A radially non-symmetric beamforming element for transforming the input energy profile of an input laser beam subject to lateral shift that is variable in radial direction and magnitude into a desired output energy profile of an output laser beam. The beam forming element includes an optical element having a profile transformation function that includes a first profile transformation function for transforming the input energy profile into the desired output energy profile and a profile correction transformation function superimposed on the first profile transformation function for modifying the first profile transformation function to correct distortions in the output energy profile introduced be a lateral shift of the input laser beam. The profile correction transformation function includes a deficiency profile transformation function or a hotspot profile transformation function and an optical axis of the optical element is aligned parallel to the beam axis of the input laser beam and is offset from an unshifted beam axis of the input laser beam by a distance proportionate to a maximum expected lateral shift of the beam axis of the input laser beam.