Some representative numerical and experimental results relevant to the spherical spiral scanning case when considering quasi-planar and electrically long antennas, respectively, are reported in the following for reader's convenience.
The following numerical simulations are relevant to the spherical spiral scanning and to a quasi-planar antenna modelled as enclosed in a double bowl, that is, a surface [SIGMA] formed by two circular "bowls"  with the same aperture diameter 2a, but with bending radii c and c' of the upper and lower arcs eventually different to fit better the actual AUT geometry (see Figure 7).
For reader's convenience, we report in the following some experimental results already published in  and relevant to the spherical spiral scanning when dealing with an electrically long antenna modelled as enclosed in a rounded cylinder, namely, a cylinder of height h' ended in two half-spheres of radius a' (see Figure 13).
Note that the number of used samples is 1024, significantly less than those (3622 and 5100) required by the NF-FF transformation with spiral scanning  based on the spherical AUT modelling and by the MI Technologies software package implementing the classical NF-FF transformation , respectively.
Among the NF-FF transformations, that employing the spherical spiral scanning [23-28], as well as that employing the spherical one [12,13,16,34-36], have attracted considerable attention, since they allow the full reconstruction of the AUT radiation pattern, even though the data processing is considerably more complex than that needed by planar and cylindrical NF facilities [1, 2].
In the spherical spiral scanning, the AUT is located at the origin of a spherical coordinate system (r, [??], [phi]) and the field radiated by it is measured by a probe scanning a spiral lying on a spherical surface M having radius d (Fig.
This section is devoted to show some experimental results assessing the effectiveness of the described NF-FF transformation with spherical spiral scanning for quasi-planar antennas.
An experimental validation of the NF-FF transformation technique with spherical spiral scanning suitable for quasi-planar antennas and using a two-bowls modelling of the AUT has been provided in this paper.
The goal of this contribution is to develop even more effective NF-FF transformations with spherical spiral scanning tailored to nonspherical antennas and based on highly flexible modelings, which allow one to further reduce the number of the NF data to be acquired (and the related measurement time) since they are able to better fit the shape of many antennas by properly choosing their geometric parameters.
Savarese, "Directivity computation by spherical spiral scanning in NF region," Journal Electromagnetic Waves and Applications, Vol.
The unified theory of spiral scannings for nonspherical antennas , obtained by paralleling the rigorous procedure  valid when adopting the spherical AUT modeling, allows one to develop the voltage representation on the sphere from a nonredundant number of its samples collected along the spiral.
Recently, an adaptive acquisition technique has been proposed in  to reduce the measurement time by rectangular spiral scanning
of the probe.