Francesco D'Agostino, Flaminio Ferrara, Claudio Gennarelli, Rocco Guerriero, Massimo Migliozzi, October 2017
Among the near-field – far-field (NF-FF) transformation techniques, the one employing the bi-polar scanning is particularly interesting, since it retains all the advantages of that using the plane-polar one, while requiring a mechanically simple, compact, and cheaper measurement facility [1]. In fact, in this scan, the antenna under test (AUT) rotates axially, while the probe is mounted at the end of an arm that rotates around an axis parallel to the AUT one. An effective probe voltage representation on the scanning plane requiring a minimum number of bi-polar NF data has been developed in [2], by properly exploiting the nonredundant sampling representations of electromagnetic (EM) fields [3] and considering the AUT as enclosed in an oblate ellipsoid. A 2-D optimal sampling interpolation (OSI) formula is then employed to efficiently recover the NF data required by the traditional plane-rectangular NF-FF transformation [4] from the acquired nonredundant bi-polar samples. It is so possible to considerably reduce the number of the needed NF data and corresponding measurement time with respect to the previous approach [1], which did not exploit the nonredundant sampling representations. 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 [5] is to retrieve the uniform samples from the nonuniform ones and then reconstruct the required NF data via an accurate and stable 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 [5] to the uniform samples retrieval in the case of cylindrical and spherical surfaces. The latter, based on the singular value decomposition (SVD) method, does not exhibit this constraint and has been applied to the nonredundant bi-polar [6] scanning technique based on the oblate ellipsoidal modeling. 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 not only to provide the experimental validation of the SVD based technique [6], but also to develop the approach using the iterative technique and experimentally assess its effectiveness.
[1] L.I. Williams, Y. Rahmat-Samii, R.G. Yaccarino, “The bi-polar planar near-field measurement technique, Part I: implementation and measurement comparisons,” IEEE Trans. Antennas Prop., vol. 42, pp. 184-195, Feb. 1994.
[2] F. D’Agostino, C. Gennarelli, G. Riccio, C. Savarese, “Data reduction in the NF-FF transformation with bi-polar scanning,” Microw. Optic. Technol. Lett., vol. 36, pp. 32-36, 2003.
[3] 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, March 1998.
[4] E.B. Joy, W.M. Leach, Jr., G.P. Rodrigue, D.T. Paris, “Application of probe-compensated near-field measurements,” IEEE Trans. Antennas Prop., vol. AP-26, pp. 379-389, May 1978.
[5] 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, April 1994.
[6]F. Ferrara, C. Gennarelli, M. Iacone, G. Riccio, C. Savarese, “NF–FF transformation with bi-polar scanning from nonuniformly spaced data,” Appl. Comp. Electr. Soc. Jour., vol. 20, pp. 35-42, March 2005.