Dp. Orofino et Pc. Pedersen, EFFICIENT ANGULAR SPECTRUM DECOMPOSITION OF ACOUSTIC SOURCES .1. THEORY, IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 40(3), 1993, pp. 238-249
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.''