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The Spatial Impulse Response (SIR) method has difficulty numerically evaluating the imaging pattern of annular ultrasonic transducer arrays. An alternative algorithm based on the direct solution of the Rayleigh integral has been developed, and this successfully evaluates the annular array pattern with good efficiency and accuracy. Furthermore, in combination with FEA this method gives good results when compared to practical results

Direct Solution of the Rayleigh Integral to Obtain the Radiation Pattern of an Annular Array Ultrasonic Transducer