An efficient technique is developed in this article to evaluate the antenna far field from the knowledge of nonuniformly distributed near-field data measured by a probe via a planar wide-mesh scanning facility. To this end, the singular value decomposition method is properly applied to reconstruct the uniformly spaced samples, whose positions are fixed by a nonredundant sampling representation of the electromagnetic field. Then, the plane-rectangular near-field data needed to perform the classical probe compensated near-field-far-field transformation are efficiently evaluated via an optimal sampling interpolation algorithm. Numerical tests, assessing the effectiveness and the stability of the far-field reconstruction process, are reported.