A mills cross multiplicative array with the power pattern of a conventional planar array

The Mills Cross can be used to obtain a multiplicative pattern equal to the power pattern of a conventional planar array but with fewer elements. As the array sizes increase the saving in elements as given by the thinning factor T_M, also increases, with significant savings for large arrays. Moreover, the multiplicative T-array can do the same but with approximately frac34 of the number of elements needed by the Mills Cross. Finally, those arrays can be used to simulate a planar array with any power pattern of the factorable form given by equation in Elliot, R. S. (1981).