This paper treats mapping (interpolation) of the output vector from an existing antenna array onto the output vector of an imaginary array when the directions of arrival (DOA) are known only to within a sector. The problem of constructing a mapping matrix, common to the sector, that minimizes DOA Mean Square Error (MSE) across the sector, is analyzed. We derive a general condition on the mapping errors that prevents them from affecting the calculated DOAs. Thereafter we propose a design, algorithm for the transformation matrix that generates mapping errors fulfilling this condition. Simulations show conspicuous. MSE improvements in relevant scenarios.