A system for imaging an object, the system comprising: a source of an imaging beam; an imaging detector in a path of the imaging beam; a grating system comprising: a steppable source grating between the source and the object position, and a phase grating and an analyzer grating between the object position and the detector, wherein the positions of the phase grating and the analyser grating are fixed during imaging; a gantry configured to rotate the source, the detector, and the grating system around the object position; wherein the steppable source grating is configured to present different grating parameters at different times during imaging of the object, a computer system configured to control at least the source, the detector and the grating system to (a) obtain background images acquired at different view angles relative to gantry rotation without the object at the object position; (b) acquire raw projection images of the object at different view angles relative to gantry rotation by differential phase contrast imaging process using the source, the detector, and the grating system; (c) acquire corrected projection images by using the background images to diminish background effects on the raw projection images; the computer system being further configured to perform a three-dimensional computer tomography reconstruction of the object using the corrected projection images; and a display configured to display images of the object derived from the reconstruction; wherein the steppable source grating comprises plural individual gratings sequentially placed in a path of the imaging beam for said acquiring of the raw projection images, and the acquiring of the raw projection images comprises rotating the gantry in a succession of subscans and wherein the steppable source grating presents a different grating parameter and a different individual grating to the imaging beam for each subscan such that the relative displacement between the source grating and the phase-analyzer grating pair (106,108) ranges from a small fraction of the period of the source grating to one grating period across different branches during imaging. a source of an imaging beam; an imaging detector in a path of the imaging beam; a grating system comprising: a steppable source grating between the source and the object position, and a phase grating and an analyzer grating between the object position and the detector, wherein the positions of the phase grating and the analyser grating are fixed during imaging; a steppable source grating between the source and the object position, and a phase grating and an analyzer grating between the object position and the detector, wherein the positions of the phase grating and the analyser grating are fixed during imaging; a gantry configured to rotate the source, the detector, and the grating system around the object position; wherein the steppable source grating is configured to present different grating parameters at different times during imaging of the object, a computer system configured to control at least the source, the detector and the grating system to (a) obtain background images acquired at different view angles relative to gantry rotation without the object at the object position; (b) acquire raw projection images of the object at different view angles relative to gantry rotation by differential phase contrast imaging process using the source, the detector, and the grating system; (c) acquire corrected projection images by using the background images to diminish background effects on the raw projection images; (a) obtain background images acquired at different view angles relative to gantry rotation without the object at the object position; (b) acquire raw projection images of the object at different view angles relative to gantry rotation by differential phase contrast imaging process using the source, the detector, and the grating system; (c) acquire corrected projection images by using the background images to diminish background effects on the raw projection images; the computer system being further configured to perform a three-dimensional computer tomography reconstruction of the object using the corrected projection images; and a display configured to display images of the object derived from the reconstruction; wherein the steppable source grating comprises plural individual gratings sequentially placed in a path of the imaging beam for said acquiring of the raw projection images, and the acquiring of the raw projection images comprises rotating the gantry in a succession of subscans and wherein the steppable source grating presents a different grating parameter and a different individual grating to the imaging beam for each subscan such that the relative displacement between the source grating and the phase-analyzer grating pair (106,108) ranges from a small fraction of the period of the source grating to one grating period across different branches during imaging.