An efficient technique to reconstruct the field radiated by an antenna in the far-field region from the knowledge of the nonuniformly spaced plane-polar data measured by a probe in the near-field region is developed in this work. The singular value decomposition method is applied to evaluate the uniformly distributed samples, whose positions are fixed by a nonredundant sampling representation of the field. Then the plane-rectangular near-field data needed to perform the classical probe-compensated near-field-far-field transformation are efficiently evaluated via the optimal sampling interpolation algorithm. As demonstrated by numerical tests, the far-field reconstruction process is accurate and stable.