Advances in nearfield acoustical holography (NAH) algorithms I. Green's functions

Abstract

For efficiency, the spatial processing algorithms of NAH, based on Rayleigh's integrals, utilize the fast Fourier transform (FFT). In NAH, the FFT has been treated as an approximation to the continuous Fourier transform, and with this view, work has been done to reduce the errors introduced by the finite and discrete FFT. In this paper, it is shown that, by using the exact discrete convolution capabilities of the FFT and inverse FFT, as opposed to its approximate correspondence to the continuous Fourier transform, algorithms yielding more accurate results are obtained. The essential step is to replace the continuous field over the surface from which the data was gathered with a piecewise constant field, each patch having the constant field value as at a contained, measured point. With the field so replaced, Rayleigh's integral is reduced to a finite, discrete convolution of the measured data with the integrals of the kernel, or Green's function, over each path. Most importantly, this proces totally elimin...