A near-field far-field transformation technique involving the amplitude of the measured data has been recently proposed. It requires two sets of near-zone amplitude measurements and relies upon a mean-square fitting of the measured amplitude by an iterative projection algorithm. In the paper the method is applied to the case of cylindrical scanning, for which all the details are explicitly worked out. Furthermore the probe effect is accounted for and the relative correction procedure is considered. The relevance of a rough phase estimate and/or a general knowledge of the source is also discussed to overcome the difficulties related to the presence of local minima which can trap the procedure. Numerical examples validating the effectiveness of the technique are provided.