Directivity factors for linear arrays of velocity sensors

Some of the features unique to beamforming a linear array of acoustic velocity sensors, which art: not present with scalar-sensing elements (such as conventional pressure sensors), are described in this paper. Four types of sensors are considered here: a uniaxial motion sensor, which measures acoustic particle velocity along a single axis; a biaxial motion sensor measuring velocity in two orthogonal directions; a triaxial motion sensor that measures all three orthogonal components of the velocity vector; and a sensor, denoted as an acoustic vector sensor, that measures acoustic pressure as well as the complete velocity vector. Comparisons are made of the directivity index for each type of sensor and for linear arrays of sensors. It is shown that uniaxial velocity sensors can have a maximum directivity factor three times greater than an omnidirectional pressure sensor, a gain in directivity index of 4.8 dB. Not surprisingly, this directivity gain is highly dependent on signal arrival direction. Indeed, a uniaxial velocity sensor's directivity can be less than that of an omnidirectional pressure, indicative of a loss in signal level. These comparisons further indicate that a single vector sensor can provide 6 dB of directivity gain, four times the directivity of a pressure sensor. Line arrays of directional sensors can have a directivity index approximately 5 dB greater than that of an identical line array of pressure sensors for approximately all azimuthal array steerings.