Radiation pattern of a focused transducer: a numerically convergent solution.

The radiation pattern of a focused transducer is reexamined. The radiation field is divided into an illuminated zone and a shadow zone. A numerically convergent solution of the pressure distribution in terms summations of Bessel functions is provided. This solution is computationally more advantageous than earlier results where a double or single integral in the complex plane is required. The pressure amplitude differs from earlier reports slightly for off-axis locations at low frequency. This difference may have significance for backscatter coefficient determination where scatterers are assumed present over a time-gated volume. The solution for a flat disk radiator is obtained as a limiting case.