The Maximum Rank of the Transfer Matrix in 1-D Mirrored Interferometric Aperture Synthesis

Because the principle of mirrored interferometric aperture synthesis (MIAS) is different from that of the conventional interferometric aperture synthesis, the antenna array for 1-D MIAS should be redesigned. And in order to get a precise estimation of the cosine visibilities, the maximum rank of the transfer matrix should be set as the key constraint condition of the array optimization model, but this has not been clearly presented before. In this letter, the maximum rank of the transfer matrix is discussed and proved by the mathematical induction method. When the position of each antenna in the array is an even multiple of 0.5, the value for the maximum rank is proven to be M - 2, and when the position of each antenna is an odd multiple of 0.5, the value for the maximum rank is proven to be M - 1, where M is the number of the spatial frequencies provided by the array. This conclusion is significant for the array design of 1-D MIAS.