Source visualization by using statistically optimized near-field acoustical holography in cylindrical coordinates

Abstract

Nearfield acoustical holography (NAH) is a useful tool for visualizing noise sources. However, to avoid spatial Fourier transform-related truncation effects, the measurement, or hologram, surface must extend beyond the source to a region where the sound pressure drops to a level significantly lower than the peak level within the measurement aperture. Statistically optimized nearfield acoustical holography (SONAH), first derived by Steiner and Hald in planar geometry, is based on a formulation similar to that of NAH. However, in SONAH, surface-to-surface projection of the sound field is performed by using a transfer matrix defined in such a way that all propagating waves and a weighted set of evanescent waves are projected with optimal average accuracy: i.e., no spatial Fourier transforms are performed. Thus the requirement that the measurement surface be extended is eliminated without compromising the accuracy of the procedure. In the present work, SONAH was re-formulated in cylindrical coordinates and was applied to the measurement of the sound field radiated by a refrigeration compressor. It was found that it is possible to visualize source regions accurately by using SONAH while using fewer measurement positions than would be required to achieve a similar level of accuracy when using conventional NAH procedures.