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Near-field signal-redundancy (NFSR) algorithms for phase-aberration correction have been proposed and experimentally tested for linear and phased one-dimensional arrays. In this paper the performance of an all-row-plus-two-column, two-dimensional algorithm has been analyzed and tested with simulated data sets. This algorithm applies the NFSR algorithm for one-dimensional arrays to all the rows as well as the first and last columns of the array. The results from the two column measurements are used to derive a linear term for each row measurement result. These linear terms then are incorporated into the row results to obtain a two-dimensional phase aberration profile. The ambiguity phase aberration profile, which is the difference between the true and the derived phase aberration profiles, of this algorithm is not linear. Two methods, a trial-and-error method and a diagonal-measurement method, are proposed to linearize the ambiguity profile. The performance of these algorithms is analyzed and tested with simulated data sets.