Reconstruction of half-space boundary impedance and sound source direct radiation based on reflection coefficient estimation

Abstract

When implementing the reconstruction of the sound field directly radiated from a source located in a half-space, the half-space basis functions with boundary impedance as a parameter, need to be formulated. And the boundary impedance is usually obtained via <i>in situ</i> sound impedance measurement techniques. In the reconstruction method based on the expansion in half-space spherical wave basis functions, a hologram surface and a single reference microphone placed in the near-field are used to collect sound pressures. The sound pressure at the reference microphone is first reconstructed and the error of the reconstructed pressure relative to the measured pressure is then calculated. The sound pressure reflection coefficient corresponding to the minimum error is chosen as the measure of the reflection coefficient at the measurement point. Thus, this method is applicable to reconstructing the directly radiated sound pressures without the knowledge of boundary impedance, free from the in situ sound impedance measurement techniques necessary for conventional methods. The purpose of this work is to discuss the various parameters affecting the accuracy of reconstruction. Moreover, the boundary impedance is reconstructed based on the estimation of the reflection coefficient, so that a sound impedance measurement technique implemented via the near-field acoustical holography is proposed. By taking the spherical source for example, numerical simulations are conducted to verify the proposed method of reconstructing the boundary impedance and the directly radiated sound pressures. The influences of reference microphone coordinate, the effective flow resistivity of the boundary, and the rate of decrease of porosity with depth of the boundary on the accuracy of reconstruction are quantitatively analyzed.