It is widely accepted that a two-dimensional array would be advantageous in medical ultrasound imaging. Such an array would be steerable in both the azimuth and elevation directions. One of the limitations on the practicality of two-dimensional arrays is the electronic channel count. Simple brute force extension of conventional systems to such large systems is not practical. Increasing the number of connections to the transducer elements through the coaxial cable to the probe becomes prohibitive. Increasing the electronics of conventional beamforming systems by a factor of four or eight would be expensive and excessively power consuming. By duplexing, it is possible to double the number of effective channels; however, there is a need for further reduction in the number of channels needed to achieve a practical two-dimensional array. T. T. Taylor [1], [2] synthesis procedure for linear and circular apertures is widely used for the design of many radars with linear, rectangular or circular apertures that need side lobe controls [3]. The Taylor method provides a nearly ideal pattern for realizable illumination of the aperture, and removes the deficiencies of classical Chebyshev arrays [4]. Further, the method has found application in related fields, e.g. pulse compression or filter design, where windowing is essential. The success of the method is due primarily to the simplicity of the procedure. Elliptical apertures and the corresponding analysis have not received great attention despite the wide potential application of elliptical aperture synthesis in modern radar applications, modern communication applications and reflector antennas [5], [6], [7]. This may be due to the unavailability of simple design procedures for synthesis of elliptical arrays or apertures. In this paper we describe a new method of circular and elliptical aperture synthesis useful in ultrasonic imaging system, for a sparse array of transducer elements steerable in two dimensions. The elements are located at selected positions on a regular grid in such a way as to reduce the side lobe levels produced by the array. We use deterministic space tapering as opposed to random placement [5]. The sparse population of the grid positions reduces the number of electronic channels needed to process the signal to and from the transducer elements. This thinning and space tapering is accomplished by a flexible, rapid procedure that optimizes the array for all steering angles. The array design is based on analytic solutions of aperture integral equations. Side lobe control is achieved by controlling the illumination of the aperture. This illumination ultimately corresponds to the density of the elements in the sparse array, with each element of the array having uniform amplitude for maximum efficiency or signal-to-noise ratio. The design goal is to produce side lobes, which are uniform around the main beam and decay asymptotically. The aperture of the transducer array is discretized into a grid in two steps. First, a continuous aperture is discretized as a set of concentric rings. Next each ring is replaced by a set of transducer elements. To determine the number of elements on each ring, a technique of zero sampling is developed. it is an iterative numerical technique derived along the original work of Taylor, but more effective. for side lobe control. Space tapering is accomplished in a manner which improves the side lobe level relative to that of the fully populated array. Another advantage of the synthesis is that the array design is valid for wideband operation centered on the design center frequency. The side lobe performance does not deteriorate when a pulsed signal is used far ultrasound imaging and, in some cases, is enhanced thereby. Examples are given for circular and elliptical aperture with high degree of thinning. The performance of these cases under wideband operation is found to be quite satisfactory.
