On optimal retreat distance of equivalent source method-based near-field acoustical holography

Abstract

This paper presents two nearfield acoustical holography (NAH) approaches using Equivalent Source Methods (ESM). The indirect ESM is derived from discretizing the simple layer potential integral, while the direct ESM is derived from discretizing the Helmholtz Integral Equation (HIE). In the indirect ESM, sound field is represented by a distribution of monopoles. In the direct ESM, on the other hand, sound field is represented by monopoles and dipoles. In the ESM formulation, it is vital that the virtual sources "retreat" from the reconstruction surface to avoid singularity. However, the distance can not be increased without limit because of the ill-posedness inherent at large reconstruction distance. It is widely believed that the retreat distance of one to two lattice spacing is appropriate. This paper revisits this issue of retreat distance, with the aid of an optimization technique: the golden ratio search with parabolic interpolation. Simulations are conducted for baffled planar and spherical pistons. The simulation results reveal that, differing from the widely accepted value, the retreat distance appropriate for the ESM is half of lattice spacing.