Advances in phase contrast imaging using fully and partially coherent wavefields

X-ray phase contrast imaging enables the visualization of an object’s features that otherwise would be impossible to obtain with conventional absorption based X–ray imaging. The first part of this thesis focuses specifically on propagation–based phase contrast imaging (PBI). It has a particular emphasis on the quantitative image reconstruction under the assumption that the source of illumination is fully coherent. It presents the existing methods of extracting quantitative information as well as original ones developed in this thesis. The second part of this thesis takes a purely theoretical route, which focuses on studying the forward problem of aberrated optical systems under partially coherent illumination. This thesis begins with a general overview and review of the relevant literature including the theory of coherent X–ray wavefield diffraction, partial coherence, phase–contrast X–ray imaging, and phase–contrast tomography. Particular emphasis is given to PBI. We then move to the original work that involved developing a method to carry out quantitative PBI based tomography on multi–material samples using only a single view per tomographic projection. The samples considered here are those for which (i) the complex refractive index of each component of the sample is known, and (ii) the component materials are spatially quantized. The method was applied to tomographic data obtained at the SPring–8 synchrotron facility in Japan. The sample used was a multi–material test phantom. The refractive index distribution of the test phantom was recovered in three dimensions with a single phase contrast image per projection. The method was applied successfully and was very stable under the presence of noise, opening the possibility of significant dose reduction incurred by samples. The next step in this work sees the application of the aforementioned method to complex biological organs. The chosen organs were the thorax of a rabbit pup and an excised rat brain. Experimental data were also acquired at the SPring–8 synchrotron facility in Japan. Tomographic slices containing the refractive index distribution for each organ were reconstructed using a single phase contrast image per projection. Signal–to–noise ratios for each reconstructions showed significant improvements of up 200 fold compared to absorption contrast reconstructions of the same slices. Finally, this thesis treats the problem of arbitrary aberrations in linear shift–invariant optical systems. This involves mathematically establishing a series of expressions considering arbitrary forms of phase contrast modalities as well as taking into account partially coherent illumination. Expressions are presented for the output cross spectral density under the space–frequency formulation of statistically stationary partially coherent fields. This could broaden the applicability of phase contrast to sources of lower quality.