Claudio Gennarelli

Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples

It is shown that the electromagnetic (EM) field, radiated or scattered by bounded sources, can be accurately represented over a substantially arbitrary surface by a finite number of samples even when the observation domain is unbounded. The number of required samples is nonredundant and essentially coincident with the number of degrees of freedom of the field. This result relies on the extraction of a proper phase factor from the field expression and on the use of appropriate coordinates to parameterize the domain. It is demonstrated that the number of degrees of freedom is independent of the observation domain and depends only on the source geometry. The case of spheroidal sources and observation domains with rotational symmetry is analyzed in detail and the particular cases of spherical and planar sources are explicitly considered. For these geometries, precise and fast sampling algorithms of central type are presented, which allow an efficient recovery of EM fields from a nonredundant finite number of samples. Such algorithms are stable with respect to random errors affecting the data.

Optimal interpolation of radiated fields over a sphere

An optimal sampling interpolation algorithm is developed that allows the accurate recovery of scattered or radiated fields over a sphere from a minimum number of samples. Using the concept of the field equivalent (spatial) bandwidth, a central interpolation scheme is developed to compute the field in theta , phi coordinates, starting from its samples. The maximum allowable sample spacing and error upper bounds are also rigorously derived. Several simulated examples of pattern reconstruction are presented, for both the cases of field and power pattern interpolation. The interpolation error, as a function of the retained sample number, has been also evaluated and compared with the theoretical upper bounds. The algorithm stability versus randomly distributed errors added to the exact samples is demonstrated. >

Fast and accurate near-field-far-field transformation by sampling interpolation of plane-polar measurements

An optimal sampling interpolation algorithm which allows the accurate recovery of plane-rectangular near-field samples from the knowledge of the plane-polar ones is developed. This enables the standard near-field-far-field (NF-FF) transformation, which takes full advantage of the fast Fourier transform (FFT) algorithm, to be applied to plane-polar scanning. The maximum allowable sample spacing is also rigorously derived, and it is shown that it can be significantly greater than lambda /2 as the measurement place moves away from the source. This allows a remarkable reduction of both measurement time and memory storage requirements. The sampling approach is compared with that based on the bivariate Lagrange interpolation (BLI) method. The sampling reconstruction agrees with the exact results significantly better than the BLI, in spite of the significantly lower number of required measurements. >

Theoretical Foundations of Near-Field-Far-Field Transformations with Spiral Scannings

In this paper, the theoretical foundations of near-field-farfield transformations with spiral scannings are revisited and a unified theory is provided. This is accomplished by introducing a sampling representation of the radiated electromagnetic field on a rotational surface from the knowledge of a nonredundant number of its samples on a spiral wrapping the surface. The obtained results are general, since they are valid for spirals wrapping on quite arbitrary rotational surfaces, and can be directly applied to the pattern reconstruction via near-field-far-field transformation techniques. Numerical tests are reported for demonstrating the accuracy of the approach and its stability with respect to random errors affecting the data.

Data reduction in the NF-FF transformation technique with spherical scanning

A fast, accurate and stable two-dimensional sampling interpolation algorithm is developed to reconstruct the electromagnetic field radiated on a sphere in the antenna near-field region. Its analytical foundation relies on the recent theoretical results concerning the nonredundant field representations on curves and surfaces. The use of an ellipsoid (prolate or oblate) as modelling of the source allows one to reduce the number of required samples with respect to the spherical source modelling that, although more general, becomes redundant when considering antennas having one or two predominant dimensions. The obtained results are properly used to get ready an effective near-field-far-field transformation technique with spherical scanning, which requires a minimum number of data, thus reducing significantly the memory storage requirements and measurement time. Numerical examples assess the efficiency and the stability of the reconstruction process.

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.

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.

THE UNIFIED THEORY OF NEAR-FIELD-FAR-FIELD TRANSFORMATIONS WITH SPIRAL SCANNINGS FOR NONSPHERICAL ANTENNAS

The unified theory of near-field–far-field transformations with spiral scannings for quasi-spherical antennas is extended in this paper to the case of nonspherical ones, i.e., antennas with two dimensions very different from the third one. To this end, these antennas are no longer considered as enclosed in a sphere, but in a proper convex domain bounded by a rotational surface. The extension, heuristically derived by paralleling the rigorous procedure valid for the spherical source modelling, allows one to overcome its main and serious drawbacks. In fact, the corresponding near-field–farfield transformations use a reduced number of near-field measurements and, above all, allow one to consider measurement surfaces at a distance smaller than one half the antenna maximum size, thus remarkably reducing the error related to the truncation of the scanning zone. These are very important features, which make the spiral scannings more and more appealing from the practical viewpoint. Some examples of the application of this theory to spirals wrapping the conventional scanning surfaces employed in the near-field–far-field transformations are reported, and the accuracy and robustness of the far-field reconstructions are assessed.

An Efficient Near-field to Far-field Transformation Using the Planar Wide-mesh Scanning

An effective procedure is here proposed for evaluating the antenna far field from the knowledge of near-field data collected on a planar wide-mesh grid. The choice of the corresponding sampling law on the considered planar surface is based on the theoretical results relevant to the nonredundant sampling representations of the radiated electromagnetic field. Then, the data needed by the standard probe-compensated near-field-far-field transformation with plane-rectangular scanning can be efficiently reconstructed by using an optimal sampling interpolation expansion of central type. The benefit of using this particular and innovative approach is that it allows one to reduce the number of near-field data with respect to the classical plane-rectangular scan, while maintaining the accuracy of the far-field reconstruction. Last but not least, the implementation of the planar wide-mesh scanning does not require to change the plane-rectangular positioning systems, but only the software for controlling them. Numerical tests are reported for assessing the effectiveness of the approach and its stability with respect to random errors affecting the data.

Near-field-far-field transformation with spherical spiral scanning

An efficient near-field-far-field transformation technique with spherical spiral scanning, which uses a minimum number of data, is proposed. A nonredundant sampling representation of the electromagnetic field on the spiral and a fast, accurate and stable interpolation algorithm are developed to this end. By choosing the elevation step of the spiral coincident with the sample spacing needed to interpolate the field on a meridian, it is possible to reconstruct the field at any point on the spherical surface. This allows the evaluation of the data required by a spherical near-field-far-field transformation. Numerical examples assessing the effectiveness of the proposed technique are reported.