The 3D visualization of the inner microstructural features of objects and materials is of relevant interest for a wide range of scientific and industrial applications. X-ray computed microtomography (?-CT) is a powerful non-destructive technique capable to satisfy these needs. This work was carried out at the hard X-ray imaging beamline of the Elettra Synchrotron Radiation Facility (Trieste, Italy). Here, the acquired experience has leaded scientists to design a complementary state-of- the-art ?-CT facility based on a micro-focus X-ray source, working both in absorption and phase contrast mode. In this dissertation a rigorous characterization of the imaging system is given in terms of the actual spatial resolution, also considering the main artefacts that concur to the degradation of the image quality. Three representative examples are then used to demonstrate the application of ?-CT to materials science, in combination with specific image processing tools: the geometrical and morphological characterisation of polyurethane foams; a new approach to analyze the resonance spruce wood microstructure; the possibility of revealing defects in hybrid-friction stir welded aluminium joints.

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