A method for processing a transparent workpiece includes directing a laser beam oriented along a beam pathway through an aspheric optical element and the transparent workpiece. The laser beam impinges the aspheric optical element radially offset from a centerline axis of the aspheric optical element by an offset distance of 30% the 1/e2 diameter of the laser beam or greater. The beam pathway and the transparent workpiece are tilted relative to one another such that the beam pathway has a beam pathway angle of less than 90° relative to an impingement surface at the impingement surface and a portion of the laser beam directed into the transparent workpiece is a laser beam focal line having an internal focal line angle of less than 80° relative to the impingement surface, such that a defect with a defect angle of less than 80° is formed by induced absorption within the transparent workpiece.