Array Manifold Geometry and Sparse Volumetric Array Design Optimization

Sparse volumetric acoustic arrays have been developed for sonar applications. The paper describes some geometric properties of the array manifold and explains how these properties may be used in array design. For sparse arrays that are subsets of uniform lattices, the array manifold has a simple characterization in terms of an array manifold lattice in phase space. The sidelobe structure of the array is determined by this array manifold lattice. The density of this lattice in phase space is proportional to the determinant of the second moment of the array. The design procedure finds element positions on the array lattice in real space that maximize nearest neighbour distances in the array manifold lattice. A low dimensional example and a practical volumetric array example are given.