Rapid calculation of acoustic fields from arbitrary continuous-wave sources

• http://asa.scitation.org/doi/10.1121/1.5021245

Acoustic fields, Green's function, arbitrary shaped transducers, k-Wave

An efficient Greens function solution is derived for calculating the acoustic field generated by phased array transducers of arbitrary shape when driven by a single frequency continuous wave excitation with spatially varying amplitude and phase. The solution is based on the Greens function for the homogeneous wave equation expressed in the spatial frequency domain or k-space. The temporal convolution integral is solved analytically, and the remaining integrals are expressed in the form of the spatial Fourier transform. This allows the acoustic pressure for all spatial positions at any time t > 0 to be calculated in a single step without numerical integration. In total, the extraction of the steady state amplitude and phase of the resulting wave field over the complete 3D domain of interest can be calculated using four fast Fourier transforms. The model is demonstrated through several numerical examples, including single element rectangular and spherically-focused bowl transducers, and multi-element linear and hemispherical arrays.