Evaluation of the angular spectrum approach for simulations of near-field pressures

The implementation of the angular spectrum approach based on the two-dimensional fast Fourier transform is evaluated for near-field pressure simulations of square ultrasound transducers, where the three-dimensional pressure field is calculated from the normal velocity distribution on the transducer surface. The pressure field is propagated in the spatial frequency domain with the spatial propagator or the spectral propagator. The spatial propagator yields accurate results in the central portion of the computational grid while significant errors are produced near the edge due to the finite extent of the window applied to the spatial propagator. Likewise, the spectral propagator is inherently undersampled in the spatial frequency domain, and this causes high frequency errors in the computed pressure field. This aliasing problem is alleviated with angular restriction. The results show that, in nonattenuating media, the spatial propagator achieves smaller errors than the spectral propagator after the region of interest is truncated to exclude the windowing error. For pressure calculations in attenuating media or with apodized pistons as sources, the spatial and spectral propagator achieve similar accuracies. In all simulations, the angular spectrum calculations with the spatial propagator take more time than calculations with the spectral propagator.