Galerkin equivalent sources method for sound field reconstruction around diffracting bodies

The rising interest for three-dimensional acoustic imaging requires the improvement of the numerical models describing the propagation between a radiating body and a microphone array. The commonly used free field transfer functions boil down to assume a full acoustic transparency of the radiating object, which, in some cases, may lead to misleading outcomes for their characterization. Among other approaches, equivalent sources methods (ESM) emerged as a convenient and powerful approach to simulate scattered sound fields. In this paper, an acoustic imaging algorithm, named Galerkin ESM, where equivalent sources are tailored to concomitantly match with microphone pressures and a Neumann boundary condition, is proposed. By means of a projected matrix inversion and backpropagation of the equivalent sources, Galerkin ESM aims at the direct synthesis of the pressure field around a diffracting body by making the most of an array measurement. This method is compared with two other existing imaging algorithms fueled by free field and computed transfer functions. The impact of the chosen transfer model is discussed, and Galerkin ESM performances are evaluated based on numerical and experimental test cases.