Fast 3-D Beamforming Methods

Abstract

This chapter describes fast beamforming methods for underwater real-time three-dimensional (3-D) acoustical imaging. Currently underwater real-time 3-D acoustical imaging algorithms focus on fast 3-D beamforming. The basic theory of conventional beamforming methods is described first. Then, the general techniques: dynamic focusing and partial overlapping for underwater real-time 3-D beamforming systems are introduced. Three typical fast beamforming methods: time-domain fast Fourier transform (FFT), chirp zeta transform (CZT), nonuniform fast Fourier transform (NUFFT) are shown. The time-domain FFT beamforming method is only suitable for narrowband uniform two-dimensional (2-D) arrays. Both the CZT and NUFFT beamforming methods is wideband, and work in the frequency domain. The CZT beamforming method is accurate, but only suitable for uniform 2-D arrays or sparse arrays thinned from uniform 2-D arrays. The NUFFT beamforming method is approximate, but suitable for arbitrary 2-D arrays. It is proven that the computation errors of the NUFFT beamforming are neglected for underwater 3-D imaging. In most cases, the computational load of the NUFFT beamforming method is lower than that of the CZT beamforming method.