A wave vector, time-domain method of forward projecting time-dependent pressure fields

A wave vector, time-domain (k−t) method of forward projecting time-dependent pressure fields from complex vibrators is developed using space-time Fourier transform methods. Axisymmetric fields are included as a special case of the general formulation in which a pressure field at one plane can be forward projected to other planes. In brief, a wave vector, time-domain representation of the field at one plane is forward projected via a temporal convolution with a wave vector, time-domain impulse response that is dependent on the projection distance. The projected field is then obtained via the use of an inverse spatial Fourier transform. A numerical study of the method illustrates the accuracy of the approach when implemented using fast Fourier transform (FFT) algorithms. The forward projections of simulated pressure fields from a planar ultrasonic transducer are shown to be in excellent agreement with corresponding results from the use of a time-domain impulse response method.