Attenuation based X-ray micro computed tomography (XCT) provides three-dimensional images with micrometer resolution. However, there is a trade-off between the smallest size of the struc- tures that can be resolved and the measurable sample size. In this letter, we present an imaging method using a compact laboratory setup that reveals information about micrometer-sized struc- tures within samples that are several orders of magnitudes larger. We combine the anisotropic dark-field signal obtained in a grating interferometer and advanced tomographic reconstruction methods to reconstruct a six dimensional scattering tensor at every spatial location in three dimen- sions. The scattering tensor, thus obtained, encodes information about the orientation of micron- sized structures such as fibres in composite materials or dentinal tubules in human teeth. The sparse acquisition schemes presented in this letter enable the measurement of the full scattering tensor at every spatial location and can be easily incorporated in a practical, commercially feasible labora- tory setup using conventional X-ray tubes, thus allowing for widespread industrial applications.     «

Attenuation based X-ray micro computed tomography (XCT) provides three-dimensional images with micrometer resolution. However, there is a trade-off between the smallest size of the struc- tures that can be resolved and the measurable sample size. In this letter, we present an imaging method using a compact laboratory setup that reveals information about micrometer-sized struc- tures within samples that are several orders of magnitudes larger. We combine the anisotropic dark-field signal obtained...     »