A tilted grating interferometer for full vector field differential x-ray phase contrast tomography

Abstract

We report on a setup for differential x-ray phase-contrast imaging and tomography, that measures the full 2D phase-gradient information. The setup uses a simple one-dimensional x-ray grating interferometer, in which the grating structures of the interferometer are oriented at a tilt angle with respect to the sample rotation axis. In such a configuration, the differential phase images from opposing tomography projections can be combined to yield both components of the gradient vector. We show how the refractive index distribution as well as its x, y, and z gradient components can be reconstructed directly from the recorded projection data. The method can equally well be applied at conventional x-ray tube sources, to analyzer based x-ray imaging or neutron imaging. It is demonstrated with measurements of an x-ray phantom and a rat brain using synchrotron radiation. Abstract:We report on a setup for differential x-ray phase-contrast imaging and tomography, that measures the full 2D phase-gradient information.The setup uses a simple one-dimensional x-ray grating interferometer, in which the grating structures of the interferometer are oriented at a tilt angle with respect to the sample rotation axis. In such a configuration, the differential phase images from opposing tomography projections can be combined to yield both components of the gradient vector. We show how the refractive index distribution as well as its x, y, and z gradient components can be reconstructed directly from the recorded projection data. The method can equally well be applied at conventional x-ray tube sources, to analyzer based x-ray imaging or neutron imaging. It is demonstrated with measurements of an x-ray phantom and a rat brain using synchrotron radiation. Pai, "Single-shot x-ray differential phase-contrast and diffraction imaging using two-dimensional transmission gratings," Opt. Lett. 35, 1932Lett. 35, -1934Lett. 35, (2010. 13. H. Itoh, K. Nagai, G. Sato, K. Yamaguchi, T. Nakamura, T. Kondoh, C. Ouchi, T. Teshima, Y. Setomoto, and T. Den, "Two-dimensional grating-based X-ray phase-contrast imaging using Fourier transform phase retrieval," Opt. , 189-195 (2007). 21. The out-of-plane component cancels out because the phase integration, which is implicit in the modified reconstruction kernel, is always performed along the same direction in the camera coordinate system. Considering for instance an integral from left to right through the PMMA cylinder at the bottom of Fig. 2(d), the signal at its left edge is ∂ t Φ + ∂ z Φ where the signal in the tomographic rotation plane is ∂ t Φ > 0 and the out-of-plane signal ∂ z Φ < 0. Integrating through the same edge of the sample in Fig. 2(e), the out-of-plane signal has changed sign ∂ z Φ > 0, while the in-plane signal has again the same sign as before ∂ t Φ > 0. Reconstructing a slice using filtered back projection over a full sample rotation of 2π, each projection pair corresponds to a single line in twodimensional Fourier space. The out of plane component cancels out since it is o...

Tilted grating phase-contrast computed tomography using statistical iterative reconstruction

“…Additionally, the sample does not provide purely horizontal features. In the case of parallel beam geometry, additional features should be observed when comparing tilted and non-tilted grating configuration 16 .

Figure 5 Difference images between different phase-contrast tomograms.

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“…The combined phase projections are then reconstructed with filtered backprojection using Ram-Lak filters. The results, which were first produced at a synchrotron facility, show an overall improvement of the phase tomogram including reduced streak artefacts 16 .…”

“…Other methods for streak artefact reduction working for DPC imaging use phase-unwrapping with energy resolving detectors 18 , 19 or an iterative bone-artefact removal algorithm 17 , but are more complicated than the presented approach. In contrast to the tilted gratings method presented at a synchrotron facility 16 , no additional processing is necessary with the approach illustrated in this work. Potential errors due to sample alignment mismatch and additional interpolation in the processing can be avoided.…”

“…When performing phase-contrast tomography with one-dimensional gratings there is an approach where the gratings are tilted by 45° with respect to the tomographic axis 16 . In detail, a full tomographic scan is executed with the tilted grating configuration over 360° sample rotation.…”

Two-dimensional ultra-small angle X-ray scattering with grating interferometry

“…8) and dark-field contrast 9 in the direction orthogonal to the grating structure in addition to absorption contrast. Sensitivity in two directions can be achieved by either rotating the gratings 10,11 or the sample 12 and scanning multiple times. Alternatively, gratings with a two-dimensional (2D) structure can be utilized to obtain 2D sensitivity, which was experimentally demonstrated without an analyzer grating [13][14][15] and with an analyzer grating present.…”