The Method of Superposition for Near-Field Acoustic Holography in a Semi-anechoic Chamber

Abstract

Near-field acoustic holography (NAH) is the process of reconstructing the vibrational behaviour of a structure from measurements of the acoustic field generated by these vibrations. Traditionally NAH was applied to planar regions where Fourier methods can be used to reconstruct the structural vibrations, even at frequencies beyond the sampling resolution limit. The Method of Superposition (MoS) is a relatively simple method for reconstructing the vibrational properties of structures with more general geometries. Recent work has shown that the MoS can also be effectively combined with sparse ℓ ₁ regularisation to generate solutions from only a small number of terms in the superposition. In this work we discuss a reformulation of the MoS for NAH experiments in a semi-anechoic chamber; experiments in fully anechoic chambers can often prove impractical. In particular, we propose a modified Green’s function approach for a semi-infinite domain with a hard reflecting boundary using the Method of Images and present the results of some supporting numerical experiments.