Xianbo Shi

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

A new ’Hybrid Method’ combining ray-tracing and wavefront propagation for X-ray optics simulation is reported. The code is fast and can handle partially coherent sources, making it a useful tool for beamline design and optimization.

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.

Circular grating interferometer for mapping transverse coherence area of X-ray beams

A circular grating interferometer was used to map the transverse coherence area of an X-ray beam. Due to the radial symmetry of the circular grating, coherence lengths along all transverse directions were obtained simultaneously by measuring the visibility decay of interferograms recorded at different distances behind a single circular π/2 phase grating. The technique is model-free and provides direct measurement of the complex coherence factor of the beam. The use of a circular grating also enables the unique capability of measuring the source shape profile. Sensitivity of this technique was demonstrated by detecting the small source tilt of a few degrees.

Simulation of X-ray diffraction profiles for bent anisotropic crystals

The equations for calculating diffraction profiles for bent crystals are revisited for both meridional and sagittal bending. Two approximated methods for computing diffraction profiles are treated: multilamellar and Penning–Polder. A common treatment of crystal anisotropy is included in these models. The formulation presented is implemented in the XOP package, completing and updating the crystal module that simulates diffraction profiles for perfect, mosaic and now distorted crystals by elastic bending.

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.

DABAM: an open-source database of X-ray mirrors metrology

DABAM, an open-source database of X-ray mirrors metrology to be used with ray-tracing and wave-propagation codes for simulating the effect of the surface errors on the performance of a synchrotron radiation beamline.

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.

Development of single grating x-ray Talbot interferometer as a feedback loop sensor element of an adaptive x-ray mirror system

The initial result of using a single 2-D checkerboard phase-grating Talbot interferometer as a feed-back loop sensor element of an adaptive x-ray mirror system is reported. The test was performed by measuring the surface profile of a deformable Pt coated Silicon mirror at five different actuation states. The reflected beam was detected at the fractional Talbot distance of a π/2 phase grating. The measured interferograms were de-convolved using the spatial harmonic imaging technique to extract the phase and amplitude of the reflected wavefront. The wavefront was then propagated to the mirror center to retrieve the surface profile of the mirror. The activation of a single actuator was easily detected from the reconstructed surface profile of the mirror. The presented results indicate that the single phase-grating x-ray Talbot interferometer is capable of sensing nano-meter scale profile changes of an adaptive mirror.

Surface curvatures and diffraction profiles of sagittally bent Laue crystals

The performance of a bent Laue crystal monochromator crucially depends on the sagittal and meridional bending curvatures of the crystal. To optimize the design of monochromator crystals, the surface curvatures and diffraction profiles of a set of sagittally bent Laue crystals with different aspect ratios have been studied experimentally by optical metrology and X-ray measurements. The results were confirmed with finite-element analysis using large-deformation theory. The nonlinear relationship between the curvatures necessitates an experimentally determined parameter in the theoretical modeling of the diffraction profiles. By taking into account the local stress and the aspect ratio of the sagittally bent Laue crystal, the modified analytical approach successfully predicts the rocking-curve width and the integrated reflecting power. The effect of extreme sagittal bending on the rocking curve is also discussed. To retain high reflectivity, the bending curvature should not exceed its critical value for the specified crystal geometry. Furthermore, the uniformity of the bending curvatures across the crystal surface has been examined, which suggests that the minimum crystal dimension should be approximately twice the size of the beam footprint.

X-ray optics testing beamline 1-BM at the advanced photon source

Beamline 1-BM at the APS has been reconfigured in part for testing of synchrotron optics with both monochromatic and white beams. Operational since 2013, it was reconfigured to accommodate users of the APS as well as users from other DOE facilities. Energies between 6 and 28 keV are available. The beamline was reconfigured to remove two large mirrors and to provide a 100 mm wide monochromatic beam at 54 m from the source. In addition a custom white beam shutter was implemented for topography exposures as short as 65 millisec over the full available horizontal width. Primary agendas include both white beam and monochromatic beam topography, Talbot grating interferometry, and tests of focusing optics. K-B mirrors, MLLs, and FZPs have been characterized. Measurements of the spatial coherence lengths on the beamline were obtained with Talbot interferometry. Topography data has been reported.