made from the same deposition, which have been used as a reference. Here a focal spot size of 28 nm × 33 nm was achieved and significant side lobes were noticed at an illuminated aperture of approximately 23 µm × 23 µm.     

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.     

Efficiency and coherence preservation studies of Be refractive lenses for XFELO application

Performance tests of parabolic beryllium refractive lenses, considered as X‐ray focusing elements in the future X‐ray free‐electron laser oscillator (XFELO), are reported. Single and double refractive lenses were subject to X‐ray tests, which included: surface profile, transmissivity measurements, imaging capabilities and wavefront distortion with grating interferometry. Optical metrology revealed that surface profiles were close to the design specification in terms of the figure and roughness. The transmissivity of the lenses is >94% at 8 keV and >98% at 14.4 and 18 keV. These values are close to the theoretical values of ideal lenses. Images of the bending‐magnet source obtained with the lenses were close to the expected ones and did not show any significant distortion. Grating interferometry revealed that the possible wavefront distortions produced by surface and bulk lens imperfections were on the level of ～λ/60 for 8 keV photons. Thus the Be lenses can be succesfully used as focusing and beam collimating elements in the XFELO.     

Finite‐element modelling of multilayer X‐ray optics

Multilayer optical elements for hard X‐rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite‐element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X‐ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100–300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10⁷) can lead to a huge number of elements for the finite‐element model. For instance, meshing by the size of the layers will require more than 10¹⁶ elements, which is an impossible task for present‐day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10⁶), which causes low solution accuracy; and the number of elements is still very large (10⁶). In this work, by use of ANSYS layer‐functioned elements, a thermal‐structural FEA model has been implemented for multilayer X‐ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.