Spectral Phase Contrast Imaging and Phase Retrieval

Phase-contrast X-ray imaging (PCI) can significantly improve the contrast of small and weakly-absorbing materials. This is because of the sensitivity of PCI measurements to changes in both the attenuation and phase of an X-ray wavefield due to interactions with matter. Yet, quantitative estimates of material properties from PCI measurements require the use of phase retrieval (PR) algorithms. Our team developed a capable PR strategy for propagation-based PCI that estimates a pair of material properties from two or more energy-resolved measurements. Part of this work is dedicated to broadening our understanding of the key advantages and practical limitations of our method. To this end, a comprehensive analysis of the underlying theory and the sensitivity to factors such as noise are provided. Based on our findings, we proposed a set of strategies that can help enhance the quality and accuracy of estimated values. We also examined the performance of the PR method with laboratory measurements of a heterogeneous sample. To simultaneously obtain multiple energy-resolved measurements, we used a polychromatic (laboratory) source in combination with high-resolution photon-counting detectors. Our findings demonstrate that the properties of multiple (more than two) unique materials can be estimated with accuracies above 90%. Additionally, our strategy produced results with satisfactory accuracy and image quality even when the detected photon counts were as low as 250 photons per pixel. The underpinning theory in our approach relies on the weak object approximation to simplify the transport-of-intensity equation (TIE). Thus, a section of this work is dedicated to examining the errors related to enforcing the weak object approximation when deriving a TIE-based PR algorithm. We also tested other prevalent methods to simplify the TIE. Experimental results revealed that errors introduced by the weak object approximation were below 5% even for the case of aluminum, which has a relatively high atomic number.