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...