Patch near-field acoustical holography in cylindrical geometry

Abstract

Spatial discrete Fourier transform-based near-field acoustical holography is known to suffer from windowing effects since the measurement aperture is necessarily finite. The latter effect can be mitigated by using patch holography, in which the measured field is extended beyond the measurement aperture based on successive smoothing operations. In this article, the application of a patch holography algorithm to cylindrical geometries is described. In planar geometry, initial zero-padding can be applied to the hologram pressure to an arbitrary degree in both in-plane directions since the pressure magnitude is expected to limit ultimately towards zero in both directions. In a cylindrical geometry, zero-padding can be implemented axially in the same way, but the number of zeros added in the circumferential direction is necessarily determined by the angular sample spacing owing to the periodic nature of the field in this direction. By using both numerical simulation and experimental results, it is shown that the patch extrapolation procedure works well in the cylindrical case, and a discussion of rigid reflecting boundaries is also included. Finally, reconstruction results obtained by the combined use of pressures measured in the finite aperture and two different regularization parameter selection techniques are compared, and the effect of projection distance is discussed.