X-ray phase-contrast imaging with polychromatic sources and the concept of effective energy

Grating-based quantitative polychromatic x-ray phase imaging is currently a very active area of research. It has already been shown that, in such systems, the retrieved differential phase depends upon the spectral properties of the source, the gratings, the detector, and the sample. In this paper, we show that the retrieved sample absorption also depends upon the spectral properties of the gratings. Further, we compare the spectral dependence of both retrieved phase and absorption for the grating interferometer and coded aperture techniques. These results enable us to conclude that in both cases quantitative phase imaging systems cannot be described by an effective energy which is independent of the sample. This has important implications for applications where an absolute measure of phase is important and in tomography.