Two efficient probe-compensated near-field-far-field transformations with spherical scanning for antennas having two dimensions very different from the third one are here developed. They rely on the nonredundant sampling representations of the electromagnetic fields and on the optimal sampling interpolation expansions, and use effective antenna modellings. In particular, an antenna with a predominant dimension is no longer considered as enclosed in a sphere but in a cylinder ended in two half spheres, whereas a surface formed by two circular “bowls” with the same aperture diameter but different lateral bends is adopted to shape an antenna with two predominant dimensions. These modellings are able to fit very well a lot of antennas by properly setting their geometric parameters. It is so possible to remarkably lower the number of data to be acquired, thus significantly reducing the measurement time. Numerical tests assessing the accuracy and the robustness of the techniques are reported.

As is well known, near-field-far-field (NF-FF) transformation techniques play a significant role in modern antenna measurements [

Among the NF-FF transformation techniques, the employing of the spherical scanning has attracted considerable attention [

In [

It must be stressed that the reduction in the number of the NF data to be acquired reflects in a decrease of the measurement time, and this is a very important issue for the antenna measurement community, since such a time is very much greater than that needed to carry out the NF-FF transformation. A measurement time reduction can also be obtained by performing a fast electronic scanning via the modulated scattering technique [

The aim of this paper is to develop even more effective NF-FF transformations with spherical scanning tailored for antennas having one or two predominant dimensions. To this end, very flexible antenna modellings will be adopted. In particular, an electrically long antenna will be considered as enclosed in a rounded cylinder, namely, a cylinder which ends in two half spheres, whereas a surface formed by two circular “bowls” with the same aperture diameter but different lateral bends (double bowl) will be adopted to shape a quasiplanar antenna. The so-obtained NF-FF transformation techniques result to be more effective from the data reduction viewpoint than those employing the prolate or oblate ellipsoidal modelling. In fact, these flexible modellings allow one to fit the shape of a lot of actual antennas better by properly setting their geometric parameters. Moreover, they remain quite general and contain the spherical modelling as a particular case.

Let us consider an AUT enclosed in a convex domain bounded by a rotational surface

When

When the observation curve is a parallel, due to the involved symmetry, the phase function is constant and it is convenient to use the azimuthal angle

In the light of these results, the reduced voltage at

The intermediate samples

The variation of

By properly matching (

An effective and flexible modelling for an AUT having a quasiplanar geometry is obtained by choosing

Spherical scanning for a quasiplanar antenna.

Relevant to the double bowl modelling.

When

When

When

When

When

For what concerns the evaluation of the maximum in (

An effective modelling for an elongated AUT is got by considering it as enclosed in a cylinder of height

Spherical scanning for an elongated antenna.

Relevant to the rounded cylinder modelling.

When

When

When

As regards the azimuthal bandwidth

For reader’s convenience, the key steps of the probe-compensated NF-FF transformation with spherical scanning [

According to [

The choice of the highest spherical wave to be considered is determined in the classical approach according to the following rule of thumb:

The vectorial functions

As shown in [

The probe’s expansion coefficients

According to (

The integration over

It must be stressed that, to take advantage of the numerical efficiency of the FFT, the number of NF parallels to be considered in the NF-FF transformation and the number of samples on them must be the first power of two greater or equal to

It is worth noting that, by inverting the summations order, the spherical wave expansion (

From a numerical viewpoint, it is convenient to apply the described FF reconstruction process to evaluate only the FF samples required by the OSI expansion in [

It is useful to note that the expansion (

Many numerical simulations have been performed in order to assess the effectiveness and robustness of the proposed NF-FF transformation techniques with spherical scanning for antennas having two dimensions very different from the third one. Two sets of simulations are reported in the following. The former (from Figure

Amplitude of the output voltage

In the first set, the numerical tests refer to a scanning sphere having radius

NF-FF transformation technique | |

Standard approach [ | 130 562 |

Standard approach as modified in [ | 80 610 |

Here proposed approach | 26 467 |

Phase of the output voltage

Normalized maximum errors in the reconstruction of the voltage

Normalized mean-square errors in the reconstruction of the voltage

Amplitude of the output voltage

Phase of the output voltage

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

Amplitude of the output voltage

The second set of figures refers to a scanning sphere having radius

NF-FF transformation technique | |

Standard approach [ | 130 562 |

Standard approach as modified in [ | 102 786 |

Here proposed approach | 27 231 |

Normalized errors in the reconstruction of the voltage

Amplitude of the output voltage

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

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

Fast and accurate probe-compensated NF-FF transformations with spherical scanning for nonspherical antennas have been here developed by employing flexible AUT modellings, which allow one to fit very well the shape of a lot of actual antennas. In particular, an electrically long antenna has been considered as enclosed in a rounded cylinder, whereas a double bowl has been adopted to shape a quasiplanar antenna. The use of these modellings makes possible to remarkably lower the number of data to be acquired, thus significantly reducing the measurement time. The developed techniques work very well as widely assessed by the numerical simulations.