Linear systems with slowly varying transfer functions and their application to x-ray phase-contrast imaging

A novel theoretical treatment of linear shift-invariant imaging systems is developed, which allows explicit solution of forward and inverse problems in the case of large values of the generalized Fresnel number. The method will be useful in a variety of domains including optical instrumentation, biomedical imaging and materials science. Our approach is used to integrate two particularly topical x-ray imaging methods, namely propagation-based and analyser-crystal-based x-ray phase-contrast imaging.