Abstract: Applying the aperture coordinate transform, this paper compares the difference between circular and elliptic aperture antenna pattern functions, derives the formula of mapping circular aperture antenna pattern properties to elliptic aperture antennas and applies the optimum circular aperture antenna pattern synthesis, Taylor synthesis to elliptic aperture antenna design. And how to use this formula on discrete elliptic aperture arrays is discussed. The paper gives an example of applying this method and compares the pattern properties of continuous circular aperture antennas and discrete elliptic aperture arrays. The method extends the conventional design approaches of elliptic aperture arrays.