Applying the Fokker-Planck equation to x-ray phase and dark-field retrieval

This thesis designs a new method of x-ray imaging, a way to capture what are known as x-ray dark-field images. These dark-field images reveal where there are tiny structures within a patient, for example the tiny air sacs that make up the lung. The new method is based upon the Fokker-Planck equation, which describes how the x-ray wavefield evolves as the x-rays pass through the air from the patient to the x-ray detector. The thesis solves this equation, allowing dark-field x-ray images to be extracted from a simple x-ray imaging set-up.