Quantification of the Effect of Array Element Pitch on Imaging Performance

This paper investigates how the pitch of elements in periodic ultrasonic arrays is related to their imaging performance, with particular emphasis on imaging artefacts (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 artefacts are always present at some level, and practical array design is therefore based on suppressing grating lobe artefacts to a level appropriate to a given application. In the current 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 artefacts to be unambiguously quantified. Numerical simulations are used to analyse the performance of one-dimensional 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.