Optimal Sampling Interpolation Research Articles

Three-Dimensional Probe Mispositioning Errors Compensation: A Feasibility Study in the Non-Redundant Helicoidal Near to Far-Field Transformation Case

A feasibility study on the compensation of 3D mispositioning errors of the probe occurring in the characterization of a long antenna, via a non-redundant (NR) near to far-field (NTFF) transformation with helicoidal scan, is conducted in this article. Such types of errors can result from imperfections in the rail driving the linear motion of the probe and from an imprecise synchronization of the linear and rotational movements of the probe and the antenna when drawing the scan helix. To correct them, an approach, which proceeds through two steps, is proposed. The former step uses a technique called cylindo rical wave (CW) correction for compensating the phase of the near-field (NF) samples, which, owing to the rail imperfections, result in not being acquired over the measurement cylinder surface. The latter exploits an iterative scheme to restore the samples at the sampling points required by the adopted NR representation along the scan helix from those obtained by applying the CW correction technique and impaired by 2D mispositioning errors. The so compensated NF samples are then effectively recovered via a 2D optimal sampling interpolation (OSI) scheme to accurately obtain the input data required to carry out the standard cylindrical NTFF transformation. The OSI representation is determined here by assuming a long antenna under test as enclosed in a prolate ellipsoid or cylinder ending into two hemispheres (cigar) in order to make, depending on the particular geometry of the considered antenna, the representation effectively non-redundant. The reported numerical simulation results show the capability of the proposed approach to compensate even severe 3D mispositioning errors, thus enabling its usage in a real measurement scenario.

An Efficient Procedure to Compensate for the Errors Due to the Probe Mispositioning in a Cylindrical Near-Field Facility.

This paper deals with the compensation of the probe mispositioning errors occurring in a cylindrical near-field (NF) facility due to the imprecise control of the linear and azimuthal positioners allowing the cylindrical scanning and/or to their limited resolution and to defects in the rails guiding the linear motion. As a result, 3-D errors in the positioning of the probe at any sampling point, as prescribed by the adopted non-redundant representation, affect the accuracy of the NF measurements. An efficient procedure is here proposed to properly compensate for these errors. It involves two steps. The former allows one to correct the mispositioning errors due to the deviation of each actual sampling point from the nominal measurement cylinder. The latter makes use of an iterative technique to restore the NF samples at any sampling point fixed by the used non-redundant representation from the ones obtained at the previous step and affected by 2-D mispositioning errors. Once these steps have been fruitfully applied, the so-compensated NF samples are effectively interpolated through a 2-D optimal sampling interpolation (OSI) formula to accurately reconstruct the input data required to perform the traditional cylindrical near-to-far-field transformation. The OSI representation is here developed by considering an elongated antenna under test as enclosed either in a prolate spheroid or in a cylinder terminated by two half spheres (rounded cylinder) in order to make the representation effectively non-redundant. Numerical test results, which thoroughly prove the efficacy of the devised procedure in correcting even severe 3-D mispositioning errors, are reported.

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.

Evaluation of interfacial misfit strain field of heterostructures using STEM nano secondary moiré method.

STEM nano-moiré can achieve high-precision deformation measurement in a large field of view. In scanning moiré fringe technology, the scanning line and magnification of the existing transmission electron microscope (TEM) cannot be changed continuously. The frequency of the crystal lattice is often difficult to match with the fixed frequency of the scanning line, resulting in mostly too dense fringes that cannot be directly observed; thus, the calculation error is relatively large. This problem exists in both the STEM moiré method and the multiplication moiré method. Herein, we propose the STEM secondary nano-moiré method, i.e., a digital grating of similar frequency is superimposed on or sampling the primary moiré fringe or multiplication moiré to form the secondary moiré. The formation principle of the secondary moiré is analyzed in detail, with deduced theoretical relations for measuring the strain of STEM secondary nano-moiré fringe. The advantages of sampling secondary moiré and digital secondary moiré are compared. The optimal sampling interpolation function is obtained through error analysis. This method expands the application range of the STEM moiré method and has better practicability. Finally, the STEM secondary nano-moiré is used to accurately measure the strain field at the Si/Ge heterostructure interface, and the theoretical strain field calculated by the dislocation model is analyzed and compared. The obtained results are more compatible with the P-N dislocation model. Our work provides a practical method for the accurate evaluation of the interface characteristics of heterostructures, which is an important basis for judging the photoelectric performance of the entire device and the optimal design of the heterostructures.

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.

Pattern Evaluation From NF Spherical Spiral Data in the Noncentered Quasi-Planar Antennas Case

The far-field reconstruction of noncentered quasi-planar antennas is here addressed by using a spherical spiral scan in the near-field region. A reduction of the near-field data is achieved by suitably exploiting the unified theory of spiral scannings for nonspherical antennas. Such a technique, relying on the nonredundant representation of electromagnetic fields, adopts an oblate spheroid as source modeling and uses a two-dimensional optimal sampling interpolation algorithm to recover the data needed to execute the classical near-field–far-field transformation. In this case, the reduction process is required since an inadequate mounting system increases the number of needed data when compared to facilities, which allow one to center the antenna under test with respect to the spherical scanning surface. The above-mentioned statement is based on the following rule: the classical near-field–far-field transformation requires a number of data depending on the smallest spherical surface, which encloses the antenna and shares the same center as the scanning surface. The reported results thoroughly prove the efficacy of the developed technique.

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.

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.

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.

Optimal sampling interpolation over a plane from transient bi‐polar near‐field data

The non-redundant sampling representations of electromagnetic fields are properly applied in this study to develop an optimal sampling interpolation formula over a plane in the time domain (TD) from a minimum number of bi-polar near-field data. To this end, the ultra wide band antennas typically employed for communication applications and modern radars and characterised by a quasi-planar geometry are modelled as enclosed either in an oblate ellipsoid or in a flexible surface formed by two circular bowls with the same aperture diameter, but with eventually different lateral bends. In both the cases, numerical examples, assessing the effectiveness of the TD interpolation schemes, are shown.

Two efficient procedures to correct the positioning errors in the plane‐polar scanning

Two techniques to effectively compensate known positioning errors in a plane-polar near-field–far-field (NF–FF) transformation, using a minimum number of NF data and adopting an oblate ellipsoid to shape the considered antenna, are proposed and validated through experimental proofs. The former makes use of the singular value decomposition method to recover the voltage samples which would be acquired by the probe at the points fixed by the non-redundant sampling representation from the collected positioning error affected ones, whereas the latter employs an iterative scheme. The NF data required by the classical NF–FF transformation with plane-rectangular scanning are then efficiently evaluated via a two-dimensional optimal sampling interpolation formula. The effectiveness of the proposed techniques is assessed by experimental tests performed at the Antenna Characterisation Lab of the University of Salerno.

Two Effective Approaches to Correct the Positioning Errors in a Spherical Near-Field–Far-Field Transformation

ABSTRACTTwo 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.

Far-Field Pattern Reconstruction From a Nonredundant Plane-Polar Near-Field Sampling Arrangement: Experimental Testing

An efficient probe-compensated near-field–far-field (NF–FF) transformation with plane-polar scanning, particularly suitable for quasi-planar antennas, is experimentally assessed in this letter. It exploits the nonredundant sampling representations of electromagnetic fields and adopts an oblate ellipsoid to model the antenna under test. A two-dimensional optimal sampling interpolation expansion is employed to accurately recover the NF data needed by the standard plane-rectangular NF–FF transformation from the nonredundant plane-polar ones collected by the probe. A remarkable reduction of the number of NF data to be acquired and of the related measurement time is so obtainable. Some results of the experimental tests, performed at the UNISA Antenna Characterization Lab and assessing the effectiveness of such a NF–FF transformation technique, are reported.