Optimal selection of parameters for the angular spectrum approach to numerically evaluate acoustic fields

Optimal selection of parameters is presented for the angular spectrum approach (ASA) to the numerical calculation of acoustic fields radiated by planar transducers and linear arrays with and without focusing. The parameters include spatial sampling interval, discretization size of a source plane in which a source is located, and the angular range over which the plane waves decomposed from the source using the discrete Fourier transform (DFT) are chosen to superimpose and construct the fields. The concept of instantaneous frequency is applied to the Fourier transformed Green’s function to determine the angular range of the plane waves used for the construction with minimal spatial aliasing error. Based on the minimization of spatial frequency and spatial aliasing errors in a constructed field, optimal selection of the parameters is worked out. The ASA with the optimal selection is then applied to computing the fields radiated by planar transducers and linear arrays into water and a layered (oil/water) medium. The results demonstrate that the methods proposed in this paper to select the parameters for the ASA allow the aliasing errors to effectively eliminate and thus yield the best computational accuracy for the parameters selected.