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Francesco D'Agostino,Flaminio Ferrara, Claudio Gennarelli, Rocco Guerriero, Massimo Migliozzi, November 2015

Among the near-field – far-field (NF–FF) transformation techniques, the one employing the plane-polar scanning has attracted a considerable attention [1]. In this framework, efficient sampling representations over a plane from a nonredundant number of plane-polar samples, which stays finite also for an unbounded scanning plane, have been developed, by applying the nonredundant sampling representations of the EM fields [2] and assuming the antenna under test (AUT) as enclosed in an oblate ellipsoid [3] or in a double bowl [4], namely, a surface formed by two circular bowls with the same aperture diameter but eventually different lateral bends. These effective representations make possible to accurately recover the NF data required by the plane-rectangular NF–FF transformation [5] from a nonredundant number of NF data acquired through the plane-polar scanning. A remarkable reduction of the number of the needed NF data and, as a consequence, of the measurement time is so obtainable. However, due to an imprecise control of the positioning systems and their finite resolution, it may be impossible to exactly locate the probe at the points fixed by the sampling representation, even though their position can be accurately read by optical devices. Therefore, it is very important to develop an effective algorithm for an accurate and stable reconstruction of the NF data needed by the NF–FF transformation from the acquired irregularly spaced ones. A viable and convenient strategy [6] is to retrieve the uniform samples from the nonuniform ones and then reconstruct the required NF data via an accurate and stable optimal sampling interpolation (OSI) expansion. In this framework, two different approaches have been proposed. The former is based on an iterative technique, which converges only if there is a biunique correspondence associating at each uniform sampling point the nearest nonuniform one, and has been applied in [6] to the uniform samples reconstruction in the case of cylindrical and spherical surfaces. The latter, based on the singular value decomposition method, does not exhibit this constraint and has been applied to the nonredundant plane-polar [7] scanning technique based on the oblate ellipsoidal modelling. However, it can be conveniently used only when the uniform samples recovery can be split in two independent one-dimensional problems. The goal of this work is to develop these two techniques for compensating known probe positioning errors in the case of the nonredundant plane-polar scanning technique using the double bowl modelling [4]. Experimental tests will be performed at the UNISA Antenna Characterization Lab in order to assess their effectiveness. [1] Y. Rahmat-Samii, V. Galindo Israel, and R. Mittra, “A plane-polar approach for far-field construction from near-field measurements,” IEEE Trans. Antennas Prop., vol. AP-28, pp. 216-230, 1980. [2] O.M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Prop., vol. 46, pp. 351-359, 1998. [3] O.M. Bucci, F. D’Agostino, C. Gennarelli, G. Riccio, and C. Savarese, “NF–FF transformation with plane-polar scanning: ellipsoidal modelling of the antenna,” Automatika, vol. 41, pp. 159-164, 2000. [4] O.M. Bucci, C. Gennarelli, G. Riccio, and C. Savarese, “Near-field–far-field transformation from nonredundant plane-polar data: effective modellings of the source,” IEE Proc. Microw. Antennas Prop., vol. 145, pp. 33-38, 1998. [5] E.B. Joy, W.M. Leach, Jr., G. P. Rodrigue and D.T. Paris, “Application of probe-compensated near-field measurements,” IEEE Trans. Antennas Prop., vol. AP-26, pp. 379-389, May 1978. [6] O.M. Bucci, C. Gennarelli, G. Riccio, C. Savarese, “Electromagnetic fields interpolation from nonuniform samples over spherical and cylindrical surfaces,” IEE Proc. Microw. Antennas Prop., vol. 141, pp. 77-84, 1994. [7] F. Ferrara, C. Gennarelli, G. Riccio, C. Savarese, “Far field reconstruction from nonuniform plane-polar data: a SVD based approach,” Electromagnetics, vol. 23, pp. 417-429, July 2003