Optical phased arrays (OPAs) are promising beam-steering devices for various applications such as light detection and ranging, optical projection, free-space optical communication, and optical switching. However, previously reported OPAs suffer from either an insufficient number of resolvable points, or complicated control requirements due to an extremely large number of phase shifters. To solve this issue, we introduce the non-redundant array (NRA) concept to the OPA devices. Based on this design, we can realize high-resolution OPAs whose number of resolvable points scales quadratically with the number of antennas N . In contrast, that of traditional OPAs scales only linearly with N . Thus, a significant reduction in the number of required phase shifters can be attained without sacrificing the number of resolvable points. We first investigate the impact of employing the NRA theoretically by considering the autocorrelation function of the array layout. We then develop a Costas-array-based silicon OPA and experimentally demonstrate 2D beam steering with ∼19,000 resolvable points using only 127 phase shifters. To the best of our knowledge, this corresponds to the largest number of resolvable points achieved by an OPA without sweeping the wavelength.