We fabricate density-modulated two-dimensional electron systems by shallow compensation doping the donor layer of a modulation-doped heterostructure. Zinc acceptor atoms are diffused from the sample surface which is heated by a focused laser beam. Low-temperature magnetotransport experiments provide evidence that high-quality lateral surface superlattices can be fabricated. In weak periodic one-dimensional potentials, commensurability oscillations are recovered, whereas in strong periodic two-dimensional potentials the semiclassically expected antidot resistance resonances are found to dominate the low-field transport. Additionally, the homogeneity of the laser-induced doping is confirmed by magnetic focusing experiments.