Rank-Full Arrays for 2-D Mirrored Aperture Synthesis

The arrangement of the antenna array of the mirrored aperture synthesis (MAS) determines the transformation matrix for solving the cosine visibilities. When the transformation matrix is rank deficient, the solved cosine visibilities will introduce the rank-deficient error. For the two-dimensional (2-D) mirrored aperture synthesis (2-D MAS), the existing literature has discussed the relationship between the arrangement of the antenna array and the rank-deficient error but has not proposed an array that can achieve a full rank transformation matrix, which is called the rank-full array (RFA). Based on a new method for calculating the rank of the transformation matrix (RTM) and the literature on one-dimensional (1-D) RFAs, this letter proves that 2-D RFA cannot be obtained when the reflectors are all metal, and by introducing a reflector made of a magnetic conductor, 2-D RFA can be obtained. Besides, this letter obtained the existence conditions for 2-D RFA. Based on those conditions, two methods are proposed to obtain 2-D RFAs.