Optimal Sampling Interpolation Algorithm 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.

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.

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.

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.

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 Positioning Errors Affected Near-Field Data Acquired via Helicoidal Scanning

In this paper, an effective technique to compensate the positioning errors in a near-field—far-field (NF-FF) transformation with helicoidal scanning for elongated antennas is presented and validated both numerically and experimentally. It relies on a nonredundant sampling representation of the voltage measured by the probe, obtained by considering the antenna as enclosed in a cylinder ended in two half-spheres. An iterative scheme is used to reconstruct the helicoidal NF data at the points fixed by the representation from the acquired irregularly spaced ones. Once the helicoidal data have been retrieved, those needed by a classical NF-FF transformation with cylindrical scanning are efficiently evaluated by using an optimal sampling interpolation algorithm. Some numerical tests, assessing the accuracy of the approach and its stability with respect to random errors affecting the data, are reported. Experimental tests performed at the Antenna Characterization Lab of the University of Salerno further confirm the validity of the proposed technique.

Spherical Near-Field - Far-Field Transformation for Quasi-Planar Antennas from Irregularly Spaced Data

An effective near-field - far-field (NF - FF) transformation with spherical scanning for quasi-planar antennas from irregularly spaced data is developed in this paper. Two efficient approaches for evaluating the regularly spaced spherical samples from the nonuniformly distributed ones are proposed and numerically compared. Both the approaches rely on a nonredundant sampling representation of the voltage measured by the probe, based on an oblate ellipsoidal modelling of the antenna under test. The former employs the singular value decomposition method to reconstruct the NF data at the points fixed by the nonredundant sampling representation and can be applied when the irregularly acquired samples lie on nonuniform parallels. The latter is based on an iterative technique and can be used also when such a hypothesis does not hold, but requires the existence of a biunique correspondence between the uniform and nonuniform samples, associ- ating at each uniform sampling point the nearest irregular one. Once the regularly spaced spherical samples have been recovered, the NF data needed by a probe compensated NF - FF transformation with spherical scanning are efficiently evaluated by using an optimal sampling interpolation algorithm. It is so possible to accurately compensate known posi- tioning errors in the NF - FF transformation with spherical scanning for quasi-planar antennas. Some numerical tests assessing the accuracy and the robustness of the proposed approaches are reported.

Two Techniques for Compensating the Probe Positioning Errors in the Spherical NF-FF Transformation for Elongated Antennas

Two effective approaches for compensating the positioning errors in a near-field-far-field (NF-FF) transformation technique with spherical scanning for long antennas using a nonredundant number of data are presented. The transformation technique relies on the nonredundant sampling representations of the electromagnetic fields and on the optimal sampling interpolation (OSI) expansions, and assumes the antenna under test as enclosed in a prolate ellipsoid, a source modelling particularly suitable to deal with elongated antennas. In order to evaluate the NF data at the points fixed by the nonredundant representation from the acquired irregularly spaced ones, the former approach employs the singular value decomposition method, whereas the latter makes use of an iterative technique. The former can be applied when the irregularly samples lie on nonuniform parallels, thus allowing to reduce the starting two-dimensional problem into two independent one-dimensional ones. The latter can be employed also when such a hypothesis does not hold, but requires the existence of a one-to-one correspondence associating at each uniform sampling point the nearest irregular one. In both the cases, the NF data needed by a probe compensated NF-FF transformation with spherical scanning are efficiently evaluated by using an OSI algorithm. Numerical tests assessing the effectiveness of the proposed approaches and their stability with respect to random errors affecting the NF data are shown.

AN ITERATIVE TECHNIQUE TO COMPENSATE FOR POSITIONING ERRORS IN THE NF-FF TRANSFORMATION WITH HELICOIDAL SCANNING FOR LONG ANTENNAS

An efiective procedure is developed in this paper to compensate the probe positioning errors when using a near-fleld to far-fleld transformation technique with helicoidal scanning for long antennas. It is based on a prolate ellipsoidal modelling of the antenna under test and makes use of an iterative scheme to retrieve the uniformly distributed helicoidal near-fleld data from the irregularly spaced acquired ones. Once these data have been recovered, those required to perform a standard near-fleld-far-fleld transformation with cylindrical scanning are e-ciently determined via an optimal sampling interpolation algorithm. Some numerical tests are reported to assess the accuracy of the approach and its robustness with respect to random errors afiecting the data. At last, the validity of the developed technique is further conflrmed by the experimental tests performed at the Antenna Characterization Lab of the University of Salerno.

Near-Field/Far-Field Transformation with Helicoidal Scanning from Irregularly Spaced Data

A fast and accurate technique for the compensation of the probe positioning errors in the near-field/far-field transformation with helicoidal scanning is proposed in this paper. It relies on a nonredundant sampling representation using a spherical modelling of the antenna under test and employs an iterative scheme to evaluate the near-field data at the points fixed by the helicoidal nonredundant representation from the acquired irregularly distributed ones. Once these helicoidal data have been recovered, those required by a classical cylindrical near-field/far-field transformation are efficiently determined by using an optimal sampling interpolation algorithm. Some numerical tests assessing the effectiveness of the proposed approach and its stability with respect to random errors affecting the near-field data are shown.

ON THE COMPENSATION OF PROBE POSITIONING ERRORS WHEN USING A NONREDUNDANT CYLINDRICAL NF-FF TRANSFORMATION

Two different approaches for compensating the probe positioning errors in a near-field-far-field transformation with cylindrical scanning using a nonredundant number of measurements are presented and experimentally validated in this paper. In order to evaluate the uniformly distributed samples from the irregularly spaced ones, the former makes use of the singular value decomposition method, whereas the latter employs an iterative technique. In both the cases, the near-field data needed by a standard near-field-far- field transformation are efficiently evaluated via an optimal sampling interpolation algorithm.

An effective NF‐FF transformation with a hybrid cylindrical and bipolar scanning

AbstractAn efficient and innovative near‐field‐far‐field transformation technique with a hybrid cylindrical and bipolar scanning is proposed in this article. It allows one to considerably reduce the truncation error, which unavoidably affects the cylindrical near‐field‐far‐field transformation. To this end, nonredundant measurements are acquired by employing a cylindrical facility integrated with a rotating arm, which allows to collect the bipolar data on the upper and lower surfaces of the cylinder. Then, by applying the equivalence theorem, the knowledge of the electric field tangential components on the top and bottom of the cylinder is properly exploited to recover the nonredundant cylindrical near‐field data external to the measurement zone. At last, the near‐field data needed to perform the classical near‐field‐far‐field transformation with cylindrical scanning are efficiently computed via an optimal sampling interpolation algorithm. The effectiveness of the approach in reducing the truncation error is assessed by numerical tests. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 772–779, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24165

LABORATORY TESTS ASSESSING THE EFFECTIVENESS OF THE NF-FF TRANSFORMATION WITH HELICOIDAL SCANNING FOR ELECTRICALLY LONG ANTENNAS

This paper deals with the experimental validation of an efiective near-fleld-far-fleld transformation technique with helicoidal scanning particularly suitable for electrically long antennas, whose validity has been numerically assessed in a previous authors' paper. Such a technique relies on the results relevant to the nonredundant sampling representations of the electromagnetic flelds and makes use of an optimal sampling interpolation algorithm, which allows the reconstruction of the near-fleld data needed by the near-fleld-far-fleld transformation with cylindrical scan. The use of a prolate ellipsoid instead of a sphere to model an elongated antenna allows one to consider measurement cylinders with a diameter smaller than the antenna height, thus reducing the error related to the truncation of the scanning zone. Moreover, a signiflcant reduction of the needed near- fleld data is also obtained. The comparison of the far-fleld patterns reconstructed from the acquired helicoidal measurements with those obtained from the data directly measured on the classical cylindrical grid assesses the efiectiveness of the near-fleld-far-fleld transformation using this innovative scanning technique. At last, its validity is further conflrmed by the very good agreement with the direct far-fleld measurements.

A singular value decomposition based approach for far‐field reconstruction from irregularly spaced planar wide‐mesh scanning data

AbstractAn efficient technique is developed in this article to evaluate the antenna far field from the knowledge of nonuniformly distributed near‐field data measured by a probe via a planar wide‐mesh scanning facility. To this end, the singular value decomposition method is properly applied to reconstruct the uniformly spaced samples, whose positions are fixed by a nonredundant sampling representation of the electromagnetic field. Then, the plane‐rectangular near‐field data needed to perform the classical probe compensated near‐field‐far‐field transformation are efficiently evaluated via an optimal sampling interpolation algorithm. Numerical tests, assessing the effectiveness and the stability of the far‐field reconstruction process, are reported. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 1768–1772, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22502

Application of an Optimal Sampling Interpolation Algorithm to the Analysis of the SRT Antenna

The aim of this work is to develop an optimized version of the Current Integration Method for reducing the computational effort required by the electromagnetic analysis of the Sardinia Radio Telescope antenna. It consists in a general purpose, fully steerable Gregorian antenna with high-efficiency operation up to 100 GHz and a very large collecting area. The optimization process is based on a non-redundant sampling representation of the induced current given in the Physical Optics approximation and can be easily extended to other reflector antenna configurations. Numerical simulations and comparisons with a commercial tool assess the efficiency of the proposed approach.

Optimization of the current integration method for a front‐fed parabolic reflector antenna

AbstractThis work centers on an optimization of the current integration method for determining the field radiated by a centered parabolic reflector fed at its focus. A nonredundant sampling representation of the physical optics (PO) current, induced on the main reflector by the electromagnetic field radiated from the primary field source, and an optimal sampling interpolation algorithm are developed to this end. Such an approach allows one to reduce the number of points where the knowledge of the current is required, so that the computation time decreases remarkably when the evaluation of the field radiated from the feed is burdensome. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 235–239, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11339

NF–FF transformation with cylindrical scanning from nonuniformly distributed data

AbstractTwo efficient probe‐compensated near‐field–far‐field (NF–FF) transformation techniques with cylindrical scanning requiring a minimum number of irregularly spaced data, are proposed. Singular value decomposition (SVD) method is applied to evaluate the uniformly distributed samples, whose positions are fixed by a nonredundant sampling representation of the field, from the irregularly spaced ones. Then, the voltage data needed by standard NF–FF transformation or by a non‐conventional one recently developed by the authors are efficiently evaluated via an optimal sampling interpolation algorithm. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 39: 4–8, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11109

Far-Field Reconstruction from Nonuniform Plane-Polar Data: A SVD-Based Approach

An efficient technique to reconstruct the field radiated by an antenna in the far-field region from the knowledge of the nonuniformly spaced plane-polar data measured by a probe in the near-field region is developed in this work. The singular value decomposition method is applied to evaluate the uniformly distributed samples, whose positions are fixed by a nonredundant sampling representation of the field. Then the plane-rectangular near-field data needed to perform the classical probe-compensated near-field-far-field transformation are efficiently evaluated via the optimal sampling interpolation algorithm. As demonstrated by numerical tests, the far-field reconstruction process is accurate and stable