Abstract: Numerous embodiments are disclosed. In one, a laser-processing apparatus includes a positioner arranged within a beam path along which a beam of laser energy is propagatable. A controller may be used to control an operation of the positioner to deflect the beam path within first and second primary angular ranges, and to deflect the beam path to a plurality of angles within each of the first and second primary angular ranges. In another, an integrated beam dump system includes a frame; and a pickoff mirror and beam dump coupled to the frame. In still another, a wavefront correction optic includes a mirror having a reflective surface having a shape characterized by a particular ratio of fringe Zernike terms Z4 and Z9. Many more embodiments are disclosed.