Quantitative phase retrieval of heterogeneous samples from spectral x-ray measurements

We recently proposed a method for retrieving absorption and phase properties of samples using a set of spectral x-ray measurements obtained in phase enhanced geometries. The spectral measurements can be obtained using state-of-the-art photon counting detectors (PCDs). These detectors permit the use of polychromatic sources and record accurate spectroscopic information in each pixel from a single X-ray exposure. In previous simulations and benchtop experiments we demonstrated that our method can be used to obtain quantitatively accurate absorption and phase properties of samples with effective atomic numbers (Z_eff) that are close to soft tissue. This report expands on those findings to include heterogeneous samples to emulate complex composition in biological materials as well as samples with relatively high Z_eff, such as bones and microcalcifications. Here we also demonstrate that excellent quantitative estimates of multiple object properties can be simultaneously obtained for these heterogeneous samples when spectral data is available. These multi-contrast estimates would allow differentiation of materials that would otherwise be indistinguishable using conventional, absorption contrast imaging. These preliminary results including phase retrieval of Aluminum rod also confirms that the slowly varying phase approximation used in PB-PCI transport of intensity models will not hinder their applicability for complex tissue imaging and small animal imaging.