## 1 Introduction
In this way, it is possible to exploit all and only the available independent information of the problem at hand, resulting in a considerable reduction in terms of computational complexity and measurement time that, otherwise, would be pointlessly lengthy. In addition, these techniques not only outperform the standard spherical NF/FFT technique in terms of required number of NF samples and acquisition time but also allow one to exactly determine the highest order spherical harmonic involved in the SWE of the field [16]. Then, after gathering the samples at the positions fixed by the NR sampling, which are non-equally spaced, the probe voltage value, at each point on the scan sphere and, hence, at the positions imposed by the traditional SNF sampling theory too, can be retrieved by using a 2-D Optimal Sampling Interpolation (OSI) expansion. This makes it possible to perform the standard NF/FFT technique to obtain the antenna FF pattern. Following the idea firstly proposed by [PERSON] et al. [35], a further saving of measurement time can be obtained by performing the acquisition on-the-fly and employing continuous and synchronized motions of the probe and antenna positioners. Such an idea has led to the development of NF/FFT techniques exploiting innovative spiral scans. Alsoin this case, the use of NR sampling representations allows for a huge reduction in the spiral turns and sampling points, resulting in additional time savings. The case of a spherical modeling of the AUT was initially addressed by choosing the spiral step, which determines the number of spiral turns, coincident with the sampling step required for the interpolation on a meridian of the sphere [10]. Then, the use of the unified theory of spiral scans for non-spherical AUTs [36] has allowed for the subsequent extension to the cases of elongated and quasi-planar AUTs [10]. Unfortunately, particular positionings of the antenna on the supporting brackets, as well as the mechanical constraints of the NF measurement system and/or its unusual configuration, could impede the mounting of the AUT in such a way that its center coincides with that of the measurement sphere (onset mounting). When these shortcomings occur, the number of NF data necessary for the classical spherical NF/FFT significantly increases because of the well-known minimum sphere rule [15], thus leading to a consequent growth of the related acquisition time and costs. [PERSON] et al. addressed this problem by proposing a modified version of the SWE, wherein the spherical waves are computed with respect to the center of the (offset) coordinate system of the antenna, rather than with respect to the measurement sphere center [37; 38]. In [39], the developed approach allowed to minimize the number of coefficients involved in the SWE of the field, highly reducing the number of required measurement points, but entailing a high computational cost, since it requires to directly solve a linear equation system via an explicit matrix inversion. This drawback has been tackled in [40], where an iterative inversion technique has been employed to highly lower the required computational time. Even so, although remarkably reducing the number of necessary NF data in the offset case, the amount of samples required when employing these techniques still remains slightly greater than that in the onset case. The goal of this work is to provide an experimental validation of NR spherical spiral scannings for offset-mounted elongated AUTs, effectively modeled by a prolate spheroid or a rounded cylinder (namely, a cylinder ended with two hemispheres), whose effectiveness has already been numerically proved in [41; 42], respectively. These NR spherical spiral scannings represent the extension to the offset case of the corresponding ones [10] for the onset case and allow the accurate reconstruction of the far field of offset mounted long AUTs, by requiring only a minimum amount of samples, equal to that required by the NR onset case.