Highly directional receivers using various combinations of scalar, vector, and dyadic sensors

The generalized theory of directional sensors is presented in the form of the Taylor series expansion of the acoustic pressure about a point in space. If the expansion is truncated to second order, the analysis of scalar, vector, and dyadic sensors can be made and corresponds to the zeroth‐, first‐, and second‐order gradient of the acoustic pressure. This translates into using a sufficient number of omni‐directional hydrophones or a multimode hydrophone in conjunction with the appropriate finite‐differencing operations to achieve the desired beam patterns. Using the linearized Euler equation, the formulation can be recast in terms of the zeroth‐order gradient of the acoustic pressure along with the zeroth‐ and first‐order gradient of the particle acceleration. In this case, the zeroth‐order terms can be measured directly with an omni‐directional hydrophone and a neutrally buoyant accelerometer. The gradient of the particle acceleration can be measured indirectly using finite differences or directly by measuring the angular acceleration akin to a Rayleigh disk. Of particular interest is the use of scalar, vector, and dyadic sensors to localize sources of sound using arc‐tangent‐squared processing and cardioid‐squared processing as opposed to conventional arc‐tangent and cardioid processing. [Work supported by ONR 321SS.]