Sparse antenna array design is of great importance in Synthetic Aperture Interferometric Radiometer(SAIR).An approach to topology design of two dimensional(2D) sparse arrays for SAIR,applicable to very large arrays,is proposed.The completeness of(u,v) plane coverage provided by a 2D sparse array resulting from our approach is proved.The upper bound of redundancy with the array is derived,and proved superior to that of U or T array.The theoretical analysis and simulation results both show that a 2D sparse array constructed by our approach can obtain more spatial frequency samples and larger(u,v) plane coverage,therefore achieve higher spatial resolution,compared to those of U or T array with the same element number.The approach can be used in 2D antenna array design in SAIR.