An efficient probe-compensated near-field/far-field transformation technique with planar spiral scanning is proposed, which uses a minimum number of data. A non-redundant sampling representation of the probe output voltage on a planar spiral and a fast, accurate and stable interpolation algorithm are developed. By choosing the angular step of the spiral coincident with the sample spacing needed to interpolate such a voltage on a radial line, it is possible to reconstruct the data required by the standard probe-compensated plane-rectangular near-field/far-field transformation technique. The use of an open-ended cylindrical waveguide as scanning probe allows probe co-rotation to be avoided. Numerical examples are reported, assessing the accuracy and the stability of the far-field reconstruction process.