Efficient angular spectrum decomposition of acoustic sources. I. Theory.

The angular spectrum decomposition is evaluated in terms of plane wave angular range, angular resolution, and spatial aliasing error using two-dimensional FFT (2-D FFT). The algorithm makes possible the source plane decomposition of normal velocity and pressure fields radiated by transducers of arbitrary shape, with significantly faster results achievable for planar sources. Although the angular spectrum is equally applicable to fields far from the transducer, the efficient calculation is derived specifically for fields in or very close to the source plane. An antialiasing algorithm is proposed that allows the source to be discretized with fewer sample points for a given accuracy than required with simple discretization techniques. Guidelines for the selection of sampling interval, discretization size, etc. are developed on an application-specific basis and indicate the best ratio of numerical accuracy to computational cost.