Forward and backward projection of acoustic fields using FFT methods

The forward and backward propagation of harmonic acoustic fields using Fourier transform methods is presented. In particular, the forward propagation of a velocity distribution to obtain a pressure field and the backward propagation of a pressure field to obtain a velocity distribution are addressed. Numerical examples are presented to illustrate the nearfield behavior of the pressure field from complex planar vibrators, e.g,—an ultrasonic transducer or plate, with nonuniform velocity distributions. The numerical results, which were obtained via the use of FFT algorithms, are presented for vibrators which are operating above and below coincidence. These results illustrate the acoustic nearfield as a function of distance from the vibrator. Numerical results are also presented to illustrate the backward projection method. The pressure field of a 3×3 focused array is back projected to obtain the velocity distribution for several cases of interest. These results illustrate the utility of the transform method and the effect of spatial windows or filters in its implementation using FFT algorithms.