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Theoretical Analysis of Open Spherical Microphone Arrays for Acoustic Intensity Measurements

Acoustic intensity is a vectorial measure of acoustic energy flow through a given region of interest. Three-dimensional measurement of acoustic intensity requires special microphone array configurations. This paper provides a theoretical analysis of open spherical microphone arrays for the 3-D measurement of acoustic intensity. The calculations of the pressure and the particle velocity components of the sound field inside a closed volume are expressed using the Kirchhoff-Helmholtz integral equation. The conditions which simplify the calculation are identified. This calculation is then constrained to a finite set of microphones positioned at prescribed points on an open sphere. Several open spherical array topologies are proposed. Their magnitude and directional errors and measurement bandwidths are investigated via numerical simulations. A comparison with conventional open-sphere 3-D intensity probes is presented.