Efficient calculation of the acoustic radiation from transiently excited uniform and apodised rectangular apertures

An efficient technique for calculating the pressure at arbitrary points in the field of a transiently excited rectangular piston is presented. Emphasis is placed on efficiency and clarity. These properties make it particularly attractive for evaluating the field characteristics of phased array systems comprising a large number of rectangular elements. It is well known that sidelobe levels in the field of an acoustic transducer can be reduced by applying an apodisation function to the source. With this in mind, an extremely efficient extension to the basic technique is presented for determining the diffracted response of a rectangular source possessing an apodisation profile composed of one or more linear apodisation segments. The technique exploits an analytic integral in place of the computationally intensive numerical integral normally employed. Finally, the algorithm has been incorporated into an array model and both theoretical and experimental results for steered phased arrays are presented