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; similarly for two and three dimensional arrays. As an example a uniformly excited cophasal elliptical array is considered. For non-uniform excitation, the method of symmetrical components may be applied despite the fact that there is no rotational 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 using 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 also be achieved.