Prediction of the far-field of a vibrating cylindrical shell using near-field acoustical holography

A long-standing problem with planar and cylindrical near-field acoustical holography is the inaccuracy of the far-field prediction for angles close to the horizon. In cylindrical holography, the subject of this paper, the far-field horizon problem corresponds to the region extending +/- 30 degrees above and below the cylinder axis. This problem arises, particularly at low frequencies, due to the common practice of extension of a measured pressure hologram with zero padding followed by a two-dimensional spatial Fourier transform, the zero padding increasing the number of points within the radiation circle for clarity in the far-field radiation patterns, but at the same time producing a null far-field in the horizon direction. This paper details the horizon problem and its solution using the single and double-layer Helmholtz potential method cast as the equivalent source method (ESM). A finite element method (FEM) numerical experiment covering a wide frequency range modeling an end-capped, framed cylinder is used as the test case. The FEM generates the near-field holograms and the complete far-field, forming the basis of the analysis. It is demonstrated that the ESM method removes the horizon problem completely.