X-ray Talbot Interferometry with Capillary Plates

In this paper we describe the design of different X-ray Talbot interferometers that have been built at the tomography beamline ID19 of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France, and give a short review of performance characteristics, of current developments, and of the results obtained with these instruments so far. Among the applications so far, soft-tissue imaging has been a particular focus, as demonstrated in a recent paper by Schulz <em>et al.</em> (<em>J. Roy. Soc. Interface</em>, in press).

X-ray Talbot and Talbot–Lau interferometers consisting of transmission gratings are widely used for X-ray phase imaging, which depicts soft materials. This study exploits the use of a pair of concave and convex parabolic gratings instead of a conventional rectangular phase grating to enhance the phase signal optically. To gain insight into the optimal design, signal enhancement is evaluated by directly measuring the self-image formed downstream of the pair. An increase in the differential phase signals is demonstrated as a function of the distance between the pair, and prospects for deploying this concept into a practical phase imaging technique are discussed.

Taking advantage of the fact that an X-ray Talbot interferometer functions with X-rays of a broad energy bandwidth, high-speed X-ray phase tomography has been demonstrated by using white synchrotron light. Time resolution in addition to three-dimensional spatial resolution has been attained, and we report this achievement as the first four-dimensional (4D) X-ray phase tomography. Moire image movies of samples rotating at a speed of 1 or 2 rps generated by a Talbot interferometer were recorded at a frame rate of up to 1 kf/s, and differential phase image movies of the same frame rate were created by the Fourier-transform method. Consequently, a sub-second time resolution was achieved in the 4D phase tomography, while the spatial resolution was below 0.1 mm and 0.05 mm in axial and in-plane directions, respectively. An X-ray Talbot interferometer generates visibility images in addition to differential phase images, showing the distribution of microstructures, which cause ultra-small angle scattering but cannot be resolved individually with system spatial resolution. Tomographic image reconstruction from the visibility images was also demonstrated.

Recently, darkfield imaging has been established as third imaging technique in X-Ray Talbot interferometry. The darkfield image shows the reduction of visibilities of the interferometer relative to the visibilities gained in reference measurements. The information perceivable from darkfield images can be different from what is observable in absorption and phase images. While the image formation for the absorption and phase image is widely understood, this is not the case for the darkfield signal. There are several attempts for an explanation. To pursue these explanations and, moreover, to get a comprehensive understanding of the darkfield image formation, an investigation based on simulations is carried out. These simulations include wave field propagation as well as Monte Carlo codes. The results suggest that small angle scattering and the micro structure of an object can not be the exclusive origins of the dark field signal. At least diffraction effects at steep edges and possibly visibility changes due to beam hardening effects also have to be accounted for.

X-ray simulations method for the large field of view

26aTN-8 Small Angle X-ray Scattering Tomography by using Visibility Contrast in X-ray Talbot Interferometry

We fabricated a 9 μ m pitch X-ray absorption grating using ultracentrifugal deposition, a fast and simple technique for producing high-aspect-ratio structures. A silicon mold was prepared via deep reactive ion etching and filled with platinum (Pt) particles in approximately 1 h. The fabricated grating was evaluated through cross-sectional scanning electron microscopy (SEM) and X-ray Talbot interferometry using a synchrotron X-ray beam. SEM analysis revealed a nominal Pt thickness of 47.1 μ m, while interferometric measurements indicated an effective thickness of 26 μ m, corresponding to a 55% filling ratio. Phase-contrast, differential-phase, and dark-field (visibility-contrast) images of a polyoxymethylene sphere were successfully obtained using the grating, demonstrating sufficient image quality and practical applicability. This method has the potential to be a scalable alternative to traditional techniques for fabricating fine-pitch X-ray gratings.

The recent use of a one-dimensional (1D) X-ray Talbot interferometer has triggered great interest in X-ray differential phase contrast imaging. As an improved version of a 1D interferometer, the development of two-dimensional (2D) grating interferometry strongly stimulated applications of grating-based imaging. In the framework of Fresnel diffraction theory, we investigated the self-image of 2D-phase gratings under partially coherent illumination. The fringe visibility of the self-image has been analyzed as a function of the spatial coherence length. From the viewpoint of self-image visibility, it is possible to find the optimal 2D grid for 2D X-ray grating interferometer imaging. Numerical simulations have been also carried out for quantitative evaluation. Results, in good agreement with theoretical analysis, indicate the spatial coherence requirements of the radiation illuminating a 2D grating interferometer. Moreover, our results can be used to optimize performances of a 2D grating interferometer and for further theoretical and experimental research on grating-based imaging systems.

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.

The X-ray radiographic imaging technique is very important in medical, biological, inspection, material science, and other fields. However, it is not enough to obtain a clear X-ray image of samples with low absorbance materials, such as biological soft tissues. Then, we have used an X-ray phase-imaging method of an X-ray Talbot interferometer. In this method, X-ray gratings were required to have a narrow pitch and high aspect ratio structure. Therefore, we have developed and fabricated high-aspect-ratio X-ray gratings with a pitch of , a height of , and a large effective area of using X-ray lithography and narrow electroforming techniques. In this paper, we discuss the fabrication process of X-ray gratings with a narrow pitch and high-aspect-ratio structure, and results of X-ray phase tomography using an X-ray Talbot interferometer with these X-ray gratings.

The influence of polychromaticity of the X-ray source on the performance of an X-ray Talbot interferometer applied for phase-contrast imaging is analyzed through numerical simulations based on the Fresnel diffraction theory. The presented simulation results show that the visibility of the self-image is fairly insensitive to the source polychromaticity and explain why the interferometer could be well combined with polychromatic X-ray sources in recent experiments. Furthermore, the self-image with a high visibility can be obtained under polychromatic illumination even at a high-order fractional Talbot distance. This fact implies that the acquired image quality for phase measurements can be improved, since the primary signal for phase measurement is proportional to the inter-grating distance. Finally, we mention that the results are also valid for Talbot-Lau interferometer and scanning double-grating configuration.

We demonstrate a simple method for obtaining slope contours of bent plates using Talbot interferometry. The technique has been used to map slope contours of polymethyl methacrylate specimens of different shapes. The Talbot image of a coarse grating is projected onto a specimen such that the self-image is backreflected onto the same grating again. As a Talbot interferometer is basically a grating shearing interferometer, it results in the generation of characteristic slope maps of the specimen under test. Results of the investigation match well with other slope-mapping techniques. Validation of experimental results with theoretical predictions in the case of a cantilever beam specimen has been undertaken. Accuracy of about 4.7% with respect to theoretical predictions is obtained.

Pioneering study on phase measurement and X-ray phase imaging by Talbot interferometry

Temporal impulse response of the Talbot interferometer

Further modification is proposed of the Talbot interferometer configuration for obtaining moire fringe shearing interferograms with increased shear. The configuration is described with the beam splitter grating rotated about the axis parallel to its lines. The second grating detects only one two-beam interference pattern at a particular angular setting of the beam splitter grating from its multiple beam interference field. This significantly reduces the low quality of the Talbot interferograms at large shear values.