A new analytic expression for fast calculation of the transient near and far field of a rectangular baffled piston

Essential to (cardiac) 3D ultrasound are 2D matrix array transducer technology and the associated (two-stage) beam forming. Given the large number of degrees of freedom and the complexity of this problem, simulation tools play an important role. Hereto, the impulse response (IR) method is commonly used. Unfortunately, given the large element count of 2D array transducers, simulation times become significant jeopardizing the efficacy of the design process. The aim of this study was therefore to derive a new analytical expression to more efficiently calculate the IR in order to speed up the calculation process. To compare accuracy and computation time, the reference and the proposed method were implemented in MATLAB and contrasted. For all points of observation tested, the IR with both methods was identical. The mean calculation time however reduced in average by a factor of 3.93±0.03 times. The proposed IR method therefore speeds up the calculation time of the IR of an individual transducer element while remaining perfectly accurate. This new expression will be particularly relevant for 2D matrix transducer design where computation times remain currently a bottle neck in the design process.