On the design of one-dimensional sparse arrays with apodized end elements

In ultrasound scanners, a two-way radiation pattern is generated by a transmit array and a receive array. The design of such arrays is simplified by treating the problem as the design of an “effective aperture function” w
_eff
(n) which is given by the convolution of the transmit aperture function w
_T
(n) and the receive aperture function w
_R
(n). In this paper we consider the design of one-dimensional sparse transmit and receive arrays with an apodized effective aperture function. The design approach is based on the factorization of a polynomial representation of the effective aperture function.