Self-calibration of dual, closed surface microphone arrays

Abstract

With the recent availability of very inexpensive, miniature digital MEMS microphones, the construction of large count microphone arrays is financially within the reach of the basic researcher. Using various mathematical techniques such as the Helmholtz-Kirchhoff integral and the equivalent source method (ESM), dual surface microphone arrays provide the ability to separate incident and scattered fields instantaneously in time. When these arrays form a closed surface, this separation is extremely accurate. However, one of the concerns with any microphone array is the calibration of the individual elements, especially near the resonance frequency of the diaphragm. In this paper, a self-calibration technique is proposed, based on ESM, that uses external loudspeakers in a simple laboratory facility not required to be anechoic. The approach is tested numerically on a dual surface, 256 element pair spherical microphone array, and uses an algorithm for the minimization of a cost function based on the extinction of the scattered field when the unknown individual calibration coefficients of the array elements are varied. Use of a Burton-Miller approach to model the ESM sources of the scattered field improves dramatically the accuracy at specific frequencies. The problematic interior Dirichlet eigenfrequencies are addressed. [Work supported by the Office of Naval Research.]