1. A method for single step x-ray phase contrast imaging, comprising: illuminating an object to be imaged with x-rays; detecting, by a spectral detector, the x-rays passing through the object; providing image data derived from the detected x-rays to an x-ray image processor; processing the image data to decompose x-ray intensity into absorption and phase components using a Transport of Intensity Equation arranged to include electronic cross-sections for Compton scattering and photo-electric emission; and generating a phase image based on the image data.