Analysis of the numerically implemented angular spectrum approach based on the evaluation of two-dimensional acoustic fields. Part I. Errors due to the discrete Fourier transform and discretization

Abstract

The numerically implemented angular spectrum approach (ASA) is investigated based on the evaluation of the 2-D fields radiated by striplike planar sources and 1-D focusing linear-phased arrays with different aperture sizes and on the comparison with those obtained by using the analytical solution derived with the point spread function method. Since the discrete Fourier transform (DFT) of a finite-size source produces an angular spectrum with spatial frequency aliasing and discretization of the source in even-numbered samples causes a half-sample length phase shift error in the angular spectrum, the effects of the aliasing and the phase shift on calculation accuracy are dealt with. The results show that the frequency aliasing causes an overestimation of the near field and the phase shift distorts the results. A numerical algorithm for eliminating the aliasing is proposed and correction of the phase shift is confirmed to be necessary. The algorithm proposed can completely remove the errors and obtain exact results. The methods used in this paper can be directly applied to the case of 3-D fields. The investigation of the characteristics of the numerically implemented ASA as a function of angular range is carried out in the companion paper [P. Wu, R. Kazys, and T. Stepinski, ‘‘Analysis of the numerically implemented angular spectrum approach based on the evaluation of two-dimensional acoustic fields. Part II. Characteristics as a function of angular range,’’ J. Acoust. Soc. Am. 99, 1349–1359 (1996)].