In a maskless particle multibeam processing apparatus, a particle beam is projected through a pattern definition system producing a regular array of beamlets according to a desired pattern, which is projected onto a target which moves at continuous speed along a scanning direction with respect to the pattern definition system. During a sequence of uniformly timed exposure steps the beam image is moved along with the target along the scanning direction, and between exposure steps the location of the beam image is changed with respect to the target. During each exposure step the target covers a distance greater than the mutual distance of neighboring image elements on the target. The location of the beam image at consecutive exposure steps corresponds to a sequence of interlacing placement grids, and after each exposure step the beam image is shifted to a position associated with a different placement grid, with a change of location generally including a component across the scanning direction, thus cycling through the set of placement grids.