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.

中文翻译：

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用于二维镜像孔径合成的满秩阵列


镜像孔径合成（MAS）的天线阵列的布置决定了求解余弦能见度的变换矩阵。当变换矩阵缺秩时，求解的余弦可见性将引入秩缺误差。对于二维（2-D）镜像孔径合成（2-D MAS），现有文献讨论了天线阵列的布置与秩亏误差之间的关系，但尚未提出能够实现满秩变换矩阵，称为满秩数组（RFA）。基于计算变换矩阵（RTM）的秩的新方法和一维（1-D）RFA的文献，这封信证明了当反射器都是金属时无法获得2-D RFA，并且通过引入由磁导体制成的反射器，可以获得2-D RFA。此外，这封信还获得了二维RFA的存在条件。基于这些条件，提出了两种获得二维 RFA 的方法。