An original laser-radiation beam having a symmetrical M2 but poor beam quality is sliced in one transverse axis, by a fanned-out stack of parallel transparent plates, into a plurality of beam slices. The beam-slices are also spread by the stack of plates in another transverse axis perpendicular to the first axis. A fanned-out stack of glass blocks aligns the spread beam-slices in the first axis to form what is effectively a single beam having an asymmetric M2, with beam quality improved in one axis and degraded in the other compared with the original beam. The effective single beam is projected into a line of radiation by a cylindrical lens, or by a homogenizing projector including spaced apart cylindrical lens arrays followed by a spherical condenser lens.