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

Diamond Light Source Ltd.

We present a reflection based coherent diffraction imaging method which can be used to reconstruct a non periodic surface image from a diffraction amplitude measured in reflection geometry. Using a He-Ne laser, we demonstrated that a surface image can be reconstructed solely from the reflected intensity from a surface without relying on any prior knowledge of the sample object or the object support. The reconstructed phase image of the exit wave is particularly interesting since it can be used to obtain quantitative information of the surface depth profile or the phase change during the reflection process. We believe that this work will broaden the application areas of coherent diffraction imaging techniques using light sources with limited penetration depth.

Coherent diffraction surface imaging in reflection geometry.

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.

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.

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.

Underwriters Laboratories 94 test bars have been imaged with X-ray K-edge tomography between 12 and 32 keV to assess the bromine and antimony concentration gradient across char layers of partially burnt samples. Phase contrast tomography on partially burnt samples showed gas bubbles and dark-field scattering ascribed to residual blend inhomogeneity. In addition, single-shot grating interferometry was used to record X-ray movies of test samples during heating (IR and flame) intended to mimic the UL 94 plastics flammability test. The UL 94 test bars were formulated with varying concentrations of a brominated flame retardant, Saytex 8010, and a synergist, Sb2O3, blended into high-impact polystyrene (HIPS). Depending on the sample composition, samples will pass or fail the UL 94 plastics flammability test. Tomography and interferometry imaging show differences that correlate with UL 94 performance. Key features such as char layer, gas bubble formation, microcracks, and dissolution of the flame retardant in the char layer regions are used in understanding the efficiency of the flame retardant and synergist. The samples that pass the UL 94 test have a thick, highly visible char layer as well as an interior rich in gas bubbles. Growth of gas bubbles from flame-retardant thermal decomposition is noted in the X-ray phase contrast movies. Also noteworthy is an absence of bubbles near the burning surface of the polymer; dark-field images after burning suggest a microcrack structure between interior bubbles and the surface. The accepted mechanism for flame retardant activity includes free radical quenching in the flame by bromine and antimony species. The imaging supports this as well as provides a fast inspection of other parameters, such as viscosity and surface tension.

Analysis of Flame Retardancy in Polymer Blends by Synchrotron X-ray K-edge Tomography and Interferometric Phase Contrast Movies.

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.

Shashidhara Marathe

X-ray Science Division,
Advanced Photon Source,
X-ray Science Division, Advanced Photon Source

Argonne National Laboratory

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

Shashidhara Marathe

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Argonne National Laboratory

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

X-ray Science Division,
Advanced Photon Source,
X-ray Science Division, Advanced Photon Source