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 several branches, multiple phase gratings and multiple analyzer gratings such that at each branch, one phase grating and one analyzer grating are fixed as a grating set which is configured to function as a shearing interferometer, wherein for each grating set the relative position of the phase grating and the analyzer grating is fixed; said grating system is configured such that x-rays from the x-ray source which have passed through the object pass through a phase grating; said grating system is configured such that x-rays which have passed through the phase grating pass through an analyzer grating; wherein the grating system is mounted on a dial adapted to rotate the grating system to successively align the grating set of each branch with the optical axis of the x-ray beam; and wherein the relative displacement between the phase gratings and the analyzer gratings ranges from a small fraction of the period of the analyzer grating to one grating period across the branches to produce different phase steps for each branch; 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 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, wherein the computer system is further configured to perform three-dimensional cone beam reconstruction from the subtracted DPC images, to output a 3D reconstruction matrix of a distribution of linear phase coefficient in accordance with the 3D reconstruction, and to generate images from the 3D matrix. 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 several branches, multiple phase gratings and multiple analyzer gratings such that at each branch, one phase grating and one analyzer grating are fixed as a grating set which is configured to function as a shearing interferometer, wherein for each grating set the relative position of the phase grating and the analyzer grating is fixed; said grating system is configured such that x-rays from the x-ray source which have passed through the object pass through a phase grating; said grating system is configured such that x-rays which have passed through the phase grating pass through an analyzer grating; wherein the grating system is mounted on a dial adapted to rotate the grating system to successively align the grating set of each branch with the optical axis of the x-ray beam; and wherein the relative displacement between the phase gratings and the analyzer gratings ranges from a small fraction of the period of the analyzer grating to one grating period across the branches to produce different phase steps for each branch; 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 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, wherein the computer system is further configured to perform three-dimensional cone beam reconstruction from the subtracted DPC images, to output a 3D reconstruction matrix of a distribution of linear phase coefficient in accordance with the 3D reconstruction, and to generate images from the 3D matrix.