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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 antenna...
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The experimental assessment of an effective near-field - far-field (NF-FF) transformation technique with plane-polar scanning, which requires a nonredundant, i.e. minimum, number of NF data, is provided in this communication. Such a technique relies on the nonredundant sampling representations of the electromagnetic fields and, to shape the antenna...
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Citations
... In this framework, a special mention must be reserved for the spherical NF-FF transformation as it is the only one that guarantees knowledge of the full radiation pattern. On the other hand, it is the most complicated from analytical and computational viewpoints, so that many efforts have been spent on its optimization (see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] as a non-exhaustive list of references). In particular, for keeping accuracy, the reduction in the time needed to perform the NF measurements is a key point of optimization strategies since it is much longer than that required to realize the NF-FF transformation (usually attained offline). ...
... As a matter of fact, according to these results, the smaller the area of surface enclosing the AUT, the lower the number of required NF samples. In particular, an appropriate choice of the AUT model permits the evaluation of the optimal parameters to be used and the reduction in the number of parallels and samples on them when going toward the poles [14][15][16][17]. Unfortunately, the AUT models proposed so far cannot best fit the geometry of some volumetric radiating systems such as those mounted on modular CubeSats. ...
... Note that, on the contrary of roids and cylinders terminated by spherical caps having only two geometri freedom, the composite surface in Figure 1 possesses four geometrical de dom, i.e., height and radius of the central body and radii of the lateral b permitting the best fit for the geometry of 3-D modular radiating system their modules are arranged. Accordingly, it minimizes the volumetric redu tains the spherical and flexible models [15,17] as particular cases, and, for racy, guarantees a non-redundant number of needed samples, thus saving time for the data acquisition. An optimal sampling interpolation (OSI) algo sequently developed to use these non-redundant data for an accurate comp NF values that are utilizable in the classical NF-FF transformation [13]. ...
A very flexible source model is proposed here to reduce the volumetric redundancy when considering the pattern reconstruction of three-dimensional modular antennas by means of a near-field spherical scan using a non-redundant sampling representation. Since this last facet is based on the appropriate choice of antenna model for the evaluation of the optimal parameters to be used, the proposed geometry guaranteed the minimum number of needed samples and then a significant time saved for data acquisition on the near-field spherical grid. Then, an optimal interpolation algorithm used these non-redundant samples for an accurate evaluation of the near-field data that were usable in the classical near-field to far-field transformation. The reliability and accuracy of the reconstruction process were proven by means of numerical tests. These last showed a remarkable reduction (about 53%) in needed near-field samples as compared to those required by the classical near-field to far-field transformation and this was achieved without any loss in accuracy.
... The corresponding probe, which compensated non-redundant NTFF transformation [18], considered a long AUT as enclosed in a cylinder terminated by two spherical caps, and a quasi-planar one in two circular bowls having the same aperture and possibly different radii of the lateral bends (two-bowls). Finally, the experimental validation [22] of this last transformation, and that [21] was relevant to the probe compensated version of the non-redundant NTFF transformation [15], thoroughly proved their efficacy from the practical point of view too. ...
This research falls in the antenna measurements related topic, and deals with the problem occurring in the classical spherical near-to-far-field (NTFF) transformation, when it becomes unpractical to mount the antenna under test (AUT) with its center at the center of the scanning sphere. This issue reflects in a growth of the number of near-field (NF) samples to be acquired, since this number depends on the radius of the minimum sphere, which contains the antenna, and is centered at the scanning sphere center. The non-redundant sampling representations of the electromagnetic field are conveniently exploited, to develop an effective spherical NTFF transformation for non-centered AUTs with quasi-planar geometry, requiring a minimum amount of NF samples, and nearly the same as that for a centered mounting of the AUT. Then, the NF data needed to perform the classical NTFF transformation are determined in efficient way from the acquired non-redundant NF samples by employing an accurate 2-D sampling interpolation scheme. Thus, it is possible to significantly save measurement time. Some simulation and laboratory results are reported to show the effectiveness of the developed technique, which takes into account a non-centered AUT mounting.
... The wanted FF radiation pattern can be then determined through near to FF transformation (NTFFT) techniques [1][2][3][4][5][6]. The most attractive NTFFT from the full FF reconstruction viewpoint is that where the NF measurements are carried out over a spherical surface [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21], since it does not suffer from the truncation error, like those using a planar or a cylindrical scanning. ...
... By applying the NR sampling representations [23,24] to the voltage detected by an electrically small probe, whose spatial bandwidth is almost the same of the AUT field [25], and shaping a quasi-planar AUT with a double bowl (a surface got by joining together two bowls with the same circular aperture) and a long antenna with a rounded cylinder (a cylinder terminated by hemispherical caps), probe compensated NR NTFFTs with spherical scan have been proposed in [15]. At last, the effectiveness of these NTFFTs and of the probe compensated version of those in [12] has been experimentally confirmed in [18] and [19], respectively. ...
The theoretical foundations of the near to far field transformation (NTFFT) techniques with spiral scannings have been properly applied to develop a non‐redundant spherical spiral NTFFT which properly accounts for a mounting of a volumetric antenna under test (AUT) in an offset configuration, due to any practical constraints. Such an NTFFT, based on the non‐redundant sampling representations of electromagnetic fields using spherical modelling of the AUT, requires the same number of near‐field (NF) spiral data when the AUT is mounted both in onset and offset configuration because this number depends only on the area of the modelling sphere centred at the AUT centre. Moreover, it employs an efficient two‐dimensional (2D) optimal sampling interpolation (OSI) formula to recover, from the spiral NF samples, the massive number of NF data required by the classical spherical NTFFT, which is related to the radius of the smallest sphere enclosing the AUT and centred at the scanning sphere centre. It is so possible to get a remarkable measurement time saving when the AUT is offset mounted. Numerical and experimental results, fully assessing the effectiveness of the developed NTFFT and the related 2D OSI algorithm, are shown.
... As a matter of fact, it has been proved [25] that the voltage detected by this type of probe exhibits practically the same spatial bandwidth of the EM field radiated by the AUT and, thus, the results in [22,23] can be utilized to achieve an NR representation of such a voltage too. At last, the NR NFTFFTs [13] and the probe compensated version of those in [10] have been experimentally assessed in [17] and [16] respectively. ...
Background
The development of fast Near-Field (NF) measurement techniques allowing the precise determination of the Far-Field (FF) radiation features of an antenna is becoming more and more challenging nowadays.
Objective
The goal of the article is the development of an NF To FF Transformation (NFTFFT) with spherical scan for offset mounted volumetric Antennas Under Tests (AUTs) requiring, unlike the classical technique, a reduced set of NF data, that is of the same amount as for the onset mounting case, thus making data gathering faster. In fact, the number of NF data needed by the standard approach may considerably increase in this case, since the size of the smallest sphere surrounding the AUT and centered at the center of the measurement sphere rises.
Methods
This goal has been achieved by profitably exploiting the non-redundant sampling representation of electromagnetic field and assuming a volumetric AUT as contained in a sphere. An optimal sampling interpolation algorithm is then employed to precisely reconstruct the input NF data for the traditional spherical NFTFFT from the reduced set of the collected ones.
Conclusion
The numerical simulations and experimental tests demonstrate the effectiveness of the developed approach accounting for an offset mounting of the AUT.
... In particular, quasi-planar AUTs have been considered as contained in an oblate ellipsoid [13] or in a surface consisting of two circular bowls having the same aperture and eventually different lateral surfaces (double bowl) [14], whereas a prolate ellipsoid [13] or a cylindrical surface with two hemispherical caps (rounded cylinder) [14] has been employed to model long antennas. The experimental validations of the aforementioned non-redundant spherical NTFF transformations [13] and [14] have been then provided by D'Agostino et al. [15] and [16], respectively. ...
... It can be easily seen that the considered hypothesis of bijective relation between every uniform sampling point and the "nearest" non-uniform one guarantees the fulfilment of these conditions. Finally, it can be shown that (16) can be rewritten in the following explicit form: ...
Background
This paper provides the experimental validation of an efficient iterative procedure to correct known position errors in a spherical near to far-field (NTFF) transformation for elongated antennas which uses a minimum number of NF measurements.
Method
This transformation exploits a non-redundant sampling representation of the voltage detected by the probe obtained by shaping a long antenna with a prolate ellipsoid. The uniform samples, those at the points set by the representation, are accurately reconstructed from the acquired not regularly distributed (non-uniform) ones by using an iterative scheme, which requires a one to one relationship between each uniform sampling point and the corresponding non-uniform one. Then a 2-D optimal sampling formula is adopted to evaluate the input data needed to perform the traditional spherical NTFF transformation from the retrieved non-redundant uniform samples.
Conclusion
Finally, laboratory proofs have been reported to demonstrate the validity of the presented technique from a practical viewpoint.
... In this context, a technique relying on the conjugate gradient iteration method and exploiting the fast Fourier transform (FFT) for unequally spaced data (Dutt & Rokhlin, 1993) has been proposed to correct known probe position errors in the classical NF-FF transformations with planar (Wittmann et al., 1998) and spherical (Wittmann et al., 2004) scannings. In any case, these techniques are unsuitable for non-redundant spherical NF-FF transformations (Bucci et al., 2001;D'Agostino et al., 2011aD'Agostino et al., , 2013aD'Agostino et al., , 2013b. ...
... and ρ′(z′) is the equation of Σ in cylindrical coordinates. Details about the determination of the maximum in Eq. (2) can be found in D'Agostino et al. (2011a).The voltage at P on the meridian at φ can be recovered via the OSI expansion(D'Agostino et al., 2011a(D'Agostino et al., , 2013b: ...
... are the Dirichlet and Tschebyscheff sampling functions, respectively, with T N ðÁÞ being the Tschebyscheff polynomial of degree N. The intermediate samples can be obtained by interpolating the samples on the parallels via the OSI expansion(D'Agostino et al., 2011a(D'Agostino et al., , 2013b: ...
Two techniques are developed to efficiently compensate known positioning errors affecting the near-field measurements in a non-redundant spherical near-field–far-field transformation for quasi-planar antennas, and they are fully assessed through numerical and experimental tests. They rely on a non-redundant sampling representation of the voltage measured by the probe, obtained by assuming that the antenna is enclosed in a surface formed by two circular bowls with the same aperture diameter. Both techniques use a two-step procedure. In the first step, the near-field data at the points fixed by the sampling representation are recovered from the irregularly spaced measured ones by properly applying an iterative technique or the singular value decomposition method. Then the near-field data needed by the standard spherical near-field–far-field transformation are effectively reconstructed by means of an optimal sampling interpolation algorithm.
... The near-field -far-field (NF-FF) transformation with spherical scanning is particularly interesting and has attracted considerable attention [1][2][3][4][5][6][7][8][9][10][11], since it allows the complete reconstruction of the radiation pattern of the antenna under test (AUT). In this framework, the application of the nonredundant sampling representations of the electromagnetic (EM) fields [12,13] to the voltage measured by the scanning probe has allowed the development of effective nonredundant spherical NF-FF transformations [8][9][10][11] typically requiring a number of NF data remarkably smaller than that needed when employing the classical transformation [4]. ...
... The near-field -far-field (NF-FF) transformation with spherical scanning is particularly interesting and has attracted considerable attention [1][2][3][4][5][6][7][8][9][10][11], since it allows the complete reconstruction of the radiation pattern of the antenna under test (AUT). In this framework, the application of the nonredundant sampling representations of the electromagnetic (EM) fields [12,13] to the voltage measured by the scanning probe has allowed the development of effective nonredundant spherical NF-FF transformations [8][9][10][11] typically requiring a number of NF data remarkably smaller than that needed when employing the classical transformation [4]. As a matter of fact, the NF data required by this last are accurately reconstructed from the acquired nonredundant data by means of an optimal sampling interpolation (OSI) expansion. ...
... To this end, an approach relying on the conjugate gradient iteration method and adopting the unequally spaced fast Fourier transform [14] has been proposed [15,16]. Unfortunately, such an approach is not suitable for the nonredundant NF-FF transformations with spherical scan [8][9][10][11], wherein the nonredundant samples are interpolated via OSI expansions to get the NF data needed to perform the classical transformation. Moreover, a direct reconstruction of the NF data needed for the transformation from the irregularly spaced samples is not advisable [17] and a more convenient and viable strategy is to first retrieve the uniform samples from the nonuniform ones and then determine the requested NF data via an accurate and stable OSI expansion. ...
An efficient technique for compensating known probe positioning errors in a nonredundant spherical near-field - far-field (NF-FF) transformation, using an oblate ellipsoid to model a quasi-planar antenna, is experimentally assessed in this work. It employs an iterative approach to recover the nonredundant NF samples at the points fixed by the sampling representation from the collected irregularly spaced ones. The NF data required by the classical spherical NF-FF transformation are then efficiently determined from the nonredundant NF samples by means of an optimal sampling interpolation algorithm. Some experimental results, carried out at the UNISA Antenna Characterization Lab and assessing the effectiveness of the technique, are shown.
... Since the AUT has been assumed quasi-planar, an effective modelling is obtained by choosing Σ coincident with the smallest surface 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 the actual AUT geometry better (see Figs. 1 and 2). Such a modelling has been successfully applied to develop nonredundant NF–FF transformations with spherical[22,23], spherical spiral[24,25], and planar wide mesh[26,27]scannings, when dealing with quasiplanar antennas. It can be easily verified that, for such a modelling, ' = 2 b + b' + c + c'' change depending on the range of the radial distance ρ (seeFig. ...
The experimental assessment of an effective near-field - far-field (NF-FF) transformation technique with plane-polar scanning, which requires a nonredundant, i.e. minimum, number of NF data, is provided in this communication. Such a technique relies on the nonredundant sampling representations of the electromagnetic fields and, to shape the antenna, adopts a surface formed by two circular bowls with the same aperture diameter, but eventually different bending radii of the upper and lower arcs. An optimal sampling interpolation algorithm allows the efficient reconstruction of the NF data needed by the classical NF-FF transformation with plane-rectangular scanning from the acquired nonredundant plane-polar ones. A remarkable measurement time saving is so obtained.
... 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 -scanner, cannot be performed at the UNISA Antenna Characterization Lab wherein, on the contrary, it has been possible to carry out several measurement campaigns assessing the validity [26][27][28][29][30][31][32][33][34] of the nonredundant NF-FF transformation techniques using cylindrical and spherical scanning geometries. Fortunately, a recent research agreement with Selex ES, a Finmeccanica company, whose antenna characterization laboratories are provided with planar NF facilities, has offered the opportunity for this experimental validation. ...
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.
... Among these transformations, those [9][10][11][12][13][14][15][16][17][18][19][20][21] based on the non-redundant sampling representations of electromagnetic (EM) fi elds [22,23] are even more effective from the measurement-time-reduction viewpoint, due to the reduced number of near-fi eld data needed, and due to the lower number of spiral turns. In particular, those employing sphericalspi ral scanning [14][15][16][17][18][19][20] are particularly attractive, since they retain the interesting feature of the spherical near-fi eld-to-farfi eld transformations [24][25][26][27][28][29][30][31][32] to allow the full reconstruction of the antenna's far fi eld, and avoid errors related to the truncation of the scan surface. The two-dimensional non-redun dant sampling representation for the voltage measured by the probe on a sphere, and the related optimal sampling interpola tion (OSI) expansion, were obtained by developing a non-redundant representation on a spiral, the pitch of which is equal to the sample spacing required for the interpolation along a meridian. ...
This paper provides the experimental assessment of an effective near-field-to-far-field (NF-FF) transformation technique with spherical-spiral scanning, particularly suitable for long antennas. Such a technique allows a remarkable measurement-time saving, due to the use of continuous and synchronized movements of the positioning systems, and due to the reduced number of required near-field measurements. This is made possible by a non-redundant sampling representation of the voltage measured by the probe, obtained by using the unified theory of spiral scans for non-spherical antennas, and adopting a prolate-ellipsoidal source modeling. The near-field data needed by the classical spherical near-field-to-far-field transformation are then efficiently retrieved from those acquired along the spiral by an optimal sampling interpolation formula.
