A new analytical expression for fast calculation of the transient far field of a rectangular baffled piston

In recent years, 3D ultrasound imaging has gained clinical importance. Essential to (cardiac) volumetric 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 (as implemented in e.g. FieldII) 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 underlying reason for this is not only the mere element count but also an inefficient analytical expression of the IR function of an individual element itself. The aim of this study was therefore to derive a new analytical expression to speed up the calculation process. In order to compare accuracy and computation time the IR function of a point of observation, the transducer surface was calculated with the conventional method and the proposed expression implemented in MATLAB. For all points of observation, the IR calculated with the classical and the proposed expression was identical. The mean calculation time however reduced from an average of 24.2ms per spatial position for the classical expression to 0.853ms for the proposed expression resulting in a total speed up of 28.03±1.53times. 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.