The current invention relates to writing or reading a pattern on a surface, such as in microlithography or inspection of mircrolithographic patterns. In particular, Applicant discloses systems recording or reading images by scanning sparse 2D point arrays or grids across the surface, e.g., multiple optical, electron or particle beams modulated in parallel. The scanning and repeated reading or writing creates a dense pixel or spot grid on the workpiece. The grid may be created by various arrays: arrays of light sources, e.g., laser or LED arrays, by lenslet arrays where each lenslet has its own modulator, by aperture plates for particle beams, or arrays of near-field emitters or mechanical probes. For reading systems, the point grid may be created by a sparse point matrix illumination and/or a detector array where each detector element sees only one spot. The idea behind the use of large arrays is to improve throughput. However, the throughput does not scale with the array size, since above a certain size of arrays, previously known schemes fall into in their own tracks and start repeating the same data over and over again. This application discloses methods to scan workpieces with large arrays while preserving the scaling of throughput proportional to array size, even for very large arrays, in fact essentially without limits.