measurement-x-ray-beam-coherence-along-multiple-directions-using-2-d

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 ...

Argonne National Laboratory

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.

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

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.

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

The first test of nanoscale-focusing Kirkpatrick-Baez (KB) mirrors in the nested (or Montel) configuration used at a hard X-ray synchrotron beamline is reported. The two mirrors are both 40 mm long and coated with Pt to produce a focal length of 60 mm at 3 mrad incident angle, and collect up to a 120 µm by 120 µm incident X-ray beam with maximum angular acceptance of 2 mrad and a broad bandwidth of energies up to 30 keV. In an initial test a focal spot of about 150 nm in both horizontal and vertical directions was achieved with either polychromatic or monochromatic beam. The nested mirror geometry, with two mirrors mounted side-by-side and perpendicular to each other, is significantly more compact and provides higher demagnification than the traditional sequential KB mirror arrangement. Ultimately, nested mirrors can focus larger divergence to improve the diffraction limit of achromatic optics. A major challenge with the fabrication of the required mirrors is the need for near-perfect mirror surfaces near the edge of at least one of the mirrors. Special polishing procedures and surface profile coating were used to preserve the mirror surface quality at the reflecting edge. Further developments aimed at achieving diffraction-limited focusing below 50 nm are underway.

Achromatic nested Kirkpatrick-Baez mirror optics for hard X-ray nanofocusing.

X-ray optics called multilayer Laue lenses (MLLs) provide a promising path to focusing hard X-rays with high focusing efficiency at a resolution between 5 nm and 20 nm. MLLs consist of thousands of depth-graded thin layers. The thickness of each layer obeys the linear zone plate law. X-ray beamline tests have been performed on magnetron sputter-deposited WSi(2)/Si MLLs at the Advanced Photon Source/Center for Nanoscale Materials 26-ID nanoprobe beamline. However, it is still very challenging to accurately grow each layer at the designed thickness during deposition; errors introduced during thickness measurements of thousands of layers lead to inaccurate MLL structures. Here, a new metrology approach that can accurately measure thickness by introducing regular marks on the cross section of thousands of layers using a focused ion beam is reported. This new measurement method is compared with a previous method. More accurate results are obtained using the new measurement approach.

A unique approach to accurately measure thickness in thick multilayers.

Grating-based X-ray and neutron interferometry tomography using phase-stepping methods generates large data sets. An improved algorithm is presented for solving for the parameters to calculate transmissions, differential phase contrast, and dark-field images. The method takes advantage of the vectorization inherent in high-level languages such as Mathematica and MATLAB and can solve a 16 × 1k × 1k data set in less than a second. In addition, the algorithm can function with partial data sets. This is demonstrated with processing of a 16-step grating data set with partial use of the original data chosen without any restriction. Also, we have calculated the reduced chi-square for the fit and notice the effect of grating support structural elements upon the differential phase contrast image and have explored expanded basis set representations to mitigate the impact.

Improved algorithm for processing grating-based phase contrast interferometry image sets.

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.

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

A new method for beamline simulation combining ray-tracing and wavefront propagation is described. The `Hybrid Method' computes diffraction effects when the beam is clipped by an aperture or mirror length and can also simulate the effect of figure errors in the optical elements when diffraction is present. The effect of different spatial frequencies of figure errors on the image is compared with SHADOW results pointing to the limitations of the latter. The code has been benchmarked against the multi-electron version of SRW in one dimension to show its validity in the case of fully, partially and non-coherent beams. The results demonstrate that the code is considerably faster than the multi-electron version of SRW and is therefore a useful tool for beamline design and optimization.

A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation.

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.

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

A method to pre-shape mirror substrates through etching with a broad-beam ion source and a contoured mask is presented. A 100 mm-long elliptical cylinder substrate was obtained from a super-polished flat Si substrate with a 48 nm root-mean-square (r.m.s.) figure error and a 1.5 Å r.m.s. roughness after one profile-etching process at a beam voltage of 600 V without iteration. A follow-up profile coating can be used to achieve a final mirror. Profile etching and profile coating combined provide an economic way to make X-ray optics, such as nested Kirkpatrick-Baez mirrors.

Profile etching for prefiguring X-ray mirrors.

X-ray imaging of soft tissue is made difficult by their low absorbance. The use of x-ray phase imaging and tomography can significantly enhance the detection of these tissues and several approaches have been proposed to this end. Methods such as analyzer-based imaging or grating interferometry produce differential phase projections that can be used to reconstruct the 3D distribution of the sample refractive index. We report on the quantitative comparison of three different methods to obtain x-ray phase tomography with filtered back-projection from differential phase projections in the presence of noise. The three procedures represent different numerical approaches to solve the same mathematical problem, namely phase retrieval and filtered back-projection. It is found that obtaining individual phase projections and subsequently applying a conventional filtered back-projection algorithm produces the best results for noisy experimental data, when compared with other procedures based on the Hilbert transform. The algorithms are tested on simulated phantom data with added noise and the predictions are confirmed by experimental data acquired using a grating interferometer. The experiment is performed on unstained adult zebrafish, an important model organism for biomedical studies. The method optimization described here allows resolution of weak soft tissue features, such as muscle fibers.

Comparison of different numerical treatments for x-ray phase tomography of soft tissue from differential phase projections.

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 3×10<sup>1</sup> and 4×10<sup>2</sup> 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.

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

Recent developments in synchrotron storage rings and free-electron laser-based x-ray sources with ever-increasing brightness and coherent flux have pushed x-ray optics requirements to new frontiers. This Special Topic gathers a set of articles derived from a subset of the key presentations of the International Workshop on X-ray Mirrors Fabrication (IWXM-2015) and Metrology held at Lawrence Berkley National Laboratory, Berkeley, California, USA, July 14-16, 2015. The workshop objective was to report on recent progress in x-ray synchrotron radiation mirrors fabrication as well as on new developments in related metrology tools and methods.

Preface: The 5th International Workshop on X-ray Mirror Design, Fabrication, and Metrology.

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.

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

Article	Year
Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors. Applied optics\| PubMed ID: 17384715	2007
Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data. Optics express\| PubMed ID: 21164684	2010
Achromatic nested Kirkpatrick-Baez mirror optics for hard X-ray nanofocusing. Journal of synchrotron radiation\| PubMed ID: 21685674	2011
A unique approach to accurately measure thickness in thick multilayers. Journal of synchrotron radiation\| PubMed ID: 22514179	2012
Improved algorithm for processing grating-based phase contrast interferometry image sets. The Review of scientific instruments\| PubMed ID: 24517772	2014
Kirkpatrick-Baez mirrors to focus hard X-rays in two dimensions as fabricated, tested and installed at the Advanced Photon Source. Journal of synchrotron radiation\| PubMed ID: 24971959	2014
A hybrid method for X-ray optics simulation: combining geometric ray-tracing and wavefront propagation. Journal of synchrotron radiation\| PubMed ID: 24971960	2014
Probing transverse coherence of x-ray beam with 2-D phase grating interferometer. Optics express\| PubMed ID: 24977503	2014
Profile etching for prefiguring X-ray mirrors. Journal of synchrotron radiation\| PubMed ID: 25723948	2015
Comparison of different numerical treatments for x-ray phase tomography of soft tissue from differential phase projections. Physics in medicine and biology\| PubMed ID: 25802946	2015
Hard x-ray spectroscopy and imaging by a reflection zone plate in the presence of astigmatism. Optics letters\| PubMed ID: 26696150	2016
Preface: The 5th International Workshop on X-ray Mirror Design, Fabrication, and Metrology. The Review of scientific instruments\| PubMed ID: 27250367	2016
Development and implementation of a portable grating interferometer system as a standard tool for testing optics at the Advanced Photon Source beamline 1-BM. The Review of scientific instruments\| PubMed ID: 27250384	2016

Lahsen Assoufid

Biography

JoVE Journal Publications

Other Publications