An equivalence theory between elliptical and circular arrays

An equivalence relation of a family of arrays defined under a linear transformation is established. By means of this theorem, the far field of an elliptical array can be obtained from that of an equivalent circular array; the theorem can be similarly applied to two- and three-dimensional arrays. A uniformly excited cophasal elliptical array is considered as an example. For nonuniform excitation, the method of symmetrical components may be applied despite the absence of axial symmetry for elliptical arrays. This theory can also be applied to the case of continuous source distribution on an ellipse or in an elliptical aperture. In so doing, solutions can be obtained without use of the complicated wave functions pertaining to the original geometry. As an example, an optimum array in the sense of Dolph-Chebyshev is considered. Similarly, a Taylor distribution for an elliptical aperture can be achieved.