Practical Concentric Open Sphere Cardioid Microphone Array Design for Higher Order Sound Field Capture

The problem of higher order sound field capture with spherical microphone arrays is considered. While A-format cardioid designs are commonplace for first order capture, interest remains in the increased spatial resolution delivered by higher order arrays. Spherical arrays typically use omnidirectional microphones mounted on a rigid baffle, from which higher order spatial components are estimated by accounting for radial mode strength. This produces a design trade-off between with small arrays for spatial aliasing performance and large arrays for reduced amplification of instrument noise at low frequencies. A practical open sphere design is proposed that contains cardioid microphones mounted at multiple radii to fulfill both criteria. A design example with a two spheres of 16-channel cardioids at 42 mm and 420 mm radius produces white noise gain above unity on third order components down to 200 Hz, a decade lower than a rigid 32-channel 42 mm sphere of omnidirectional microphones.