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\udEdge illumination (EI) X-ray phase-contrast imaging (XPCI) has potential for applications in different fields of research, including materials science, non-destructive industrial testing, small-animal imaging, and medical imaging. One of its main advantages is the compatibility with laboratory equipment, in particular with conventional non-microfocal sources, which makes its exploitation in normal research laboratories possible. In this work, we demonstrate that the signal in laboratory implementations of EI can be correctly described with the use of the simplified geometrical optics. Besides enabling the derivation of simple expressions for the sensitivity and spatial resolution of a given EI setup, this model also highlights the EI's achromaticity. With the aim of improving image quality, as well as to take advantage of the fact that all energies in the spectrum contribute to the image contrast, we carried out EI acquisitions using a photon-counting energy-resolved detector. The obtained results demonstrate that this approach has great potential for future laboratory implementations of EI

Laboratory implementation of edge illumination X-ray phase-contrast imaging with energy-resolved detectors