Experimental determination of the effects of boundary reflection on the angular resolution of microphone arrays

Abstract

The Rayleigh criterion has long been considered the standard criterion for angular resolution of imaging systems, including microphone arrays. However, advanced beamforming methods have been developed in the past 20 years that have dramatically improved the angular resolution of microphone array systems. In this investigation, the angular resolution performance of three scaled microphone arrays and one alternative array geometry were tested with both approximately free-field and reflective boundary conditions. All of the arrays were subjected to a thorough regimen of testing with broadband acoustic sources. Beamforming analysis was performed with the Delay-and-Sum, TIDY, DAMAS, DAMAS2, and CLEAN-SC algorithms. The Delay-and-Sum algorithm is shown to offer the lowest angular resolution performance because it does not separate the acoustic source map from the point spread function of the array. The DAMAS algorithm offers the greatest angular resolution because it numerically deconvolutes the acoustic source map from the point spread function. However, deconvolution-based algorithms (DAMAS and DAMAS2) were the most negatively affected by boundary reflection effects. The logarithmic spiral array is shown to offer versatile performance across a wide range of frequencies, while an alternative quasi-periodic array yields results that are highly frequency-dependent. It is demonstrated that this is because of gaps in the source-to-element differences coverage, and the gaps in coverage correspond to half-wavelengths of frequency bands with significantly lower angular resolution performance.