On Estimation of Reflection Coefficient to Reconstruct HalfSpace Boundary Impedance and Acoustic Field Directly Radiated from a Source

Abstract

When implementing the reconstruction of the acoustic 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 in situ acoustic impedance measurement techniques. The reconstruction method based on the expansion in half-space spherical wave basis functions, uses a hologram surface and a single reference microphone placed in the near-field to collect acoustic pressures. The acoustic pressure at the reference microphone is reconstructed firstly and the error of the reconstructed pressure relative to the measured pressure is then calculated. The acoustic pressure reflection coefficient corresponding to the minimum error is chosen as the estimation of the reflection coefficient at the measurement points. Thus, this method is applicable to reconstruct the directly radiated acoustic pressures without the knowledge of boundary impedance, free from the in situ acoustic impedance measurement techniques necessary for conventional methods. The purpose of this thesis 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 an acoustic impedance measurement technique implemented via the near-field acoustical holography is proposed. By taking the spherical source as an example, numerical simulations are conducted to verify the proposed method in reconstruction of the boundary impedance and the directly radiated acoustic pressures. The impacts 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.