Comparison of Three Theoretical Approaches to Quantitative Analyzer-Based Imaging

We present a comprehensive analysis, comparison and refinement of three new methods for quantitative X-ray phase-contrast imaging using analyzer crystals. The first method is a new version of the geometric optics approximation for dynamical diffraction, which takes into account the variation of the incident intensity as well as the phase. The second method is based on the linearization of the Takagi transfer function, while the third represents a special variant of the Born approximation with relaxed validity conditions. We compare the methods theoretically as well as using numerically simulated images.