Acoustic field prediction for a single planar continuous-wave source using an equivalent phased array method

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Abstract
Phased array theory is combined with the Rayleigh–Sommerfeld diffraction integral to predict measured acoustic fields generated by a single-source ultrasonic transducer. The idea is to treat a single-source as a “phased array,” which is composed of many small elements. The goal is to find the excitation source for the phased array, that is, the amplitude and phase for each array element, which produces an acoustic field similar to the experimentally measured field generated by the single-source transducer. A pressure field measured at a given plane parallel and close to the face of the transducer in degased water was used to calculate the excitation source of the equivalent phased array using an inverse technique. The excitation source of the equivalent phased array was then used to calculate the acoustic field from this measurement plane to the far field. It was demonstrated that this phased array approach accurately predicted the location of major grating lobes and the general distributions of the near and far pressure fields for four different transducers. This equivalent phased array method (EPAM) used to model a single-source transducer should be useful in both diagnostic and therapeutic ultrasound applications.

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