A fast method for computing the acoustic field of ultrasound transducers is presented with application to rectangular elements that are cylindrically focused. No closed-form solutions exist for this case but several numerical techniques have been described in the ultrasound imaging literature. Our motivation is the rapid calculation of imaging kernels for physics-based diagnostic imaging for which current methods are too computationally intensive. Here, the surface integral defining the acoustic field from a baffled piston is converted to a 3-D spatial convolution of the element surface and the Green's function. A 3-D version of the overlap-save method from digital signal processing is employed to obtain a fast computational algorithm based on spatial Fourier transforms. Further efficiency is gained by using a separable approximation to the Green's function through singular value decomposition and increasing the effective sampling rate by polyphase filtering. The tradeoff between accuracy and spatial sampling rate is explored to determine appropriate parameters for a specific transducer. Comparisons with standard tools such as Field II are presented, where nearly 2 orders of magnitude improvement in computation speed is observed for similar accuracy.
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