High-frequency reconstruction of radiation patterns from a rectangular baffled plate using the Helmholtz equation least squares method

Abstract

The Audio Engineering Society (AES) Standards require that full-sphere polar measurements of a sound field be taken at a very fine angular increment (1 deg) to ensure the accuracy in describing high-frequency radiation patterns of a source. This super fine angular resolution coupled with a far-field measurement requirement leads to an excessive number of measurements. For example, at 1 m and 1 degree angular resolution we would need more than 64<th>000 measurement points. To alleviate this difficulty, the HELS (Helmholtz Equation Least Squares)-based near-field acoustical holography is used to reconstruct the radiation patterns. It is shown that HELS can provide accurate reconstruction of radiation patterns for dimensionless frequencies up to ka=25 based on the sound field sampled on a spherical surface at a rate lower than that required by AES Standards. HELS allows for accurate reconstruction even for sample spacing that violates the Nyquist spatial sampling rate in certain directions. In this paper, the convergence of HELS solutions is examined by comparing reconstructed radiation patterns with the analytic solution for a rectangular baffled plate. In particular, the impacts of the number of expansion terms in HELS and measurement points, and that of errors imbedded in the input data on the accuracy of reconstruction are analyzed.