X-ray Interior Tensor Tomography with 2D Gratings

X-ray tensor tomography is a promising imaging modality for probing the micro structure of a sample by reconstructing small-angle scattering densities in different scattering directions. However, the current x-ray grating technique still faces an obstacle when a divergent x-ray beam from a point x-ray source propagates through a large object and reaches large planar gratings. In this situation, tensor interior tomography is essential to perform the image reconstruction over a region of interest (ROI) in the object. Therefore, we propose interior tensor tomography with 2D gratings to extract dark field images isotropically. Our numerical results demonstrate that the proposed methods are promising for reconstruction of local images from truncated dark field projection data.