Nonredundant Sampling Representations Research Articles

An Effective Spherical NF/FF Transformation Suitable for Characterising an Antenna under Test in Presence of an Infinite Perfectly Conducting Ground Plane

An effective near-field to far-field transformation using a reduced number of near-field measurements collected via a spherical scan over the upper hemisphere, due to the presence of a flat metallic ground, is devised in this paper. Such a transformation relies on the non-redundant sampling representations of electromagnetic fields and exploits the image principle to properly account for the metallic ground, supposed to be of infinite extent and realised by perfectly conducting material. The sampling representation of the probe voltage over the upper hemisphere is developed by modelling the antenna under test and its image by a very adaptable convex surface, which is able to fit as much as possible the geometry of any kind of antenna, thus minimising the volumetric redundancy and, accordingly, the number of required samples as well as the measurement time. Then, the use of a two-dimensional optimal sampling interpolation algorithm allows the reconstruction of the voltage value at each sampling point of the spherical grid required by the classical near-field-to-far-field transformation developed by Hansen. Numerical examples proving the effectiveness of the developed sampling representation and related near-field-to-far-field transformation techniques are reported.

An Effective Near-Field to Far-Field Transformation with Planar Spiral Scanning for Flat Antennas under Test.

The goal of this article is to provide numerical and experimental assessments of an effective near-field to far-field transformation (NF-FF T) technique with planar spiral scanning for flat antennas under test (AUTs), which requires a non-redundant, i.e., minimum, number of NF measurements. This technique has its roots in the theory of non-redundant sampling representations of electromagnetic fields and was devised by suitably applying the unified theory of spiral scans for non-volumetric antennas to the case in which the considered AUT is modeled by a circular disk having its radius equal to half of the AUT's maximum dimension. It makes use of a 2D optimal sampling interpolation (OSI) formula to accurately determine the massive amount of NF data required by the classical plane-rectangular NF-FF T technique from the non-redundant data gathered along the spiral. It must be emphasized that, when considering flat AUTs, the developed transformation allows one to further and significantly save measurement time as compared to that required by the previously developed NF-FF T techniques with planar spiral scans based on a quasi-planar antenna modeling, because the number of turns of the spiral and that of NF data to be acquired depend somewhat on the area of the modeling surface. The reported numerical simulations assess the accuracy of the proposed NF-FF T technique, whereas the experimental tests prove its practical feasibility.

Pattern Reconstruction from Near-Field Data Affected by 3D Probe Positioning Errors Collected via Planar-Wide Mesh Scanning

An effective procedure to correct known 3D probe positioning errors affecting the near-field–far-field transformation (NF–FF) with non-conventional plane rectangular scanning, named planar wide-mesh scanning (PWMS), is developed in this paper. It relies on the non-redundant sampling representations of electromagnetic fields and related optimal sampling interpolation (OSI) expansions and has been devised when a quasi-planar antenna under test is considered as suitably modelled by either a double bowl or an oblate spheroid. Such an algorithm first makes use of the so-called k-correction to compensate for the errors occurring when the actual sampling points deviate from the acquisition plane and then adopts an iterative procedure to restore the NF samples at the points specified by the used non-redundant sampling representation from those obtained at the previous step and affected by 2D positioning errors. Finally, once the regularly arranged PWMS samples have been calculated, the NF data required to compute the classic plane-rectangular NF–FF transformation are accurately evaluated by using an effective 2D OSI algorithm. Several numerical results are presented in order to assess the effectiveness of the devised approach.

Prediction of the far field radiated by a flat antenna under test from a reduced set of near‐field bi‐polar measurements

In this article, a bi-polar near-field-to-far-field (NFTFF) transformation with probe compensation, which is very convenient from the data reduction standpoint when characterising a flat antenna under test (AUT), is developed. It takes advantage from the non-redundant sampling representations of the electromagnetic fields to devise a sampling representation on the scanning plane, which requires the knowledge of the bi-polar NF samples at a reduced number of sampling points. To account for the AUT geometry, it properly adopts as modelling surface a disc having diameter equal to the largest size of such an AUT. This surface allows a more effective AUT modelling from the NF data reduction standpoint than the formerly proposed modelling surfaces for quasi-planar antennas (the oblate ellipsoid or the two-bowls), because, unlike these last, it has the capability to best fit the AUT geometry, thus reducing very significantly the involved volumetric redundancy. An ad hoc developed two-dimensional optimal sampling, interpolation formula is then employed to reconstruct the plane-rectangular NF data which would be necessary to execute the classical NFTFF transformation developed by Leach and Paris. Some results of numerical simulations and experimental proofs are reported to demonstrate the efficiency of the so developed technique.

Pattern Reconstruction of 3-D Modular Antennas by Means of a Non-Redundant Near-Field Spherical Scan

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.

Dimension and Sampling of the Near-Field and Its Intensity Over Curves

The paper addresses the question of efficiently sampling the near field and its intensity over an arbitrary curved line. It aims at finding the minimum number of measurements and their position for discretizing the near field and its square amplitude without loss of information and follows a common approach for both the radiation operator and the correspondent lifting operator. A scalar geometry is examined for both electric and magnetic current sources. At first, the singular values of the radiation / lifting operator are evaluated by an asymptotic approach and a change of variables which lead to an operator with a widely investigated spectrum. As the number of relevant singular values is available in closed form, the dimensions of the near field and its intensity over the curve are found. Next, starting from a sampling expansion of the pertinent left singular functions, a non-redundant sampling representation of the near field and its square amplitude is provided. Some numerical results confirm the analysis. The results may be of great interest especially in antenna testing by near field data (both standard and phaseless) with an unconventional field scanning system as, for instance, an UAV mounted probe.

Optimization of the near-field spherical spiral scanning for the radiation pattern reconstruction of an offset quasi-planar antenna

An optimization of the near-field data acquisition on a spherical spiral for recovering the radiation pattern of a quasi-planar antenna, which is non-centred with respect to the scanning system, is here presented. As a matter of fact, such an unusual antenna positioning reflects negatively on the number of the needed near-field data, since this last depends on the smallest spherical surface enclosing the antenna under test and sharing the same centre as the scanning surface. The proposed optimization reduces such a number through a non-redundant sampling representation of the measured voltage adopting a suitable source modelling. The so collected samples are then employed in a two-dimensional optimal sampling interpolation algorithm for retrieving the near-field data indispensable to carry out the classical near-field to far-field transformation. Numerical and experimental tests endorse the effectiveness of the proposed method.

A Useful Sampling Representation for Mapping the Antenna Near-Field

A convenient sampling distribution and an optimal sampling interpolation algorithm are here presented for mapping the antenna near-field values on a planar surface. The mapping procedure is based on the theoretical background related to a non-redundant sampling representation of the electromagnetic field and uses an unconventional arrangement of the sampling points. Their position results from the standard plane-rectangular allocation by properly increasing the distance between near sampling points as their distance from the antenna grows. This permits to map the values in a given area by using the knowledge of a reduced number of samples and, therefore, the measurement time is conveniently shorted. Numerical simulations and antenna measurements in anechoic chamber have been executed to test the effectiveness of the mapping procedure, whose accuracy has been proved by means of maximum and mean-square reconstruction errors at given output points.

Plane-Wave Synthesis: A Sparse Representation Perspective

Using plane-wave generator (PWG), an array consisting of a number of radiating sources, to emulate incoming signals from the far-field zone across the aperture of the antenna-under-test (AUT) is an alternative solution for antenna testing, especially for electrically large AUTs. The locations and weights of PWG elements need to be carefully designed to satisfy the required accuracy of the far-field distribution. Conventionally, the theory of nonredundant sampling representation was exploited to determine the geometry of the PWG. In this letter, we revisit this problem from the perspective of sparse representation and propose a novel method based on the orthogonal matching pursuit algorithm to derive the geometrical features of the PWG. Numerical results confirm the superiority of the proposed method over the conventional one. Furthermore, a penalty-based convex optimization framework is proposed to suppress radiation energy in the outer zone around the AUT aperture.

A Spherical Near-to-far-Field Transformation Using a Non-Redundant Voltage Representation Optimized for Non-Centered Mounted Quasi-Planar Antennas

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.

Reconstruction of the far field radiated by an offset mounted volumetric AUT from non‐redundant spherical spiral near‐field measurements

This work provides an experimental assessment of the near to far-field transformation (NTFFT) with spherical spiral scan, which properly accounts for the mounting of a volumetric AUT in offset configuration. Such a NTFFT, based on the nonredundant sampling representations of electromagnetic fields using a spherical modelling of the antenna under test (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. The reported experimental results prove the effectiveness of the developed NTFFT and of the related two-dimensional optimal sampling interpolation scheme used to reconstruct, from the spiral NF samples, the NF data at the raster grid points required by the classical spherical NTFFT.

Two approaches to get efficient NF/FF transformations from inaccurately positioned planar wide-mesh scanning samples

This paper aims to give the experimental proof of two effective procedures for the compensation of severe and pessimistic positioning errors, which alter the gathered near-field samples in a near-field to far-field (NF/FF) transformation with planar wide-mesh scanning (PWMS). This scanning is so called since it has a sampling lattice whose meshes are wider and wider as their distance from the measurement plane centre grows, so that it allows a drastic reduction of the acquisition time as compared to the classical plane-rectangular (PR) scan. The here considered NF/FF transformation with PWMS relies upon a nonredundant sampling representation of the voltage detected by the scanning probe, attained by modelling the antenna under test with a double bowl, that is, a surface got by joining together two bowls with the same circular aperture, and exploits an optimal sampling interpolation formula to precisely reconstruct, from the gathered PWMS samples, the huge NF data required by the PR NF/FF transformation. The retrieval of the NF samples at the points prescribed by the representation is got from the collected PWMS samples, corrupted by known positioning errors, by employing either a singular value decomposition based procedure or an iterative algorithm. Some experimental results, which fully assess the effectiveness of both the developed procedures, are shown.

A Nonredundant Sampling Representation Managing an Offset Mounting of an Elongated Antenna in a Spherical Near-Field Facility

An efficient spherical near-field-to-far-field transformation (NFTFFT), which takes into account the offset mounting of an elongated antenna and employs the same nonredundant (NR) amount of near-field (NF) data as in the onset mounting case, is presented. The interest for this NFTFFT is due to the fact that, for practical reasons, a mounting where the antenna and the scan sphere centers coincide is not always possible. In this case, the amount of NF measurements required by the traditional spherical NFTFFT can significantly increase. In the developed NFTFFT, this drawback has been overcome by accurately recovering these NF data from the gathered NR probe voltage samples through a sampling expansion, attained by suitably using the NR sampling representations and assuming the antenna as enclosed in a prolate spheroid. Numerical and experimental results are reported in order to assess the efficacy of the developed technique.

A Non-Redundant Sampling Representation Requiring the Same Number of Spherical Near-Field Measurements for Both Onset and Offset Mountings of a Quasi-Planar Antenna

An effective non-redundant near-field to far-field transformation (NFTFFT) with spherical scan, which accounts for the offset mounting of a quasi-planar antenna and employs the same number of NF data as in the case of onset mounting, is developed in this paper. The interest for this NFTFFT arises from the fact that the mounting where the antenna and the measurement sphere centers coincide could result to be impracticable. In this case, the amount of NF data required by the traditional spherical NFTFFT can significantly increase. In the proposed NFTFFT, this drawback has been overcome by accurately recovering these NF data from the collected non-redundant ones via a sampling expansion, obtained by exploiting the non-redundant sampling representations and assuming the antenna as enclosed in an oblate spheroid. Numerical and experimental results assessing the effectiveness of the developed technique are reported.

Laboratory testing of an SVD‐based approach to recover the non‐redundant bi‐polar NF data from the positioning error affected ones

This study deals with the problem of the correction of known probe positioning errors, which can occur in an actual planar near-field facility when adopting a non-redundant near-field to far-field (NFTFF) transformation with a bi-polar scan for quasi-planar antennas. To this end, a singular value decomposition based approach is developed to recover the uniform bi-polar samples, whose position is set by the non-redundant sampling representation got by shaping the antenna with a double bowl, from those affected by positioning errors. Then, a 2D optimal sampling interpolation formula is used to accurately reconstruct the plane rectangular near-field data needed by the standard NFTFF transformation from the retrieved non-redundant uniform samples. Experimental results, assessing the capability of the developed procedure to correct even pessimistic positioning errors, are shown.

Non-redundant Spherical Near-Field to Far-Field Transformation for a Volumetric Antenna in Offset Configuration

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.

Laboratory tests on an near‐field to far‐field transformation technique from non‐redundant bi‐polar data

An experimental verification of a fast and accurate technique, which allows the evaluation of the antenna radiation pattern from a non-redundant, i.e. minimum, number of near-field (NF) measurements acquired via a bi-polar scan, is provided in this study. This probe compensated NF-to-far-field (NFTFF) transformation exploits a non-redundant sampling representation of the voltage acquired by the probe, achieved by shaping the antenna with a double bowl, a very flexible model particularly tailored to antennas characterised by a quasi-planar geometry. The input NF data necessary for executing the standard plane-rectangular NFTFF transformation are efficiently recovered from the acquired non-redundant bi-polar ones by applying a two-dimensional optimal sampling interpolation formula, so that a remarkable measurement time saving is attained. Some results of laboratory proofs performed at the Antenna Characterization Lab of the University of Salerno are reported to demonstrate the accuracy and the practical effectiveness of the presented NFTFF transformation technique.

TD optimal sampling interpolation over a plane from NF data collected through a non‐conventional plane‐rectangular scanning

A time domain (TD) optimal sampling interpolation (OSI) scheme to efficiently reconstruct the transient field radiated by an ultra-wide band (UWB) antenna over a plane in the near-field (NF) region from a minimum number of its NF TD samples, acquired through a non-conventional plane-rectangular scanning, is developed in this study. Such a result has been achieved by properly exploiting the non-redundant sampling representations of electromagnetic fields and modelling the antenna by a proper rotational surface. Since the UWB antennas are usually quasi-planar, such a surface can be conveniently chosen coincident with that of an oblate ellipsoid or with that formed by two bowls with the same circular aperture and possibly different lateral bends. Numerical examples, which assess the accuracy of the related TD OSI representations, are reported.

Correction of Known Position Errors in a Spherical Near to Far-Field Transformation for Long Antennas

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.

Fast and Accurate Far-Field Prediction by Using a Reduced Number of Bipolar Measurements

This letter gives the experimental assessment of a near-to-far-field transformation (NTFFT) technique allowing the fast and accurate reconstruction of the antenna far field from a nonredundant, i.e., minimum number of near-field (NF) data collected through a bipolar scanning. Such a NTFFT relies on a nonredundant sampling representation of the voltage detected by the scanning probe, attained by shaping the antenna with an oblate ellipsoid, a model suitable to deal with quasi-planar antennas, as typically are the measured ones in a planar NF facility. The NF data necessary to execute the traditional plane-rectangular NTFFT are then effectively recovered from the acquired (nonredundant) bipolar ones by exploiting a 2-D optimal sampling interpolation formula. This makes possible to achieve a remarkable acquisition time saving, which is a very relevant outcome, because this time is nowadays much greater than that needed to carry out the NTFFT.