Acoustical imaging of vibrating structures using the extended angular spectrum method

A field expansion technique for analyzing the surface velocity patterns of vibrating structures is presented. The technique is based on the angular spectrum method of field analysis. In this approach, acoustic wave propagation between parallel planes is modeled by applying the two-dimensional discrete Fourier transform to a cross section of an acoustic pressure field. The transform decomposes the cross section into plane-wave components, each of which is multiplied by an appropriate phase factor taking into account the propagation distance and the characteristics of the propagation media. The resulting propagated spatial spectrum is then inversely transformed to yield a cross-sectional reconstruction of the field. The technique developed is applicable to both monochromatic and wideband pulsed fields. An experimental system was built to determine the vibrational patterns of complex acoustic radiators. Sources examined included those with circular planar, circular focused, and rectangular phase-steered geometries. The results demonstrate the ability of the extended angular spectrum method to reconstruct accurately the surface velocity distributions of complex vibrating structures