X–ray phase imaging utilizes a variety of techniques to render phase information as intensity contrast and these
intensity images can in some cases be processed to retrieve quantitative phase. A subset of these techniques
use free space propagation to generate phase contrast and phase can be recovered by inverting differential
equations governing propagation. Two techniques to generate quantitative phase reconstructions from a single
phase contrast image are described in detail, along with regularization techniques to reduce the influence of
noise. Lastly, a recently developed technique utilizing a binary–amplitude grid to enhance signal strength in
propagation–based techniques is described.
We demonstrate a quantitative X-ray phase contrast imaging (XPCI) technique derived from propagation dependent phase change. We assume that the absorption and phase components are correlated and solve the Transport of Intensity Equation (TIE). The experimental setup is simple compared to other XPCI techniques; the only requirements are a micro-focus X-ray source with sufficient temporal coherence and an X-ray detector of sufficient spatial resolution. This method was demonstrated in three scenarios, the first of which entails identification of an index-matched sphere. A rubber and nylon sphere were immersed in water and imaged. While the rubber sphere could be plainly seen on a radiograph, the nylon sphere was only visible in the phase reconstruction. Next, the technique was applied to differentiating liquid samples. In this scenario, three liquid samples (acetone, water, and hydrogen peroxide) were analyzed using both conventional computed tomography (CT) and phase contrast CT. While conventional CT was capable of differentiating between acetone and the other two liquids, it failed to distinguish between water and hydrogen peroxide; only phase CT was capable of differentiating all three samples. Finally, the technique was applied to CT imaging of a human artery specimen with extensive atherosclerotic plaque. This scenario demonstrated the increased sensitivity to soft tissue compared to conventional CT; it also uncovered some drawbacks of the method, which will be the target of future work. In all cases, the signal-to-noise ratio of phase contrast was greatly enhanced relative to conventional attenuation-based imaging.