An efficient near-field-far-field transformation technique with spherical spiral scanning, which uses a minimum number of data, is proposed. A nonredundant sampling representation of the electromagnetic field on the spiral and a fast, accurate and stable interpolation algorithm are developed to this end. By choosing the elevation step of the spiral coincident with the sample spacing needed to interpolate the field on a meridian, it is possible to reconstruct the field at any point on the spherical surface. This allows the evaluation of the data required by a spherical near-field-far-field transformation. Numerical examples assessing the effectiveness of the proposed technique are reported.