Design and Evaluation of a Spherical Segment Array with Double Cone

This article discusses modal beamforming applied to a new microphone array prototype for panoramic audio recordings. Modal beamforming using conventional spherical microphone arrays is usually based on the decomposition of the sound pressure into spherical harmonics. To keep the error of the decomposition into spherical harmonics small a distribution of microphones covering all directions is required, even if only a limited range of directions is of interest. For panoramic audio recordings the angular range of interest is bounded above and below towards the north and the south pole, which corresponds to a spherical segment. Solving the Helmholtz equation for a two-point Neumann boundary condition to the zenith angle yields orthogonal functions for sound field decomposition on a spherical segment, which we will refer to as spherical segment harmonics. This angular restriction is physically equivalent to a sound field delimited by a rigid infinite double conical surface. The prototype consists of microphones distributed on the surface of a spherical segment and a double cone of finite length. We show that modal beamforming is applicable with this prototype, even though the practical implementation does not meet the theoretical model of infinitely long boundaries. The array pattern synthesis approach is verified by acoustic measurements of the array prototype.