Optical apparatus includes first and second diffractive optical elements (DOEs) arranged in series to diffract an input beam of radiation. The first DOE is configured to apply to the input beam a pattern with a specified divergence angle, while the second DOE is configured to split the input beam into a matrix of output beams with a specified fan-out angle. The divergence and fan-out angles are chosen so as to project the radiation onto a region in space in multiple adjacent instances of the pattern.