Computationally efficient sound field calculations for a circular array transducer

A computationally efficient method is presented for calculating field pressure distributions from a circular phased array transducer. This method employs a form of the rectangular radiator approach modified for use with the geometry of a circular array. The curved surface of the elements, radiating either continuous wave or pulsed excitation signals, is divided into incremental rectangular areas small enough so that the Fraunhofer approximation can be applied. Once the directivity of a single element is found, the array beam pattern can be calculated using superposition and suitable coordinate transformations. The validity of this approach is verified through comparisons with experimental data from a circular phased array. The results show that the location and amplitude of the grating lobes and main lobe width can be predicted with reasonable accuracy by using this method.