Optimal Sampling Interpolation Research Articles

Efficient reconstruction of the pattern radiated by a long antenna from data acquired via a spherical-spiral-scanning near-field facility [measurements corner

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.

Near-Field to Far-Field Transformation Techniques with Spiral Scannings: A Comprehensive Review

An overview of the near-field-far-field (NF-FF) transformation techniques with innovative spiral scannings, useful to derive the radiation patterns of the antennas commonly employed in the modern wireless communication systems, is provided in this paper. The theoretical background and the development of a unified theory of the spiral scannings for quasi-spherical and nonspherical antennas are described, and an optimal sampling interpolation expansion to evaluate the probe response on a quite arbitrary rotational surface from a nonredundant number of its samples, collected along a proper spiral wrapping it, is presented. This unified theory can be applied to spirals wrapping the conventional scanning surfaces and makes it possible to accurately reconstruct the NF data required by the NF-FF transformation employing the corresponding classical scanning. A remarkable reduction of the measurement time is so achieved, due to the use of continuous and synchronized movements of the positioning systems and to the reduced number of needed NF measurements. Some numerical and experimental results relevant to the spherical spiral scanning case when dealing with quasi-planar and electrically long antennas are shown.

Far-Field Pattern Reconstruction from Near-Field Data Collected via a Nonconventional Plane-Rectangular Scanning: Experimental Testing

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.

Phaseless Antenna Measurement on Non-Redundant Sample Points Via Leith-Upatnieks Holography

A scheme for reducing the number of sample points in phaseless acquisition based on Leith-Upatnieks holography is presented. An appropriate choice of the phase of the reference field enables to drastically decrease the sampling rate by acquiring the so-called “reduced” field instead of the real radiated field. The reference phase changes are enabled by applying the recent developments on the synthesis of the reference wave. Moreover, optimal sampling interpolation can be applied to the retrieved field so that the real field can be computed at any point on the acquisition surface. The method is illustrated by means of multiple simulations for observation domains such as straight lines, azimuthal circles as well as for a plane-polar acquisition scheme.

An Experimental Validation of the Near-Field - Far-Field Transformation with Spherical Spiral Scan [AMTA Corner

This paper concerns the experimental validation of a probe-compensated near-field-to-far-field (NF-FF) transformation technique using spherical spiral scanning. This allows one to significantly reduce the measurement time, by means of continuous and synchronized movements of the positioning systems of the probe and antenna under test. Such a technique relies on the non-redundant sampling representations of the electromagnetic fields. It makes use of a two-dimensional optimal sampling interpolation formula to recover the near-field data needed to perform the classical spherical near-field-to-far-field transformation. The very good accuracy obtained both in the near-field and the far-field reconstructions establishes the effectiveness of the approach.

Experimental Assessment of an Effective Near-Field–Far-Field Transformation With Spherical Spiral Scanning for Quasi-Planar Antennas

Experimental tests on a near-field-far-field (NF-FF) transformation technique with spherical spiral scanning suitable for quasi-planar antennas are presented in this letter. Such a technique is based on the nonredundant sampling representations of the electromagnetic fields and employs an oblate ellipsoid to model the antenna under test. A two-dimensional optimal sampling interpolation formula is then employed to recover the NF data at any point on the scanning sphere and, in particular, at those needed by the classical spherical NF-FF transformation. It is so possible to lower the number of needed measurements, as well as the time required to acquire the data. Both the reported NF and FF reconstructions assess the effectiveness of the technique.

Experimental Testing of Nonredundant Near-Field to Far-Field Transformations with Spherical Scanning Using Flexible Modellings for Nonvolumetric Antennas

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 antennas characterized by two dimensions very different from the other one. In particular, a cylinder ended in two half-spheres is adopted for modelling long antennas, whereas the quasi-planar ones are considered as enclosed in a rotational surface formed by two circular “bowls” having the same aperture diameter, but eventually different bending radii. The NF data needed to perform the classical spherical NF-FF transformation are then accurately and efficiently retrieved from the acquired nonredundant ones via optimal sampling interpolation formulas. A remarkable reduction of the number of the required NF data and, as a consequence, a significant measurement time saving can be so obtained. The experimental tests have been carried out at Antenna Characterization Lab of the University of Salerno and both the NF and FF reconstructions are resulted to be very good, thus confirming the accuracy and reliability of these NF-FF transformations from the experimental viewpoint too.

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.

Application of Nonredundant Sampling Representations of Electromagnetic Fields to NF-FF Transformation Techniques

An overview of the application of the band-limitation properties and nonredundant sampling representations of electromagnetic fields to NF-FF transformations is presented. The progresses achieved by applying them to data acquired on conventional NF scanning surfaces are discussed, outlining the remarkable reduction in the number of needed NF samples and measurement time. An optimal sampling interpolation expansion for reconstructing the probe response on a rotational scanning surface from a non-redundant number of its samples is also discussed. A unified theory of the NF-FF transformations with spiral scannings, which allow a remarkable reduction of the measurement time, is then reviewed by describing a sampling representation of the voltage on a quite arbitrary rotational surface from its nonredundant samples collected on a proper spiral wrapping it. Some numerical and experimental results assessing the effectiveness of the considered NF-FF transformations are shown too.

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.

Effective Antenna Modellings for NF-FF Transformations with Spherical Scanning Using the Minimum Number of Data

Two efficient probe-compensated near-field-far-field transformations with spherical scanning for antennas having two dimensions very different from the third one are here developed. They rely on the nonredundant sampling representations of the electromagnetic fields and on the optimal sampling interpolation expansions, and use effective antenna modellings. In particular, an antenna with a predominant dimension is no longer considered as enclosed in a sphere but in a cylinder ended in two half spheres, whereas a surface formed by two circular “bowls” with the same aperture diameter but different lateral bends is adopted to shape an antenna with two predominant dimensions. These modellings are able to fit very well a lot of antennas by properly setting their geometric parameters. It is so possible to remarkably lower the number of data to be acquired, thus significantly reducing the measurement time. Numerical tests assessing the accuracy and the robustness of the techniques are reported.

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.

Experimental Results Validating the Near-Field to Far-Field Transformation Technique with Helicoidal Scan

This paper concerns the experimental validation of the near-field - far-field transformation technique with heli- coidal scanning. Such a technique, based on the theoretical results concerning the nonredundant sampling representations of the electromagnetic fields, makes use of a two-dimensional optimal sampling interpolation formula to reconstruct the near-field data needed to perform the classical near-field - far-field transformation with cylindrical scan. The comparison of the far-field patterns reconstructed from the acquired helicoidal measurements with those obtained from the data di- rectly measured on the classical cylindrical grid assesses the effectiveness of the near-field - far-field transformation us- ing this innovative scanning technique. Its validity is further confirmed by the very good agreement with the direct far- field measurements.

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.

A Nonredundant Near-Field to Far-Field Transformation with Spherical Spiral Scanning for Nonspherical Antennas

A Nonredundant Near-Field to Far-Field Transformation with Spherical Spiral Scanning for Nonspherical Antennas

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.

An efficient technique to lower the error due to the truncation of the scanning region in a bipolar facility

AbstractAn efficient technique is developed in this article to extrapolate the near‐field data falling outside the measurement region in the bipolar scanning. It is based on the nonredundant sampling representations of the electromagnetic field and on the optimal sampling interpolation expansions. The singular value decomposition method is properly employed for estimating the external data. This allows one to reduce in a significant way the truncation error occurring in the near‐field–far‐field transformation with bipolar scanning. Numerical examples assessing the effectiveness of the technique are shown. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 3033–3037, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22936