A method and system are disclosed for producing an x-ray image of a sample using a lamella-shaped target to improve the usual tradeoff between imaging resolution and image acquisition time. A beam of electrons impacts the lamella-shaped target normal to the narrower dimension of the lamella which then determines the virtual source size along that axis. For low-energy x-ray generation, the small electron penetration depth parallel to the wider dimension of the lamella determines the virtual source size along that axis. Conductive cooling of the target is improved over post targets with the same imaging resolution. The lamella-shaped target is long enough to ensure that the electron beam does not impact the support structure which would degrade the imaging resolution. Target materials may be selected from the same metals used for bulk or post targets, including tungsten, molybdenum, titanium, scandium, vanadium, silver, or a refractory metal.