On optimal retreat distance for the equivalent source method-based nearfield acoustical holography

As a basic form of the equivalent source method (ESM) that is used to nearfield acoustical holography (NAH) problems, discrete monopoles are utilized to represent the sound field of interest. When setting up the virtual source distribution, it is vital to maintain a "retreat distance" between the virtual sources and the actual source surface such that reconstruction would not suffer from singularity problems. However, one cannot increase the distance without bound because of the ill-posedness inherent in the reconstruction process with large distance. In prior research, 1-2 times lattice spacing, or the inter-element distance of microphones, is generally recommended as retreat distance in using the ESM-based NAH. While this rule has shown to yield good results in many cases, the optimal choice is a complicated issue that depends on frequency, geometry of the physical source, content of evanescent waves, distribution of sensors and virtual sources, etc. This paper deals about attaining the best compromise between the reconstruction errors induced by the point source singularity; the reconstruction ill-posedness is an interesting problem in its own right. The paper revisits this issue, with the aid of an optimization algorithm based on the golden section search and parabolic interpolation. Numerical simulations were conducted for a baffled planar piston source and a spherically baffled piston source. The results revealed that the retreat distance appropriate for the ESM ranged from 0.4 to 0.5 times the spacing for the planar piston, while from 0.8 to 1.7 times average spacing for the spherical piston. Experiments carried out for a vibrating aluminum plate also revealed that the retreat distance with 0.5 times the spacing yielded better reconstructed velocity than those with 1/20 and 1 times the spacing.