Quantitative evaluation of in-line x-ray phase contrast for a class of edge objects

In order to quantify the effect of phase contrast on X-ray image formation, the theory of statistical decision making has been applied to a binary classification task between two signals known exactly, namely, a phase-contrast image (that combines both the absorption and phase contrast) and the corresponding hypothetical pure absorption image that would be obtained under the same imaging conditions but without diffraction/refraction effects. The signal-to-noise ratio (SNR) for two widely used observers, including the ideal observer (also known as the prewhitening matched filter) and a non-ideal observer (the non-prewhitening matched filter) has been estimated in the case of in-line phase-contrast imaging, thus providing a figure-of-merit for the optimisation of the imaging conditions. A broad class of edge objects has been investigated and simple analytical expressions for the corresponding SNRs have been obtained and discussed.