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This paper presents the first theory for general planar radio interferometers. Previously published results for the three antenna linear inteferometer are completely generalized to interferometers consisting of any number of antennas in arbitrary planar configurations. For any interferometer in this much wider class, the maximum likelihood bearing estimation algorithm can be derived, and its performance calculated using the results derived here. The antenna phase centers are viewed as generating a two dimensional lattice in the array plane. This lattice is the dual or reciprocal of the lattice in the direction cosine plane consisting of all direction cosine pairs which represent angles which are ambiguous with the array boresight. It is shown that the likelihood function for the unknown integer portions of the phase measurements can be reduced to an integer quadratic form which represents a generalized distance squared between an (N-2) dimensional projection of the phase measurement and the points of a lattice in phase space. The ambiguity resolution procedure is thus reduced to determining the closest lattice point to a given point.