Imaging or beam-steering systems employing a periodic array of microlenses or micromirrors suffer from diffraction problems resulting from the destructive interference of the beam segments produced by the array. Simple formulas are derived for beam steering with segmented apertures that do not suffer from diffraction problems because of the introduction of a moving linear phase shifter such as a prescan lens before the periodic structure. The technique substantially increases the resolution of imaging systems that employ microlens arrays or micromirror arrays. Theoretical, numerical, and experimental results demonstrating the high-resolution imaging concept using microlens arrays are presented.