Data Extrapolation Method Based on Patch Near-Field Acoustic Holography

Near-field acoustical holography (NAH) requires the measurement of the pressure field over a closed surface in order to recover the normal velocity on a nearby concentric surface. It is impractical for large structure when the reconstruction of the field is required only on a partial structure surface. The method of superposition may be applied to reconstruct the field on a partial surface on a structure form measurements made on a nearby limited surface. According to the wave superposition method (WSM), the field on and near the measurement surface may be approximated by the field produced by virtual source points placed on a surface inside the structure. The source strengths are evaluated by applying boundary conditions on the measurement surface. Here, an iterative procedure is applied to extend the measurement surface in order to obtain better reconstruction precision. The algorithm requires the inversion of the Green's function matrix which may be ill-conditioned. Tikhonov regularization method is used to invert it, and the value of the regularization parameter is determined based on use of the L-curve criteria. A numerical simulation of two ball sound sources as an example to validate the results is used. The result of experiment shows the superiority and applicability of the data extrapolation based on patch-NAH.