Phase Retrieval Methods for Polychromatic Propagation-Based Phase-Contrast X-ray Imaging

X-ray imaging, based on conventional attenuation methods, is employed in various industrial, medical and scientific imaging application. Phase-contrast X-ray imaging is an emerging modality that has shown promise to image and characterize weakly absorbing objects, such as three-dimensional printed plastics and imaging breast tissue. Propagation-based phase-contrast X-ray imaging is the simplest of the existing phase-contrast methods as it does not require any additional optics and can easily be integrated into current X-ray systems that utilize polychromatic X-ray sources. This novel imaging technique requires post-image processing using an algorithm called phase retrieval to extract phase information from the measured intensity. Although propagation-based phase-contrast X-ray imaging offers the simplest setup, it possesses the most mathematically intensive methods to retrieve the phase. Phase retrieval is a nonlinear inverse technique used to estimate the phase shift, thickness or electron density throughout an image. Many of these phase retrieval methods have been developed assuming a monochromatic source, although can be extended to a polychromatic source. This work compares seven phase retrieval methods under various conditions in the presence of a polychromatic source in simulation of different objects and materials. Six of these phase retrieval methods are single-shot algorithms that require only one phase-contrast image; whereas one method is iterative and requires an absorption and phase-contrast image. Each method is derived under different assumptions, but all should produce the same result of retrieved phase shift, thickness or electron density.Overall, Paganin's method performed the best under all test cases and was further applied to experimental data. Polytetrafluoroethylene, varying in thickness and shape, was imaged using a polychromatic source under numerous conditions and Paganin's method was applied to determine its limitations. In general, Paganin's method resulted in a high relative error in experiment, which is not what was seen in simulation. From these results and analysis, sources of error were determined to arise from the detector, the object and/or the spectrum. Isolating the source of error is difficult to accomplish in experiment because it is hard to eliminate certain variables completely. For this reason, further analysis on the sources of error were accomplished in simulation. The effect of material parameters was investigated using different spectrums, source-to-object distances and object-to-detector distances. This research suggests that Paganin's method is highly material dependent and what is considered sufficiently thin for one material may not apply to another material. Generally, a filtered spectrum using 2 mm of aluminum gives the lowest relative error for all materials. Also, the trend between the retrieved thickness and the measured thickness of the object is observed to be polynomial when the object thickness exceeds 100 micron. Further analysis shows that the polychromatic spectrum needs to be well calibrated to give accurate phase or thickness results and using different X-ray sources can affect the error produced by Paganin's method. Paganin's method uses Fourier filtering that allows it to increase the signal-to-noise ratio in an image and, thus, makes the algorithm resilient to noise. This research suggests that although Paganin's method is one of the best phase retrieval methods derived to date, it has its limitations that include imaging thick materials; therefore it may not be the best-suited for industrial imaging where thick plastic objects are imaged for defects. Another limitation of this method is that it is unable to retrieve the thickness of high-density, high-atomic number materials. Finally, it appears that the spectrum utilized in imaging needs to be well characterized and calibrated for Paganin's method to work