Hindawi Publishing Corporation International Journal of Antennas and Propagation Volume 2010, Article ID 859396, 8 pages doi:10.1155/2010/859396 Research Article Near-Field/Far-Field Transformation with Helicoidal Scanning from Irregularly Spaced Data Francesco D’Agostino, Flaminio Ferrara, Claudio Gennarelli, Rocco Guerriero, and Massimo Migliozzi Dipartimento di Ingegneria dell’Informazione ed Ingegneria Elettrica, University of Salerno, Via Ponte Don Melillo, 84084 Fisciano, Italy Correspondence should be addressed to Claudio Gennarelli, gennar@diiie.unisa.it Received 14 June 2010; Accepted 14 September 2010 Academic Editor: Krishnasamy Selvan Copyright © 2010 Francesco D’Agostino et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A fast and accurate technique for the compensation of the probe positioning errors in the near-field/far-field transformation with helicoidal scanning is proposed in this paper. It relies on a nonredundant sampling representation using a spherical modelling of the antenna under test and employs an iterative scheme to evaluate the near-field data at the points fixed by the helicoidal nonredundant representation from the acquired irregularly distributed ones. Once these helicoidal data have been recovered, those required by a classical cylindrical near-field/far-field transformation are efficiently determined by using an optimal sampling interpolation algorithm. Some numerical tests assessing the effectiveness of the proposed approach and its stability with respect to random errors affecting the near-field data are shown. 1. Introduction As well-known, far-field (FF) range size limitations, trans- portation, and mounting problems can make impossible or impractical the measurement of antenna radiation patterns on a conventional FF range. In these cases, it is convenient to exploit near-field (NF) measurements and recover the FF patterns by using NF-FF transformation techniques [1–3]. In addition, the NF measurements may be performed in a controlled environment, as an anechoic chamber, thus overcoming those drawbacks that cannot be eliminated in FF outdoor measurements. In this framework, the reduction of the time needed for acquiring the NF data is assuming an ever growing relevance for the antenna measurement community, since this time is currently very much greater than that required to perform the corresponding NF-FF transforma- tion. Such a reduction can be achieved by decreasing the number of the NF data to be collected and/or by making faster the acquisition of each NF value. A significant reduc- tion of the number of required NF data has been obtained for all the conventional scannings [4–8] by applying the nonredundant sampling representations of electromagnetic (EM) fields and the optimal sampling interpolation (OSI) expansions [9], whereas, the use of the modulated scattering technique employing arrays of scattering probes has been proposed in [10] to realize a very fast electronic scanning. However, antenna testing NF facilities based on such a tech- nique are not very flexible as those employing mechanical scans. These last can be made faster by exploiting innovative spiral scannings which use, as suggested by Yaccarino et al. in [11], continuous and synchronized movements of the positioning systems of the probe and antenna under test (AUT). In particular, accurate, stable, and efficient NF-FF transformations using the helicoidal scanning, the planar and spherical spiral scannings have been developed [12– 19]. They are based on the aforementioned nonredundant representations and reconstruct the NF data needed by the NF-FF transformation with the corresponding classical scanning by interpolating, via appropriate OSI formulas, the nonredundant samples acquired on the spiral. The required two-dimensional algorithm has been obtained (a) by assuming the AUT enclosed in a proper convex domain