Propagation-based phase-contrast X-ray imaging is the earliest developed phase-contrast X-ray imaging method, however, it requires mathematically intensive algorithms to retrieve phase information. For quantitative analysis, an algorithm called phase retrieval must be applied to the phase-contrast image to retrieve the phase information because the phase and the attenuation coefficient are encoded in the intensity values obtained by the detector. Phase retrieval is a nonlinear inverse technique used to estimate the object X-ray phase shift, thickness or electron density. Many of these phase retrieval methods have been developed assuming a monochromatic X-ray source, although some have been reported to work for a polychromatic X-ray source with some modifications. In this work, we compare seven reported phase retrieval methods for polychromatic sources using a weighted average to calculate the wavelength dependent parameters. Six of the methods compared are single distance approaches and one is an iterative approach that requires an absorption and phase-contrast image. These seven phase retrieval methods are compared for varying object thicknesses in the presence of a polychromatic source in simulation of different materials. The materials investigated in this work are polytetra uorethylene, polystyrene and Kapton. Overall, Paganin's method performed with the lowest relative error for all materials when a polychromatic source is applied to object thicknesses less than 400 microns.
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