Discrete approximations of acoustic source distributions

The modeling of source distributions of finite spatial extent in ultrasound and medical imaging applications is a problem of longstanding interest. In time domain methods, such as the finite difference time domain or pseudospectral approaches, one requirement is the representation of such distributions over a grid, normally Cartesian. Various artefacts, including staircasing errors, can arise. In this short contribution, the problem of the representation of a distribution over a grid is framed as an optimisation problem in the Fourier domain over a preselected set of grid points, thus maintaining control over computational cost, and allowing the fine tuning of the optimisation to the wavenumber range of interest for a particular numerical method. Numerical results are presented in the important special case of the spherical cap or bowl source.