Quantitative phase retrieval of multi-material heterogeneous objects from spectral X-ray measurements

We recently proposed a simple yet robust method to retrieve the complete refractive properties of a sample from a single phase-enhanced spectroscopic X-ray measurement, which can be obtained using photon counting detectors. The idea was demonstrated via simulations and bench-top lab experiments for two prominent phase contrast imaging techniques, i.e. free-space propagation and coded aperture. Unlike some popular alternatives, our method is not restricted to overly simplified geometries and homogeneous materials in order to yield quantitative results. The only requirement is a set of well-constrained values that accurately describe the effective energies corresponding to each measurement. A persisting challenge with this approach relates to the photon count starvation caused by energy binning, which typically deteriorates the signal-to-noise ratio of the data. Another challenge involves the accuracy of retrieved quantities when dealing with heterogeneous objects, particularly when different constituents demonstrate significantly different properties. This work will illustrate how our technique and its implementation address these two problems.