A probe-compensated near-field-far-field (NF-FF) transformation with planar spiral scan, particularly suitable for flat antennas under test (AUTs), is proposed in this communication. It relies on the nonredundant sampling representations of electromagnetic fields and has been achieved by properly applying the unified theory of spiral scannings for nonvolumetric antennas, when such a kind of AUT is considered as enclosed in a dish with diameter equal to its maximum dimension, thus better shaping its geometry. An efficient two-dimensional optimal sampling interpolation (OSI) algorithm is then developed to recover the NF data required by the standard NF-FF transformation with plane-rectangular scan from those collected along the spiral. Since ...