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This paper deals with the experimental validation of an efficient near-field-far-field (NF-FF) transformation using the planar wide-mesh scanning (PWMS). Such a nonconventional plane-rectangular scanning technique is so named, since the sample grid is characterized by meshes wider and wider when going away from the center, and makes it possible to lower the number of needed measurements, as well as the time required for the data acquisition when dealing with quasi-planar antennas. It relies on the use of the nonredundant sampling representations of electromagnetic fields which employ an oblate ellipsoid or a surface formed by two circular “bowls” with the same aperture diameter but eventually different bending radii to shape a quasi-planar antenna. A two-dimensional optimal sampling interpolation formula allows the reconstruction of the NF data at any point on the measurement plane and, in particular, at those required by the classical NF-FF transformation with the conventional plane-rectangular scanning. The measurements, performed at the planar NF facility of the antenna characterization laboratories of Selex ES, have confirmed the effectiveness of this innovative scanning also from the experimental viewpoint.

As well known, the evaluation of the radiation characteristics represents a crucial step in the design of an antenna to verify whether the initial specifications are met and the antenna may be effectively employed for the desired application. The simplest measurement method consists in the direct far-field (FF) measurement. In order to perform accurate antenna measurements, the influence of uncontrollable environment conditions (rain, snow, electromagnetic interferences, etc.) can be reduced as much as possible by carrying out the measurements in anechoic chambers, which, making negligible the reflections from the walls, ensure free-space propagation conditions. Unfortunately, the FF distance requirements cannot be practically satisfied when dealing with antennas having large or even medium electrical sizes, so that only near-field (NF) measurements can be performed. Accordingly, the FF pattern can be determined by postprocessing the acquired NF data via NF-FF transformations [

Two main kinds of NF-FF transformation techniques can be distinguished to characterize the FF pattern of an antenna under test (AUT) from NF measurements: the ones based on the equivalent electromagnetic (EM) sources reconstruction methods and those using a modal expansion approach.

In the former, the equivalent currents on a selected surface enclosing the antenna are evaluated by solving a set of integral equations relating these (unknown) currents to the NF data acquired on the scanning surface [

In the latter, the measured NF data are transformed into FF patterns by using an expansion of the field of the AUT in terms of modes, namely, a complete set of solutions of the vector wave equation in the region outside the antenna. Plane, cylindrical, or spherical waves are generally used. The type of employed modal expansion determines the kind of the NF scanning surface, which accordingly will be a plane, a cylinder, or a sphere. The orthogonality properties of the modes on such surfaces are then exploited to obtain the modal expansion coefficients, which allow the reconstruction of the AUT far field. The development and spreading of NF-FF transformation techniques using planar [

Among them, that employing the standard plane-rectangular scanning is the most simple and efficient one from the NF data acquisition, analytical, and computational viewpoints. Its development stems from the plane wave spectrum representation of EM fields [

On the contrary, such information has been properly taken into account in the NF-FF transformation techniques using the innovative planar wide-mesh scanning (PWMS) [

Planar wide-mesh scanning for a quasi-planar antenna.

Flowchart of the algorithm.

It is worthy to note that an adaptive sampling technique for reducing the planar NF data needed for reconstructing the AUT radiation pattern has been developed in [

The aim of this paper is to provide the experimental assessment of the NF-FF transformations with PWMS using both the two-bowl modelling and the oblate ellipsoidal one to shape a quasi-planar AUT. However, such a validation, due to the unavailability of an

In the plane-rectangular scanning, the probe mounted on an

The resulting bandlimitation error, which exhibits a step-like behaviour [

When

According to the strategy defined by the nonredundant representations, the number of the needed NF data can be reduced more and more by employing effective antenna modellings able to fit better and better an AUT characterized by a quasi-planar geometry. Therefore, it is convenient to choose the surface

Oblate ellipsoidal modelling of the AUT.

Two-bowl modelling of the AUT.

It is worthy to note that, besides the remarkable reduction of the NF data, these AUT modellings, in spite of the spherical one, allow to consider a measurement plane located at a distance less than one half the antenna maximum size, thus lowering the error related to the truncation of the scanning region.

In order to factorize the two-dimensional interpolation scheme into one-dimensional OSI expansions along lines [

It must be stressed that, since all scanning lines have the same linear sampling rate, the acquisition points are aligned also along lines perpendicular to the scanning ones (see Figure

According to the above described nonredundant sampling representation, the reduced voltage can be evaluated at any observation point

The OSI formula (

This section is devoted to show some experimental results assessing the effectiveness of the described NF-FF transformation technique with PWMS suitable for quasi-planar antennas.

The measurement campaign has been performed in the anechoic chamber (13 m × 10 m × 7 m sized) of the antenna characterization laboratories of Selex ES, equipped with the planar NF facility. Such a facility is realized with an advanced three-dimensional scanner, formed by a mechanical arm able to move along the

In order to reduce the overall acquisition time, both the classical and nonconventional scanning modules controlling the linear movements of the positioning systems have implemented in such a way that the motions in the vertical direction are alternated.

The AUT employed in the experimental testing is shown in Figure

Photo of the X-band flat plate slot array.

An accurate alignment procedure, performed with a quadrant detector and a laser, has been made in order to ensure that the scanning plane is nominally parallel to the slot plane of the AUT. Moreover, the mounting structure supporting the probe, an open-ended WR-90 rectangular waveguide, has been well covered with absorbers to minimize the scattering toward the AUT.

Since a multifrequency acquisition is planned, the parameters relevant to the considered AUT modellings are defined by referring to the highest working frequency. The AUT has been fitted by a two-bowl modelling having parameters

In order to assess the effectiveness of the two-dimensional OSI expansion (

AUT @ 9.3 GHz. Amplitude of the probe voltage on the line at

AUT @ 9.4 GHz. Amplitude of the probe voltage on the line at

As can be seen, the reconstructions are everywhere accurate save for the peripheral zone where the directly measured voltages result to be more oscillating as compared to the reconstructed ones, which exhibit a smoother behaviour. This is due to the low pass filtering properties of the interpolation functions, which cut away the spatial harmonics related to the noise sources outside the AUT spatial bandwidth. Moreover, the voltage reconstruction obtained when using the oblate ellipsoidal modelling seems to degrade in the peripheral zone with respect to that achieved when employing the two-bowl modelling. This occurs since, having used the same number of PWMS lines for both of the examples, the scanning area coverage attainable by employing the two-bowl modelling is greater than that achievable by the oblate ellipsoidal one. In such a case, the reconstruction can be improved if the AUT modelling parameters are set in such a way to take into account an increased number of PWMS lines to cover the same measurement plane. It must be stressed that the use of the OSI expansions, instead of the cardinal series ones, improves the robustness of the technique when dealing with noisy data, since it prevents the propagation of the errors affecting the data from higher to lower voltage regions.

At last, the FF patterns in the principal planes

AUT @ 9.3 GHz.

AUT @ 9.3 GHz.

AUT @ 9.4 GHz.

AUT @ 9.4 GHz.

It must be stressed, for sake of comparison, that the number of PWMS data for covering the considered measurement plane is 2 601 against the 40 401 ones needed by the classical NF-FF transformation with plane-rectangular scanning [

An experimental validation of the NF-FF transformations with PWMS, suitable for quasi-planar antennas, has been provided in this paper. The experimental tests have been possible thanks to the research agreement with Selex ES, whose antenna characterization laboratories are equipped with planar NF facilities. The very good results achieved both in the near-field and in the far-field reconstructions confirm also from the experimental viewpoint the validity of such a nonconventional scanning, which allows a drastic NF data reduction, as well as measurement time saving, without losing the accuracy of that using the conventional scan and without requiring drastic changes in an existing plane-rectangular NF facility.

When considering the AUT as enclosed in the smallest oblate ellipsoid having major and minor semiaxes equal to

(a) Relevant to the oblate ellipsoidal modelling. (b) Relevant to the two-bowl modelling.

When adopting the two-bowl modelling (Figure

When

The authors declare that there is no conflict of interests regarding the publication of this paper.

The authors would like to express their thanks to Dr. Stefano Pitta for his priceless support in performing the testing.