Increased spatial coherence length from an asymmetric crystal reflection at grazing exit.

Coherent X-ray imaging is an active field at synchrotron sources. The images rely on the available coherent flux over a limited field of view. At many synchrotron beamlines a double-crystal monochromator (DCM) is employed in a standard nondispersive arrangement. For coherent diffraction imaging it is advantageous to increase the available field of view by increasing the spatial coherence length (SCL) of a beam exiting such a DCM. Here, Talbot interferometry data together with ray-tracing simulations for a (+ - - +) four-reflection experimental arrangement are presented, wherein the first two reflections are in the DCM and the final fourth reflection is asymmetric at grazing exit. Analyses of the interferometry data combined with the simulations show that compared with the beam exiting the DCM a gain of 76% in the SCL was achieved, albeit with a factor of 20 reduction in flux density, which may not be a severe penalty at a synchrotron beamline. Previous efforts reported in the literature to increase the SCL that employed asymmetric crystal diffraction at grazing incidence are also discussed. A much reduced SCL is found presently in simulations wherein the same asymmetric crystal is set for grazing incidence instead of grazing exit. In addition, the present study is compared and contrasted with two other means of increasing the SCL. These are (i) focusing the beam onto an aperture to act as a secondary source, and (ii) allowing the beam to propagate in vacuum an additional distance along the beamline.

Diffuse X-ray scattering from polished silicon: application of the distorted wave Born approximation.

Measured diffuse X-ray scattering data for a `smooth' as well as for a `rough' silicon sample were fit to theoretical expressions within the distorted wave Born approximation (DWBA). Data for the power spectral density (PSD) for both samples were also obtained by means of atomic force microscopy and optical interferometry. The Fourier transforms of trial correlation functions were fit to the PSD data and then applied to the DWBA formalism. The net correlation functions needed to fit the PSD data for each sample comprised the sum of two terms with different cutoff lengths and different self-affine fractal exponents. At zero distance these correlation functions added up to yield net values of σ2 = (2)2 and (71)2 Å2 for the smooth and rough samples, respectively. X-ray scattering data were obtained at beamline 1-BM of the Advanced Photon Source. Data and fits at values of qz = 0.05 and 0.10 Å-1 for the smooth sample are reported. Good fits for the smooth sample were obtained at both qz values simultaneously, that is, identical fitting parameters were applied at both values of qz. The smooth sample also exhibited weak Yoneda wings and a clear distinction between the strong specular scattering and the weak diffuse scattering. Data for the rough sample were qualitatively different and exhibited very weak scattering at the specular condition in contrast to extremely large Yoneda wings. Fits for the rough sample are reported for qz = 0.04, 0.05, and 0.06 Å-1. Although the large Yoneda wings could be fit quite well in both position and amplitude, scattering near the specular condition could not be equally well fit by applying the same fitting parameters at all values of qz. Albeit imperfect, best-fitting results at the specular condition were obtained by invoking only diffuse scattering, that is, without including a separate theoretical expression for specular scattering.

Takagi-Taupin dynamical X-ray diffraction simulations of asymmetric X-ray diffraction from crystals: the effects of surface undulations.

Dynamical X-ray diffraction simulations from crystals with surface undulations are reported. The Takagi-Taupin equations are applied and used to derive results in good agreement with experimental data reported in a separate paper [Macrander, Pereira, Huang, Kasman, Qian, Wojcik & Assoufid (2020). J. Appl. Cryst. 53, 789-792]. The development of Uragami [J. Phys. Soc. Jpn, (1969), 27, 147-154] is followed. Although previous work by Olekhnovich & Olekhnovich [Acta. Cryst. (1980), A36, 22-27] treated a crystal in the shape of a round cylinder, there do not seem to be any reports of previous dynamical X-ray diffraction treatments specifically for surface undulations. The significance of the present work is that it bridges the diffraction treatment of more classical dynamical diffraction theory, which assumes a flat surface, and the simple kinematic diffraction theory. The kinematic theory has, to date, been the primary means of simulating X-ray diffraction from surfaces.

Effects of surface undulations on asymmetric X-ray diffraction: a rocking-curve topography study.

The results are reported of an X-ray diffraction study of an Si crystal designed and fabricated for very asymmetric diffraction from the 333 reflection for X-ray energies of 8.100 and 8.200 keV. A crystal with an asymmetry angle of 46 ±â€…0.1° between the surface and the (111) planes was studied. The grazing angles of incidence were near 1.08 and 0.33° for these two energies, respectively. Features arising from surface undulations were not observed at 8.100 keV, but were observed at 8.200 keV. The results at 8.100 keV allow an alternative explanation based on strain near the surface to be ruled out. Topographic images were obtained as a function of rocking angle, and in the case of 8.200 keV the surface morphology is evident. The results are found to be in agreement with dynamical X-ray diffraction calculations made with the Takagi-Taupin equations specialized to a surface having convex or concave features, as reported in the accompanying paper [Macrander (2020). J. Appl. Cryst. 53, 793-799].

Large Aperture and Wedged Multilayer Laue Lens for X-ray Nanofocusing.

Diffraction optics fabricated from multilayers offer an intriguing alternative to lithography-based zone plates due to their advantages of virtually limitless aspect ratio and extremely small feature size. However, other issues, intrinsic to thin-film deposition, such as film stress and deposition rate instability, for example, limit the total achievable aperture. Over the last decade, Multilayer Laue Lens (MLLs) have progressed from a mere curiosity with initial aperture sizes in the 3-10 µm range, to real beamline-deployed optics with apertures in the 40-50 µm range (X. Huang, et al., Scientific Reports 3, 3562 (2013); E. Nazaretski, et al., Rev. Sci. Instrum. 85, 033707 (2014); E. Nazaretski, et al., Journal of Synchrotron Radiation 24, 1113 (2017)). By optimizing deposition conditions and incorporating new materials, MLLs have now broken the 100 µm thickness milestone. A flat WSi2/Al-Si MLL with a deposition thickness of 102 µm, the largest MLL to date, is reviewed. New large aperture wedged MLLs (wMLL), which were first fabricated by APS in 2006 using the WSi2/Si material system, are presented which demonstrate high focusing efficiency across a broad energy range. These results confirm findings by other groups who have also independently fabricated wMLL (A. J. Morgan, et al., Scientific Reports 5, 9892 (2015); S. Bajt, et al., Nature Light: Science and Applications 7, 17162 (2017)) based on a similar material system.

Measurement of X-ray Beam Coherence along Multiple Directions Using 2-D Checkerboard Phase Grating.

A procedure for a technique to measure the transverse coherence of synchrotron radiation X-ray sources using a single phase grating interferometer is reported. The measurements were demonstrated at the 1-BM bending magnet beamline of the Advanced Photon Source (APS) at Argonne National Laboratory (ANL). By using a 2-D checkerboard π/2 phase-shift grating, transverse coherence lengths were obtained along the vertical and horizontal directions as well as along the 45° and 135° directions to the horizontal direction. Following the technical details specified in this paper, interferograms were measured at different positions downstream of the phase grating along the beam propagation direction. Visibility values of each interferogram were extracted from analyzing harmonic peaks in its Fourier Transformed image. Consequently, the coherence length along each direction can be extracted from the evolution of visibility as a function of the grating-to-detector distance. The simultaneous measurement of coherence lengths in four directions helped identify the elliptical shape of the coherence area of the Gaussian-shaped X-ray source. The reported technique for multiple-direction coherence characterization is important for selecting the appropriate sample size and orientation as well as for correcting the partial coherence effects in coherence scattering experiments. This technique can also be applied for assessing coherence preserving capabilities of X-ray optics.

Development and implementation of a portable grating interferometer system as a standard tool for testing optics at the Advanced Photon Source beamline 1-BM.

We developed a portable X-ray grating interferometer setup as a standard tool for testing optics at the Advanced Photon Source (APS) beamline 1-BM. The interferometer can be operated in phase-stepping, Moiré, or single-grating harmonic imaging mode with 1-D or 2-D gratings. All of the interferometer motions are motorized; hence, it is much easier and quicker to switch between the different modes of operation. A novel aspect of this new instrument is its designed portability. While the setup is designed to be primarily used as a standard tool for testing optics at 1-BM, it could be potentially deployed at other APS beamlines for beam coherence and wavefront characterization or imaging. The design of the interferometer system is described in detail and coherence measurements obtained at the APS 34-ID-E beamline are presented. The coherence was probed in two directions using a 2-D checkerboard, a linear, and a circular grating at X-ray energies of 8 keV, 11 keV, and 18 keV.

Hard x-ray spectroscopy and imaging by a reflection zone plate in the presence of astigmatism.

The feasibility of an off-axis x-ray reflection zone plate to perform wavelength-dispersive spectroscopy, on-axis point focusing, and two-dimensional imaging is demonstrated by means of one and the same diffractive optical element (DOE) at a synchrotron radiation facility. The resolving power varies between 3×101 and 4×102 in the range of 7.6 keV to 9.0 keV, with its maximum at the design energy of 8.3 keV. This result is verified using an adjustable entrance slit, by which horizontal (H) and vertical (V) focusing to 0.85 µm(H) and 1.29 µm(V) is obtained near the sagittal focal plane of the astigmatic configuration. An angular and axial scan proves an accessible field of view of at least 0.6 arcmin × 0.8 arcmin and a focal depth of ±0.86 mm. Supported by the grating efficiency of around 17.5% and a very short pulse elongation, future precision x-ray fluorescence and absorption studies of transition metals at their K-edge on an ultrashort timescale could benefit from our findings.

Diffraction properties of multilayer Laue lenses with an aperture of 102 µm and WSi2/Al bilayers.

We report on the characterization of a multilayer Laue lens (MLL) with large acceptance, made of a novel WSi2/Al bilayer system. Fabrication of multilayers with large deposition thickness is required to obtain MLL structures with sufficient apertures capable of accepting the full lateral coherence length of x-rays at typical nanofocusing beamlines. To date, the total deposition thickness has been limited by stress-buildup in the multilayer. We were able to grow WSi2/Al with low grown-in stress, and asses the degree of stress reduction. X-ray diffraction experiments were conducted at beamline 1-BM at the Advanced Photon Source. We used monochromatic x-rays with a photon energy of 12 keV and a bandwidth of ΔE/E=5.4·10(-4). The MLL was grown with parallel layer interfaces, and was designed to have a large focal length of 9.6 mm. The mounted lens was 2.7 mm in width. We found and quantified kinks and bending of sections of the MLL. Sections with bending were found to partly have a systematic progression in the interface angles. We observed kinking in some, but not all, areas. The measurements are compared with dynamic diffraction calculations made with Coupled Wave Theory. Data are plotted showing the diffraction efficiency as a function of the external tilting angle of the entire mounted lens. This way of plotting the data was found to provide an overview into the diffraction properties of the whole lens, and enabled the following layer tilt analyses.

Achieving hard X-ray nanofocusing using a wedged multilayer Laue lens.

We report on the fabrication and the characterization of a wedged multilayer Laue lens for x-ray nanofocusing. The lens was fabricated using a sputtering deposition technique, in which a specially designed mask was employed to introduce a thickness gradient in the lateral direction of the multilayer. X-ray characterization shows an efficiency of 27% and a focus size of 26 nm at 14.6 keV, in a good agreement with theoretical calculations. These results indicate that the desired wedging is achieved in the fabricated structure. We anticipate that continuous development on wedged MLLs will advance x-ray nanofocusing optics to new frontiers and enrich capabilities and opportunities for hard X-ray microscopy.

Probing transverse coherence of x-ray beam with 2-D phase grating interferometer.

Transverse coherence of the x-ray beam from a bending magnet source was studied along multiple directions using a 2-D π/2 phase grating by measuring interferogram visibilities at different distances behind the grating. These measurements suggest that the preferred measuring orientation of a 2-D checkerboard grating is along the diagonal directions of the square blocks, where the interferograms have higher visibility and are not sensitive to the deviation of the duty cycle of the grating period. These observations are verified by thorough wavefront propagation simulations. The accuracy of the measured coherence values was also validated by the simulation and analytical results obtained from the source parameters. In addition, capability of the technique in probing spatially resolved local transverse coherence is demonstrated.

Kirkpatrick-Baez mirrors to focus hard X-rays in two dimensions as fabricated, tested and installed at the Advanced Photon Source.

The micro-focusing performance for hard X-rays of a fixed-geometry elliptical Kirkpatrick-Baez (K-B) mirrors assembly fabricated, tested and finally implemented at the micro-probe beamline 8-BM of the Advanced Photon Source is reported. Testing of the K-B mirror system was performed at the optics and detector test beamline 1-BM. K-B mirrors of length 80 mm and 60 mm were fabricated by profile coating with Pt metal to produce focal lengths of 250 mm and 155 mm for 3 mrad incident angle. For the critical angle of Pt, a broad bandwidth of energies up to 20 keV applies. The classical K-B sequential mirror geometry was used, and mirrors were mounted on micro-translation stages. The beam intensity profiles were measured by differentiating the curves of intensity data measured using a wire-scanning method. A beam size of 1.3 µm (V) and 1.2 µm (H) was measured with monochromatic X-rays of 18 keV at 1-BM. After installation at 8-BM the measured focus met the design requirements. In this paper the fabrication and metrology of the K-B mirrors are reported, as well as the focusing performances of the full mirrors-plus-mount set-up at both beamlines.

Oxidation of PtNi nanoparticles studied by a scanning X-ray fluorescence microscope with multi-layer Laue lenses.

We report a study of the oxidation process of individual PtNi nanoparticles (NPs) conducted with a novel scanning multi-layer Laue lens X-ray microscope. The elemental maps reveal that alloyed PtNi NPs were transformed into Pt/NiO core-shell NPs by thermal oxidation. The observations furthermore indicate that a coalescence of Pt/NiO core-shell NPs occurred during oxidation.

Heat bump on a monochromator crystal measured with X-ray grating interferometry.

Deformation of the first crystal of an X-ray monochromator under the heat load of a high-power beam, commonly referred to as `heat bump', is a challenge frequently faced at synchrotron beamlines. Here, quantitative measurements of the deformations of an externally water-cooled silicon (111) double-crystal monochromator tuned to a photon energy of 17.6 keV are reported. These measurements were made using two-dimensional hard X-ray grating interferometry, a technique that enables in situ at-wavelength wavefront investigations with high angular sensitivity. The observed crystal deformations were of the order of 100 nm in the meridional and 5 nm in the sagittal direction, which lead to wavefront slope errors of up to 4 µrad in the meridional and a few hundred nanoradians in the sagittal direction.

Two dimensional hard x-ray nanofocusing with crossed multilayer Laue lenses.

Hard x-ray microscopy with nanometer resolution will open frontiers in the study of materials and devices, environmental sciences, and life sciences by utilizing the unique characterization capabilities of x-rays. Here we report two-dimensional nanofocusing by multilayer Laue lenses (MLLs), a type of diffractive optics that is in principle capable of focusing x-rays to 1 nm. We demonstrate focusing to a 25 × 27 nm(2) FWHM spot with an efficiency of 2% at a photon energy of 12 keV, and to a 25 × 40 nm(2) FWHM spot with an efficiency of 17% at a photon energy of 19.5 keV.

Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data.

We have used coherent X-ray diffraction experiments to characterize both the 1-D and 2-D foci produced by nanofocusing Kirkpatrick-Baez (K-B) mirrors, and we find agreement. Algorithms related to ptychography were used to obtain a 3-D reconstruction of a focused hard X-ray beam waist, using data measured when the mirrors were not optimally aligned. Considerable astigmatism was evident in the reconstructed complex wavefield. Comparing the reconstructed wavefield for a single mirror with a geometrical projection of the wavefront errors expected from optical metrology data allowed us to diagnose a 40 µrad misalignment in the incident angle of the first mirror, which had occurred during the experiment. Good agreement between the reconstructed wavefront obtained from the X-ray data and off-line metrology data obtained with visible light demonstrates the usefulness of the technique as a metrology and alignment tool for nanofocusing X-ray optics.

Observation of the Talbot effect using broadband hard x-ray beam.

We demonstrated the Talbot effect using a broadband hard x-ray beam (Δλ/λ ~1). The exit wave-field of the x-ray beam passing through a grating with a sub micro-meter scale period was successfully replicated and recorded at effective Talbot distance, Z(T). The period was reduced to half at Z(T)/4 and 3/4Z(T), and the phase reversal was observed at Z(T)/2. The propagating wave-field recorded on photoresists was consistent with a simulated result.

Wedged multilayer Laue lens.

A multilayer Laue lens (MLL) is an x-ray focusing optic fabricated from a multilayer structure consisting of thousands of layers of two different materials produced by thin-film deposition. The sequence of layer thicknesses is controlled to satisfy the Fresnel zone plate law and the multilayer is sectioned to form the optic. An improved MLL geometry can be created by growing each layer with an in-plane thickness gradient to form a wedge, so that every interface makes the correct angle with the incident beam for symmetric Bragg diffraction. The ultimate hard x-ray focusing performance of a wedged MLL has been predicted to be significantly better than that of a nonwedged MLL, giving subnanometer resolution with high efficiency. Here, we describe a method to deposit the multilayer structure needed for an ideal wedged MLL and report our initial deposition results to produce these structures.

Sectioning of multilayers to make a multilayer Laue lens.

We report a process to fabricate multilayer Laue lenses (MLL's) by sectioning and thinning multilayer films. This method can produce a linear zone plate structure with a very large ratio of zone depth to width (e.g., >1000), orders of magnitude larger than can be attained with photolithography. Consequently, MLL's are advantageous for efficient nanofocusing of hard x rays. MLL structures prepared by the technique reported here have been tested at an x-ray energy of 19.5 keV, and a diffraction-limited performance was observed. The present article reports the fabrication techniques that were used to make the MLL's.

Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors.

Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a 15 keV point source, which indicate nearly diffraction-limited focusing at the 40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than 0.1 mm have a minor effect on the focal spot size and intensity.