EFFICIENT ANGULAR SPECTRUM DECOMPOSITION OF ACOUSTIC SOURCES .1. THEORY

The angular spectrum decomposition is evaluated via the two-dimensiona l FFT (2-D-FFT) in terms of plane wave angular range, angular resoluti on, and spatial aliasing error. The algorithm enables the source plane decomposition of normal velocity and pressure fields radiated by tran sducers of aribtrary shape, with significantly faster results achievab le for planar sources. Although the angular spectrum is equally applic able to fields far from the transducer, the efficient calculation here is derived specifically for fields in or very close to the source pla ne. An antialiasing algorithm is proposed that allows the source to be discretized with fewer sample points for a given accuracy than requir ed with simple discretization techniques. Guidelines for the selection of sampling interval, discretization size, etc., are developed on an application-specific (in contrast to a source-specific) basis, and ind icate the best ratio of numerical accuracy to computational cost. Fina lly, the accuracy of the angular spectrum decomposition is evaluated b y comparison to known analytical solutions, and results based on the c omputed angular spectra are presented in detail. The presentation of t his topic is divided into two parts, consisting of the present paper. ''Part 1: Theory,'' and the companion paper, ''Part 11: Results.''