Fast numerical scheme of computing acoustic pressure fields for planar circular ultrasound transducers

The velocity potential field and thus the acoustic-pressure field of planar circular ultrasound transducers are theoretically derived. By applying the Hankel transform, the solution of the wave equation induced by the transducer can be expressed as a single integral in which both the wavelength of the emitted ultrasound and the radius of the transducer become mere parameters. Two-dimensional surface and contour plots of acoustic pressure fields for planar circular transducers with different values of a/λ, the ratio of transducer radius to wavelength, are compared with previously published plots calculated by other methods. The comparison reveals that the computational time in obtaining accurate calculations is dramatically reduced for high frequency and/or large transducers.