This paper investigates how the pitch of elements in periodic ultrasonic arrays is related to their imaging performance, with particular emphasis on imaging artifacts (grating lobes) arising from discrete spatial sampling. Although the classical Nyquist rules for array element pitch are well known, they only provide the limiting condition needed to eliminate grating lobes from an array with an infinitely large aperture at a single frequency. Physical arrays have finite-sized apertures and most applications employ broadband pulses. For these reasons, grating lobe artifacts are always present at some level, and practical array design is, therefore, based on suppressing grating lobe artifacts to a level appropriate to a given application. In this paper, a theoretical framework is developed that enables the point spread function of a periodic imaging array to be decomposed into the sum of contributions from a main lobe and different orders of grating lobes, thus allowing grating lobe artifacts to be unambiguously quantified. Numerical simulations are used to analyze the performance of 1-D linear arrays in both far-field (steering only) and near-field (focusing only) scenarios, and design guidelines are deduced. It is shown that in general, the classical Nyquist rules are overly conservative and that the pitch of an array can be increased without significantly compromising image quality, provided that certain constraints on ray angles are implemented in the imaging algorithm. Experimental examples are shown that illustrate the practical application to arrays in two configurations.