Beam-patterns of a collocated unit of three orthogonally oriented second-order directional sensors

Abstract

A microphone or a hydrophone measures the incident acoustic wavefield as a scalar field of pressure. Underlying this pressure scalar is the particle-velocity vector, which constitutes the spatial gradient of the wavefield. Each Cartesian component of this gradient vector may be directly measured (without computing any spatial derivative) by a particle-velocity sensor aligned in parallel to that Cartesian coordinate. The entire 3 × 1 gradient vector may be measured at any point in space, using three such particle-velocity sensors, collocated but orthogonally oriented among themselves. Such a collocated triad has an array manifold independent of signal frequency, thus uncoupling azimuth-elevation beamforming from the frequency-dimension. This triad’s beam-pattern has already been investigated by Wong and Chi ["Beam patterns of an underwater acoustic vector hydrophone located away from any reflecting boundary,” IEEE J. Ocean. Eng. 27(3), 628–637 (2002)]. While the particle-velocity sensor measures the first-order spatial derivative of the pressure field, a second-order spatial derivative of the pressure-field could likewise be defined and be measured by a “second-order directional sensor” that would have sharper directivity. This paper follows up that investigation, but now for second-order directional sensors.