Radiated fields of a circular transducer and a time-delay spherically focused transducer array are analyzed and compared using classical impulse response method and finite element analysis. In the first approach, the velocity potential at an observation point is expressed as the convolution of the excitation velocity and the impulse response, while the pressure is obtained by the differentiation of the velocity potential. The impulse response for an array is expressed as the superposition of those of a series of circular pistons and is dependent on the observation point and piston/array structure. The finite element method starts with the formulation for elastic waves, and the pressure fields are obtained through the pressure analog method. No paraxial or farfield approximation is needed and excellent agreement is observed between results from the two methods.
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