Second order x-ray in-line phase-contrast imaging

X-ray phase imaging is sensitive to structural variation of soft tissue, and offers excellent contrast resolution for characterization of cancerous tissues. Also, the cross-section of x-ray phase shift is a thousand times greater than that of x-ray attenuation in soft tissue over the diagnostic energy range, allowing a much higher signal-to-noise ratio at a substantially lower radiation dose than attenuation-based x-ray imaging. In this paper, we present a second order approximation model with respect to phase shift based on the paraxial Fresnel-Kirchhoff diffraction theory, and also discuss in-line dark-field imaging based on the second order model. This proposed model accurately establishes a quantitative correspondence between phases and recorded intensity images, outperforming the linear phase approximation model widely used in the conventional methods of x-ray in-line phase-contrast imaging. This new model can be iteratively solved using the algebraic reconstruction technique (ART). The state of the art compressive sensing ingredients can be incorporated to achieve high quality image reconstruction. Our numerical simulation studies demonstrate the feasibility of the proposed approach that is more accurate and stable, and more robust against noise than the conventional approach.