Controlling cantilevered adaptive X-ray mirrors.

Modeling the behavior of a prototype cantilevered X-ray adaptive mirror (held from one end) demonstrates its potential for use on high-performance X-ray beamlines. Similar adaptive mirrors are used on X-ray beamlines to compensate optical aberrations, control wavefronts and tune mirror focal distances at will. Controlled by 1D arrays of piezoceramic actuators, these glancing-incidence mirrors can provide nanometre-scale surface shape adjustment capabilities. However, significant engineering challenges remain for mounting them with low distortion and low environmental sensitivity. Finite-element analysis is used to predict the micron-scale full actuation surface shape from each channel and then linear modeling is applied to investigate the mirrors' ability to reach target profiles. Using either uniform or arbitrary spatial weighting, actuator voltages are optimized using a Moore-Penrose matrix inverse, or pseudoinverse, revealing a spatial dependence on the shape fitting with increasing fidelity farther from the mount.

Characterization of silicon pore optics for the NewAthena X-ray observatory in the PTB laboratory at BESSY II.

The New Advanced Telescope for High ENergy Astrophysics (NewAthena) will be the largest space-based X-ray observatory ever built. It will have an effective area above 1.1 m2 at 1 keV, which corresponds to a polished mirror surface of about 300 m2 due to the grazing incidence. As such a mirror area is not achievable with an acceptable mass even with nested shells, silicon pore optics (SPO) technology will be utilized. In the PTB laboratory at BESSY II, two dedicated beamlines are in use for their characterization with monochromatic radiation at 1 keV and a low divergence well below 2 arcsec: the X-ray Pencil Beam Facility (XPBF 1) and the X-ray Parallel Beam Facility (XPBF 2.0), where beam sizes up to 8 mm × 8 mm are available while maintaining low beam divergence. This beamline is used for characterizing mirror stacks and controlling the focusing properties of mirror modules (MMs) - consisting of four mirror stacks - during their assembly at the beamline. A movable CCD based camera system 12 m from the MM registers the direct and the reflected beams. The positioning of the detector is verified by a laser tracker. The energy-dependent reflectance in double reflection through the pores of an MM with an Ir coating was measured at the PTB four-crystal monochromator beamline in the photon energy range 1.75 keV to 10 keV, revealing the effects of the Ir M edges. The measured reflectance properties are in agreement with the design values to achieve the envisaged effective area.

Ion beam figuring for X-ray mirrors: history, state-of-the-art and future prospects.

Synchrotron light sources require X-ray optics with extremely demanding accuracy for the surface profile, with less than 100 nrad slope errors and sub-nanometre height errors. Such errors are challenging to achieve for aspheres using traditional polishing methods. However, post-polishing error correction can be performed using techniques such as ion beam figuring (IBF) to improve optics to the desired quality. This work presents a brief overview of the history of IBF, introduces some of the challenges for obtaining such demanding figure errors, and highlights the work done at several in-house IBF facilities at synchrotron light sources worldwide to obtain state-of-the-art optical quality.

Soft X-ray wavefront sensing at an ellipsoidal mirror shell.

A reliable `in situ' method for wavefront sensing in the soft X-ray domain is reported, developed for the characterization of rotationally symmetric optical elements, like an ellipsoidal mirror shell. In a laboratory setup, the mirror sample is irradiated by an electron-excited (4.4 keV), micrometre-sized (∼2 µm) fluorescence source (carbon Kα, 277 eV). Substantially, the three-dimensional intensity distribution I(r) is recorded by a CCD camera (2048 × 512 pixels of 13.5 µm) at two positions along the optical axis, symmetrically displaced by ±21-25% from the focus. The transport-of-intensity equation is interpreted in a geometrical sense from plane to plane and implemented as a ray tracing code, to retrieve the phase Φ(r) from the radial intensity gradient on a sub-pixel scale. For reasons of statistical reliability, five intra-/extra-focal CCD image pairs are evaluated and averaged to an annular two-dimensional map of the wavefront error {\cal W}. In units of the test wavelength (C Kα), an r.m.s. value \sigma_{\cal{W}} = ±10.9λ0 and a peak-to-valley amplitude of ±31.3λ0 are obtained. By means of the wavefront, the focus is first reconstructed with a result for its diameter of 38.4 µm, close to the direct experimental observation of 39.4 µm (FWHM). Secondly, figure and slope errors of the ellipsoid are characterized with an average of ±1.14 µm and ±8.8 arcsec (r.m.s.), respectively, the latter in reasonable agreement with the measured focal intensity distribution. The findings enable, amongst others, the precise alignment of axisymmetric X-ray mirrors or the design of a wavefront corrector for high-resolution X-ray science.

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.

The diamond-silicon carbide composite Skeleton® as a promising material for substrates of intense X-ray beam optics.

The paper considers the possibility of using the diamond-silicon carbide composite Skeleton® with a technological coating of polycrystalline silicon as a substrate for X-ray mirrors used with powerful synchrotron radiation sources (third+ and fourth generation). Samples were studied after polishing to provide the following surface parameters: root-mean-square flatness ≃ 50 nm, micro-roughness on the frame 2 µm × 2 µm σ ≃ 0.15 nm. The heat capacity, thermal conductivity and coefficient of linear thermal expansion were investigated. For comparison, a monocrystalline silicon sample was studied under the same conditions using the same methods. The value of the coefficient of linear thermal expansion turned out to be higher than that of monocrystalline silicon and amounted to 4.3 × 10-6 K-1, and the values of thermal conductivity (5.0 W cm-1 K-1) and heat capacity (1.2 J K-1 g-1) also exceeded the values for Si. Thermally induced deformations of both Skeleton® and monocrystalline silicon samples under irradiation with a CO2 laser beam have also been experimentally studied. Taking into account the obtained thermophysical constants, the calculation of thermally induced deformation under irradiation with hard (20 keV) X-rays showed almost three times less deformation of the Skeleton® sample than of the monocrystalline silicon sample.

Spexwavepy: an open-source Python package for X-ray wavefront sensing using speckle-based techniques.

In situ wavefront sensing plays a critical role in the delivery of high-quality beams for X-ray experiments. X-ray speckle-based techniques stand out among other in situ techniques for their easy experimental setup and various data acquisition modes. Although X-ray speckle-based techniques have been under development for more than a decade, there are still no user-friendly software packages for new researchers to begin with. Here, we present an open-source Python package, spexwavepy, for X-ray wavefront sensing using speckle-based techniques. This Python package covers a variety of X-ray speckle-based techniques, provides plenty of examples with real experimental data and offers detailed online documentation for users. We hope it can help new researchers learn and apply the speckle-based techniques for X-ray wavefront sensing to synchrotron radiation and X-ray free-electron laser beamlines.

Sub-nanometre quality X-ray mirrors created using ion beam figuring.

Ion beam figuring (IBF) is a powerful technique for figure correction of X-ray mirrors to a high accuracy. Here, recent technical advancements in the IBF instrument developed at Diamond Light Source are presented and experimental results for figuring of X-ray mirrors are given. The IBF system is equipped with a stable DC gridded ion source (120 mm diameter), a four-axis motion stage to manipulate the optic, a Faraday cup to monitor the ion-beam current, and a camera for alignment. A novel laser speckle angular measurement instrument also provides on-board metrology. To demonstrate the IBF system's capabilities, two silicon X-ray mirrors were processed. For 1D correction, a height error of 0.08 nm r.m.s. and a slope error of 44 nrad r.m.s. were achieved. For 2D correction over a 67 mm × 17 mm clear aperture, a height error of 0.8 nm r.m.s. and a slope error of 230 nrad r.m.s. were obtained. For the 1D case, this optical quality is comparable with the highest-grade, commercially available, X-ray optics.

X-ray optics for the cavity-based X-ray free-electron laser.

A cavity-based X-ray free-electron laser (CBXFEL) is a possible future direction in the development of fully coherent X-ray sources. CBXFELs consist of a low-emittance electron source, a magnet system with several undulators and chicanes, and an X-ray cavity. The X-ray cavity stores and circulates X-ray pulses for repeated FEL interactions with electron pulses until the FEL reaches saturation. CBXFEL cavities require low-loss wavefront-preserving optical components: near-100%-reflectivity X-ray diamond Bragg-reflecting crystals, outcoupling devices such as thin diamond membranes or X-ray gratings, and aberration-free focusing elements. In the framework of the collaborative CBXFEL research and development project of Argonne National Laboratory, SLAC National Accelerator Laboratory and SPring-8, we report here the design, manufacturing and characterization of X-ray optical components for the CBXFEL cavity, which include high-reflectivity diamond crystal mirrors, a diamond drumhead crystal with thin membranes, beryllium refractive lenses and channel-cut Si monochromators. All the designed optical components have been fully characterized at the Advanced Photon Source to demonstrate their suitability for the CBXFEL cavity application.

The mechanism of moire artifacts in single-grating imaging systems and image quality optimization.

In the X-ray single-grating imaging system, the acquisition of frequency information is the key step of phase-contrast and scattering information recovery. In the process of information extraction, it is easy to lead to the degradation of imaging quality due to the Moire Artifact, thus limiting the development and application of X-ray single-grating imaging system. In order to address the above problems, in this article, based on the theoretical analysis of the generation principle of Moire Artifact in imaging system, the advantages and disadvantages of grating rotation method are analyzed, and a method of suppressing Moire artifacts by adjusting grating projection frequency is proposed. The experimental results show that the method proposed here can suppress the Moire noise in the background noise, resulting in a reduction of more than 50% in the standard deviation of the background noise. High quality phase-contrast and scattering images are obtained experimentally, which is of great value to the development of X-ray single-grating imaging technology.