Intrinsic Spatial Resolution Limit in Analyzer-Based X-Ray Phase Contrast Imaging Technique
Dynamical diffraction effects always play a role when working with perfect single crystals. The penetration of X-rays respect to the surface normal during diffraction (extinction depth, $1/\sigma_e$) in perfect single crystals does not have a constant value. The value changes for different angular positions on the crystal diffraction condition. For higher X-ray energies this value can change from few micrometers to tens of millimeters for each different crystal angular position in the small angular range of the diffraction condition. This effect may spread a single point in the object (sample) as a line in the image detector, especially if the crystal is set (or if the sample angularly deviates the beam) at lower diffraction angle positions, where the surface component of X-ray penetration can achieve huge values. Then, for imaging experiments where the dynamical diffraction occurs, such intrinsic property can affect the image resolution. We have modeled and experimentally checked such a dynamical diffraction property using, as example, an Analyzer-based X-ray phase contrast imaging setup (ABI) at two different X-ray energies: 10.7 keV and 18 keV. The results show that our theoretical model is consistent with the measured results. For higher energies the blur effect is enhanced and intrinsically limits the image spatial resolution.