For over one hundred years, the tissue attenuation differences have been the sole contrast mechanism for medical x-ray imaging. However, when x-rays traverse the body parts, as a wave x-rays undergo phase shifts as well. The amount of the phase shift along an exit ray is determined by the tissue refractive indices along the ray. Note that x-ray refractive index, n, is a complex number and equal to n=1-δ + i β, where δ is the refractive index decrement and responsible for x-ray phase shift, while β is the imaginary part of the refractive index and responsible for x-ray attenuation. The amount of x-ray phase shift along an exit ray is given by φ=-(2π/λ)δds, where λ is the x-ray wavelength, and the integral is over the ray path. In other words, the phase shift is equal to the projection of refractive index decrements scaled by a factor (2π/λ). On the other hand, x-ray attenuation along an exit ray is determined by the projection of the tissue linear attenuation coefficients along the ray, which is equal to (4π/λ)βds. We have estimated δ and β values for the biological tissues, and found that the tissue δ and β  values (10-6 - 10-8) and (10-9 -- 10-11) for 10-150 keV x-rays respectively. Hence the differences in x-ray phase shifts between different tissues are about 1000 times greater than their differences in the projected linear attenuation coefficients. Therefore, the phase-contrast imaging techniques may greatly increase the lesion-detection sensitivity for x-ray imaging.

Our research is focused on the inline phase contrast imaging. The settings for the inline phase-sensitive imaging are similar to that of conventional x-ray imaging, provided a source with very small focal spot and a sufficiently large object-detector distance are required.  In the inline imaging setting, x-rays undergo phase-shifts as traversing the imaged object, and then diffract freely over a sufficiently large distance before reaching the detector. In this way the tissues' phase contrast manifests as the dark-bright diffraction fringes at tissues'  boundaries and interfaces in the measured images.  Hence the inline phase contrast imaging has good potential of greatly enhancing the detection sensitivity and reducing radiation doses involved in the imaging.

However, as the interfaces and boundaries of the different tissue compartments are greatly accentuated in a phase-contrast image, the bulk phase contrast in a given tissue compartment, where the phase shifts may vary slowly, could get lost.  This is because the phase contrast is proportional to the Laplacian and gradient differentials of the phase-shifts. Moreover, the information about x-ray phase shifts are valuable for tissue characterizations, since x-ray phase shift along a ray is proportional to the projected tissue electron density, that is, φ=-λre ρeds, where re is the classic electron radius and ρe denotes tissue electron density and the integral is over the ray path. In order to fully exhibit tissue phase contrast and reconstruct tissue projected electron densities for quantitative tissue characterizations, one needs to extract the tissue phase-shifts from the mixed contrast exhibited in a phase-sensitive projection. The procedure of retrieving the phase-shift map of an object from its phase-sensitive projections is called the phase retrieval. A retrieved phase map is able to provide a quantitative map of the object's projected electron densities, which could be used for quantitative tissue characterizations. Moreover, performing phase retrieval is necessary for reconstructing volumetric 3-D maps of tissue attenuation coefficients and refractive indices respectively, and for eliminating the phase-contrast caused artifacts in the volumetric 3-D images. In our research we developed several innovative phase retrieval methods: the phase-attenuation duality based method, and the attenuation partition based method.  These methods has overcome the shortcomings of the phase retrieval methods in the literature.  Our phase-attenuation duality based method of phase retrieval has been adopted by several synchrotron radiation research groups in the world for implementing the quantitative phase contrast computed tomography.