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The aim of this PhD thesis is to develop the technic of X-ray phase imaging with Hartmann wavefront sensor for various applications and to compare this new system against well-established phase-contrast techniques. The X-ray phase imaging will be mainly performed in 3D using tomographic setup. The main application includes the study of alteractions in the central nervous system induced by neurodegenerative diseases. The first introductory section describes the basic aspects of X-ray interaction with matter and of yhe coherence theory with specific application to the Hartmann wavefront sensor design. In the second chapter, an introduction to the free-space propagation technique. The third chapter examines the principles of tomography acquisitions and the available reconstruction algorithms. A separate chapter, labeled 4, is dedicated to the theory of Hartmann wavefront sensor. A 3D wave propagation model based on Fresnel propagator was developed to optimize the architecture of the full wavefront sensor including the Hartmann plate, the distances between the different elements of the set-up as well as the X-ray source. The model can manage any degree of spatial coherence, enabling the accurate simulation of a wide range of X-ray sources. Several simulations of standard experimental situations are described to valid the program. Then, the main wavefront reconstruction algorithms have been analyzed. In chapter 5, we will present experimental results obtained with the X-ray Hartmann wavefront sensor using both a parallel beam geometry (synchrotron measurements) and a cone beam geometry (laboratory measurements …