On qualitative and quantitative analysis in analyser-based imaging

Using rigorous wave-optical formalism, a general expression is obtained for the image intensity distribution in combined analyser-based/propagation-based phase-contrast imaging. This expression takes into account partial coherence of the wave incident on the object as well as the finite resolution of the detector system. Using this general expression, two approaches based on the geometrical optics and weak-object approximations are applied to derive simple solutions to the inverse problem of reconstruction of the phase and amplitude of the object wave. With the help of numerical experiments, the two approaches are compared in terms of their validity conditions and are shown to impose certain restrictions on the properties of the object wave. In particular, it is shown that violation of the validity conditions of the geometrical optics or weak-object approximations results in the appearance of strong reconstruction artefacts in the transmitted intensity near the edges of the objects. The effect of the incident wavefront non-uniformity due to imperfections of the imaging set-up on image formation and phase/amplitude reconstruction is also discussed. A solution to this problem is proposed in the form of a multi-image phase/amplitude reconstruction algorithm based on the geometrical optics approximation. This algorithm and an algorithm based on the weak-object approximation are applied to simulated and experimental images of fibres.