The fractional Talbot effect in differential x-ray phase-contrast imaging for extended and polychromatic x-ray sources

The influence of different physical parameters, such as the source size and the energy spectrum, on the functional capability of a grating interferometer applied for phase-contrast imaging is discussed using numerical simulations based on Fresnel diffraction theory. The presented simulation results explain why the interferometer could be well combined with polychromatic laboratory x-ray sources in recent experiments. Furthermore, it is shown that the distance between the two gratings of the interferometer is not in general limited by the width of the photon energy spectrum. This implies that interferometers that give a further improved image quality for phase measurements can be designed, because the primary measurement signal for phase measurements can be increased by enlargement of this distance. Finally, the mathematical background and practical instructions for the quantitative evaluation of measurement data acquired with a polychromatic x-ray source are given.