Sound field planarity characterized by superdirective beamforming

The ability to replicate a plane wave represents an essential element of spatial sound field reproduction. In sound field synthesis, the desired field is often formulated as a plane wave and the error minimized; for other sound field control methods, the energy density or energy ratio is maximized. In all cases and further to the reproduction error, it is informative to characterize how planar the resultant sound field is. This paper presents a method for quantifying a region's acoustic planarity by superdirective beamforming with an array of microphones, which analyzes the azimuthal distribution of impinging waves and hence derives the planarity. Estimates are obtained for a variety of simulated sound field types, tested with respect to array orientation, wavenumber, and number of microphones. A range of microphone configurations is examined. Results are compared with delay-and-sum beamforming, which is equivalent to spatial Fourier decomposition. The superdirective beamformer provides better characterization of sound fields and is effective with a moderate number of omni-directional microphones over a broad frequency range. Practical investigation of planarity estimation in real sound fields is needed to demonstrate its validity as a physical sound field evaluation measure.