Laboratory tests on an near‐field to far‐field transformation technique from non‐redundant bi‐polar data

Abstract

An experimental verification of a fast and accurate technique, which allows the evaluation of the antenna radiation pattern from a non‐redundant, i.e. minimum, number of near‐field (NF) measurements acquired via a bi‐polar scan, is provided in this study. This probe compensated NF‐to‐far‐field (NFTFF) transformation exploits a non‐redundant sampling representation of the voltage acquired by the probe, achieved by shaping the antenna with a double bowl, a very flexible model particularly tailored to antennas characterised by a quasi‐planar geometry. The input NF data necessary for executing the standard plane‐rectangular NFTFF transformation are efficiently recovered from the acquired non‐redundant bi‐polar ones by applying a two‐dimensional optimal sampling interpolation formula, so that a remarkable measurement time saving is attained. Some results of laboratory proofs performed at the Antenna Characterization Lab of the University of Salerno are reported to demonstrate the accuracy and the practical effectiveness of the presented NFTFF transformation technique.

Laboratory testing of an SVD‐based approach to recover the non‐redundant bi‐polar NF data from the positioning error affected ones

“…The parameter η and the phase function ψ are obtained by substituting the proper values of R 1, 2 and s 1, 2 ′ in relations (3) and (4). It is a simple matter to verify that, for ρ < a, the points P 1, 2 are located on the upper bowl, whereas, when ρ>a, P 1 is still on the ′ can be found in [9,15]. The searching of the maximum in (5) allowing the evaluation of W φ is detailed in [9,15].…”

“…The intermediate samples Ṽ η n , φ in the OSI formula (6) can be determined by interpolating the samples on the rings through a quite similar OSI expansion along the rings [9,15]…”

“…Among the NFTFF transformations, those employing a planar scanning, (plane-rectangular (PR) [5,6], plane-polar (PP) [7][8][9][10], and bi-polar (BP) [11][12][13][14][15]) are especially convenient when characterising high gain, quasi-planar, antennas, radiating pencil beam patterns. The PR NFTFF transformation is the most simple and effective from the analytical and computational viewpoints, being the AUT far field efficiently evaluated via the 2D fast Fourier transform (FFT) from the complex voltage data measured by the probe and rotated probe on the PR raster grid.…”

“…Indeed, this approach did not exploit the nonredundant sampling representations of EM fields [16,17], thus requiring a uselessly large number of NF data. On the contrary, unlike the approach in [11,12], those in [13][14][15] properly apply these representations to the voltage detected by the measurement probe, thus making available 2D OSI schemes, which allow the precise recovery of the required PR NF data from a minimum number of the BP samples. In particular, an oblate spheroid has been considered in [13,14] as surface modelling the AUT, whereas the antenna has been assumed in [15] as contained in a surface made by two bowls having the same aperture (double bowl).…”

“…To this end, Wittmann et al proposed in [18,19] a procedure based on the conjugate gradient iteration technique, which, by properly exploiting the FFT for non-equispaced data [20], allows one to compensate known errors of probe positioning in the standard NFTFF transformations with planar and spherical scans, respectively. Unfortunately, this procedure is inappropriate for the non-redundant BP NFTFF transformations [13][14][15]. As suggested in [21], where the interested reader can find a more complete discussion on this issue, the formulae for the direct recovery of the NF data needed by the corresponding standard NFTFF transformation from the positioning errors affected samples are not robust and easy to use, and can be applied only for particular samples grids.…”