New quantitative methods in analyser-based phase contrast X-ray imaging

New quantitative methods are developed for analyser-based phase contrast imaging (ABI) with hard X-rays. In the first instance we show that quantitative ABI may be implemented using an extended incoherent source. Next, we outline how complex Green’s functions may be reconstructed from phase contrast images and we apply this method to reconstruct the thick perfect crystal Green’s function associated with an ABI imaging system. The use of quantitative ABI with incoherent X-ray sources is not widespread and the first set of results pertains to the feasibility of quantitative ABI imaging and phase retrieval using a rotating anode X-ray source. The necessary conditions for observation of ABI phase contrast are deduced from elementary coherence considerations and numerical simulations. We then focus on the problem of extracting quantitative information from ABI images recorded using an extended incoherent X-ray source. The results of an experiment performed at Friedrich-Schiller University, Germany using a rotating anode X-ray source demonstrate the validity of our approach. It is shown that quantitative information may be extracted from such images under quite general and practicable conditions. We then develop a new use for phase contrast imaging systems that allows the Green’s function associated with a linear shift-invariant imaging system to be deduced from two phase contrast images of a known weak object. This new approach is applied to X-ray crystallography where the development of efficient methods of inferring the phase of rocking curves is an important open problem. We show how the complex Green’s function describing Bragg reflection of a coherent scalar X-ray wavefield from a crystal may be recovered from a single image over a wide range of reciprocal space simultaneously. The solution we derive is fast, non-iterative and deterministic. When applied to crystalline structures for which the kinematic scattering approximation is valid, such as thin crystalline films, our technique is shown to solve the famous one-dimensional phase retrieval problem which allows us to directly invert the Green’s function to retrieve the depth-dependent interplanar spacing. Finally we implement our Green’s function retrieval method on experimental data collected at the SPring-8 synchrotron in Hyogo, Japan. In the experiment we recorded analyser-based phase contrast images of a known weak object using a thick perfect silicon analyser crystal. It is then demonstrated that these measurements can be inverted to recover the complex Green’s function associated with the analyser crystal Bragg peak. The reconstructed Green’s function is found to be in good agreement with the prediction of dynamical diffraction theory.