1. A device for imaging an object, the device comprising: a gantry frame; at least one motor for moving the gantry frame for a data acquisition geometry; an x-ray source disposed on the gantry frame to be on a first side of the object; a grating system disposed on the gantry; said grating system comprising a phase grating, so that x-rays from the x-ray source which have passed through the object pass through the phase grating; said grating system further comprising an analyzer grating, so that x-rays which have passed through the phase grating pass through the analyzer grating; an x-ray detector on the gantry frame, disposed so that x-rays which have passed through the analyzer grating are incident on the x-ray detector, for producing a signal in response to the x-rays which are incident on the x-ray detector; and a computer system, in communication with the gantry, x-ray source, the grating system and the detector, for controlling the gantry motion, x-ray emission, and grating system movement and for analyzing the signal from the x-ray detector to image the object; wherein the grating system is configured to produce a plurality of phase steps, and wherein the computer system is configured such that an intensity image is acquired for each phase step, from which a differential phase-contrast (DPC) image is calculated using the phase stepping algorithm; both background DPC images and object DPC images are obtained, and the background DPC image is subtracted from the object DPC image to generate the subtracted DPC images for reconstruction; and wherein the gantry, controlled by the computer system, moves the x-ray source, the grating system and the detector around the object to take a plurality of subtracted DPC images at different view angles, performing three-dimensional (3D) cone beam reconstruction in the computer system from the subtracted DPC images, outputting a 3D reconstruction matrix of a distribution of linear phase coefficient in accordance with the 3D reconstruction, and generating images from the 3D matrix in the computer system.