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This lecture covers the techniques and applications of synchrotrons and X-ray free-electron lasers, focusing on higher-dimensional imaging. Starting from scalar properties, the lecture progresses to vector and tensor properties within each voxel, such as magnetic direction and piezoelectricity. The use of vector phase-contrast X-ray tomography (PXCT) for studying nanomagnetism in materials is discussed, along with the limitations of current microscopy techniques. The lecture also delves into scanning small-angle X-ray scattering (SAXS) tensor tomography, showcasing its ability to study tensor properties in each voxel and providing insights into the hierarchical ordering of biological structures like bone at multiple length scales.