This paper deals with the experimental testing of effective probe compensated near-field-far-field (NF-FF) transformations with spherical scanning requiring a minimum number of NF data. They rely on nonredundant sampling representations of the voltage measured by the probe, based on very flexible source modellings suitable for nonvolumetric antennas characterized by two dimensions very different from the other one. In particular, a cylinder ended in two half-spheres is adopted for modelling long antennas, whereas the quasi-planar ones are considered as enclosed in a rotational surface formed by two circular “bowls” having the same aperture diameter, but eventually different bending radii. The NF data needed to perform the classical spherical NF-FF transformation are then accurately and efficiently retrieved from the acquired nonredundant ones via optimal sampling interpolation formulas. A remarkable reduction of the number of the required NF data and, as a consequence, a significant measurement time saving can be so obtained. The experimental tests have been carried out at Antenna Characterization Lab of the University of Salerno and both the NF and FF reconstructions are resulted to be very good, thus confirming the accuracy and reliability of these NF-FF transformations from the experimental viewpoint too.

As is well known, most of the characteristic parameters of an antenna, as for example the radiation pattern, are defined in its far-field (FF) region. On the other hand, an accurate measurement of the electromagnetic (EM) field radiated by an antenna can be carried out only in an anechoic chamber, wherein the reflections from the walls become negligible, thus emulating the free-space propagation. However, for antennas having large or even medium electrical sizes, the FF requirements cannot be practically satisfied in an anechoic chamber, wherein only near-field (NF) measurements can be performed. Accordingly, the NF-FF transformation techniques, which allow an accurate reconstruction of the antenna far-field from measurements in the NF region, have been widely investigated and employed in the last four decades [

The classical spherical NF-FF transformation technique [

At last, NF-FF transformation techniques with spherical spiral scanning, maintaining the aforementioned feature of the spherical one and exploiting continuous and synchronized movements of the positioning systems of the probe and AUT [

The goal of this paper is to provide the experimental validation of the nonredundant NF-FF transformations with spherical scanning for quasi-planar and electrically long antennas [

Spherical scanning for a quasi-planar antenna.

Spherical scanning for an elongated antenna.

In this section, a nonredundant and effective sampling representation [

Let us consider an AUT located at the origin of a spherical coordinate system

The bandwidth

When considering a parallel, the phase function

In this relation,

It must be stressed that, according to [

In light of the above considerations, when dealing with an antenna having a quasi-planar geometry, an effective and convenient modelling is obtained by choosing

Relevant to the two-bowl modelling.

On the other hand, an effective and convenient modelling for an electrically long antenna is the rounded cylinder modelling, obtained by considering the AUT as enclosed in a cylinder of height

Relevant to the rounded cylinder modelling.

The explicit expressions of the parameters involved in the nonredundant sampling representation using the two-bowl and the rounded cylinder modellings are reported in Appendices

In the following a two-dimensional OSI expansion, which allows the fast and accurate reconstruction of the probe voltage at any point on the scanning sphere from a minimum number of samples, is presented. Such an expansion is formally the same for both the considered AUT modellings, but the values of the parameters determining the nonredundant representation and the sampling arrangement are obviously different.

As shown in [

The intermediate samples can be obtained by interpolating the samples on the parallels by means of a similar OSI expansion along

By applying the two-dimensional OSI formula (

The described nonredundant NF-FF transformations with spherical scanning for nonvolumetric antennas have been experimentally assessed in the anechoic chamber of the Antenna Characterization Lab of the University of Salerno, where a roll (

Photo of the spherical NF facility with the X-band flat plate slot array.

The former set of figures (from Figure

The former antenna is an X-band flat plate slot array of Rantec Microwave Systems Inc., having a diameter of about 46 cm and operating at 9.4 GHz (see Figure

Amplitude of

Phase of

Amplitude of

Phase of

E-plane pattern. Solid line: reference. Crosses: reconstructed from nonredundant NF data.

H-plane pattern. Solid line: reference. Crosses: reconstructed from nonredundant NF data.

Photo of the X-band resonant slotted waveguide array.

The latter antenna is an X-band resonant slotted waveguide array of PROCOM, located on the plane

Amplitude of

Amplitude of

Phase of

E-plane pattern. Solid line: reference. Crosses: reconstructed from nonredundant NF data.

H-plane pattern. Solid line: reference. Crosses: reconstructed from nonredundant NF data. Dashed line: reconstruction error.

FF pattern in the cut plane at

Reconstruction error over the full far-field sphere.

An experimental validation of the nonredundant NF-FF transformations with spherical scanning for quasi-planar and elongated antennas, based on the two-bowl and rounded cylinder modellings, respectively, has been provided. The very good agreements found both in the near-field and in the far-field reconstructions confirm also from the experimental point of view the effectiveness and reliability of these transformation techniques, which allow a drastic measurement time saving retaining the accuracy of the classical spherical NF-FF transformation.

The explicit expressions of the parameters involved in the nonredundant sampling representation using the two-bowl modelling (see Figure

It can be easily verified that, for such a modelling,

For

For

For

For

For

As regards the determination of the maximum in (

In this appendix, the explicit expressions of the parameters relevant to the nonredundant sampling representation based on the rounded cylinder modelling (see Figure

In such a case, it results in

For

For

At last for

For what concerns the azimuthal bandwidth