A method for dark-field imaging includes acquiring dark-field image projections of an object with an imaging apparatus that includes an x-ray interferometer, applying a pressure wave having a predetermined frequency to the object for each acquired projection, wherein the predetermined frequency is different for each projection, and processing the acquired projections, thereby generating a 3D image of the object. In other words, the method corresponds to acoustically modulated X-ray dark field tomography. An imaging system (400) includes a scanner (401) configured for dark-field imaging, the scanner including: a source/detector pair (402/408) and a subject support (416), a pressure wave generator (420) configured to generate and transmit pressure waves having predetermined frequencies, and a console (424) that controls the scanner and the pressure wave generator to acquire at least two dark-field projection of an object with different pressure waves having different frequencies applied to the object.
