Methods for maintaining a specified beam profile of an x-ray beam extracted from an x-ray target over a large range of extraction angles relative to the target. A beam of electrons is generated and directed toward a target at an angle of incidence with respect to the target, with the beam of electrons forming a focal spot corresponding to the cross-section of the electron beam. At least one of a size, shape, and orientation of the electron beam cross-section is dynamically varied as the extraction angle is varied, and the extracted x-ray beam is collimated. Dynamically varying the size, shape or orientation of the electron beam cross-section may be performed using focusing and stigmator coils.