Patch nearfield acoustical holography

Abstract

Nearfield acoustical holography (NAH) requires the measurement of the pressure field over a complete surface in order to recover the normal velocity on a nearby vibrating concentric surface. Patch NAH provides a major advancement by eliminating the need for complete surface pressure scans—only a small area needs to be scanned to determine the normal velocity on the corresponding (small area) concentric patch on the vibrator. The theory of patch NAH is based on: (1) an analytic continuation of the patch pressure which provides a spatially tapered aperture extension of the field; and (2) a decomposition of the transfer function (pressure to velocity and/or pressure to pressure) between the two surfaces using the singular value decomposition for general shapes and the fast Fourier transform for planar surfaces. Inversion of the transfer function is stabilized using Tikhonov regularization and the Morozov discrepancy principle. Experimental results show that the normal velocity reconstruction errors (rms) for a point-driven vibrator over 200–2700 Hz average less than 20% for two surfaces 0.4 cm apart. Reconstruction of the active normal acoustic intensity was also achieved, with less than 30% rms error over the frequency band. [Work supported by ONR.]