Spherical Wave Diffraction for Microphone Arrays Operating in Near Field

Microphone arrays for spatial audio recording and reproduction became very popular in the last decade, due to the spread of virtual and augmented reality for entertainment, remote work, and teleconferencing. Several systems have been distributed on the market, and most of them are made of a rigid sphere. In this way, it is possible to rely on the theoretical solution of the plane wave diffraction to get the beamforming filters. Such filters are employed for synthesizing virtual microphones of arbitrary directivity by combining the signals recorded by the real microphones. However, the plane wave assumption corresponds to a far field condition, in which the wave fronts are planar or with negligible curvature.As the sound sources, or reflections, are closer to the array, the wave fronts tend to become spherical, and the planar hypothesis cannot be accepted. In this paper, the diffraction of spherical waves over a rigid sphere is investigated through numerical simulations based on Finite Elements Method and experimental measurements. It will be shown that the spatial performance is significantly degraded when theoretical filters are employed in near field conditions, while numerically calculated filters can provide a reliable improvement for near field beamforming.