This study deals with the problem of the correction of known probe positioning errors, which can occur in an actual planar near-field facility when adopting a non-redundant near-field to far-field (NFTFF) transformation with a bi-polar scan for quasi-planar antennas. To this end, a singular value decomposition based approach is developed to recover the uniform bi-polar samples, whose position is set by the non-redundant sampling representation got by shaping the antenna with a double bowl, from those affected by positioning errors. Then, a 2D optimal sampling interpolation formula is used to accurately reconstruct the plane rectangular near-field data needed by the standard NFTFF transformation from the retrieved non-redundant uniform samples. Experimental results, assessing the capability of the developed procedure to correct even pessimistic positioning errors, are shown.