Near-field Far-field Transformation Research Articles

Fully Probe-Corrected Near-Field Far-Field Transformations With Unknown Probe Antennas

Fully Probe-Corrected Near-Field Far-Field Transformations With Unknown Probe Antennas

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.

Reliable Linearized Phase Retrieval for Near-Field Antenna Measurements With Truncated Measurement Surfaces

Most methods tackling the phase retrieval problem of magnitude-only antenna measurements suffer from unrealistic sampling requirements, from unfeasible computational complexities, and, most severely, from the lacking reliability of nonlinear and nonconvex formulations. As an alternative, we propose a partially coherent (PC) multi-probe measurement technique and an associated linear reconstruction method which mitigate all these issues. Hence, reliable and accurate phase retrieval can be achieved in near-field far-field transformations (NFFFTs). In particular, we resolve the issues related to open measurement surfaces (as they may emerge in drone-based measurement setups) and we highlight the importance of considering the measurement setup and the phaseless NFFFT simultaneously. Specifically, the influence of special multi-probe arrangements on the reconstruction quality of PC solvers is shown.

Plane-Wave Synthesis Employing Propagating Plane-Wave Expansion for 3-D and 2-D RCS Prediction Including the Multiple Scattering Effects

The plane-wave synthesis (PWS) methods are proposed to predict the 3-D and 2-D RCS accurately with multiple scattering effects. The 3-D method employs the propagating plane-wave expansion and can be implemented identically as the near-field far-field transformation (NFFFT). Either the single-level or multilevel implementation can be applied, and in the single-level implementation, a single pseudo-inverse matrix can be used to synthesize plane waves propagating various incident directions. In addition to the 3-D formulation, the single-cut variation of the method (SC-PWS) is also presented for the 2-D RCS prediction. This method is based on the 2-D propagating plane-wave expansion and formulated employing the approximations on the 3-D Green's function. The numerical and experimental results are presented for the PWS and the SC-PWS.

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.

Near-field measurement of continuously modulated fields employing the time-harmonic near- to far-field transformation

Abstract. Near-field far-field transformations (NFFFTs) are commonly performed for time-harmonic fields. Considering arbitrary in-situ measurement scenarios with given transmission signals, time-varying aspects of modulated signals have to be taken into consideration. We investigate and characterize two methods for the measurement of modulated fields, which work with a time-domain representation of the radiated fields and, at the same time, allow to employ the standard time-harmonic NFFFT. One method is based on the fact that the modulation signal can be assumed to be constant in a short enough measurement interval under the condition that the modulation and carrier frequencies are several decades apart. The second method performs long-time measurements in order to obtain the complete frequency spectrum in every single measurement. Both methods are verified by the NFFFT of synthetic field data.

Reconstruction of Squared Field Magnitudes and Relative Phases From Magnitude-Only Near-Field Measurements

An optimization-free method is presented for the retrieval of the individual phases of phaseless antenna measurements in the near-field (NF) zone of an antenna under test (AUT). Based on a bilinear expression for the magnitude-only measurements, the result for any desired magnitude-only measurement sample is synthetically calculated as a linear combination of sufficiently many previous measurement samples. In this way, signals, which allow for a straightforward computation of the phase difference between a pair of measurement samples, are obtained. Its high numerical complexity limits the algorithm to problems of moderate size, but understanding and using the algorithm delivers new insight into the phase retrieval problem and allows to evaluate the feasibility of specific measurement procedures and configurations. In particular, we show that there exist at most $N_{\mathrm {DOF}}^{2}$ independent phaseless measurements for an AUT with $N_{\mathrm {DOF}}$ degrees of freedom (DoFs). Any additional phaseless measurement can be calculated as a linear combination of those $N_{\mathrm {DOF}}^{2}$ measurement samples. Under certain circumstances, much less than $N_{\mathrm {DOF}}^{2}$ measurement samples are sufficient to retrieve the magnitude and phase of the measured field at desired locations. A numerical example shows that the presented method is capable, in principle, to reconstruct all relevant NF information needed for a conventional NF far-field transformation (NFFFT) from noiseless irregularly distributed squared magnitude field samples only. In addition, it is shown that measurements with specialized probes can bring more information into the problem than measurements on surfaces with different distances to the AUT. When it comes to true noisy measurement data, the presented method can reconstruct NF magnitudes reliably, but the reconstruction of phase information is sensitive to noise.

Single-Cut Near-Field Far-Field Transformation Technique Employing Two-Dimensional Plane-Wave Expansion

A single-cut near-field (NF) far-field transformation technique is proposed for antenna measurements, which utilizes a two-dimensional (2-D) plane-wave expansion. This technique enables the prediction of single-cut far-field from the NF sampled on the same plane, having the flexibility of the NF data acquisition. The proposed method involves an approximation of 3-D Green's function under the assumption that the heights of the antenna under test and probe is small enough in comparison to the measurement distance. The proposed technique is validated numerically and experimentally.

A Novel Far-Field Transformation via Complex Source Beams for Antenna Near-Field Measurements on Arbitrary Surfaces

This paper presents a general technique for an efficient and accurate near-field (NF) to far-field (FF) transformation based on the complex source beam (CSB) method. This CSB-based NF–FF transformation is applicable to all three conventional NF measurement techniques, namely, to the planar, cylindrical, and spherical as well as to an arbitrary measurement surface. In this technique, a set of CSBs launched radially out from the antenna under test (AUT) is used to represent its NF. The weights of these CSB radiation basis functions are found by matching them to the measured AUT NF on the measurement surface. Once the CSB weights are found, the same CSBs remain continuously valid everywhere from NF to FF. It is noted that due to the occurrence of a natural Gaussian-like field taper away from each beam axis, only a relatively few CSBs are typically needed to represent the AUT fields at any point in its far zone in comparison to the conventional plane wave or vector wave function expansions for a given size of AUT. The remaining CSBs can be discarded with negligible error. This property among a few others leads to some advantages over conventional NF–FF methods.

Phaseless Near-Field Far-Field Transformation Utilizing Combinations of Probe Signals

Phaseless near-field far-field transformations based on nonconvex optimization suffer from local stationary points. In order to avoid the corresponding suboptimal solutions, the incorporation of combinations of probe signals into the cost functional is proposed and investigated. The nonconvex optimization based on the Wirtinger Calculus relies on forward and adjoint radiation operator evaluations via the fast irregular antenna field transformation algorithm (FIAFTA) and is performed by a memory-limited Quasi-Newton method. This allows the solution of large scale problems with utilization of the full flexibility of the FIAFTA in terms of measurement probe correction and arbitrary sample locations. Results for synthetic and measured near-field data reveal significant improvements when the knowledge of probe signal combinations is utilized, especially in applications with a large number of unknowns.

Comparison of non-convex cost functionals for the consideration of phase differences in phaseless near-field far-field transformations of measured antenna fields

Abstract. This work introduces two methods which extend the non-convex minimization problem arising in phaseless (NF) far-field (FF) transformations. With the new extensions, knowledge about phase differences between measurement points can be incorporated into the minimization problem. The additional information helps to avoid stationary points of the minimization cost functional which would otherwise compromise the result of the near-field far-field transformation. The methods are incorporated into the Fast Irregular Antenna Field Transformation Algorithm (FIAFTA), analyzed and compared. Their effectiveness is shown by transforming synthetic near-field data sets with partial knowledge of phase differences to the far-field.

Spherical Near-Field Scanning With Pointwise Probe Correction

Spherical wave expansion algorithms based on matrix inversion are flexible. They allow arbitrary sampling schemes and higher order probe correction. However, the probe correction technique assumes, up until now, the same measurement probe at every measurement point. This is a limitation, especially for dual-polarized measurement probes and multiprobe measurement systems. In this communication, a spherical near-field (SNF) far-field transformation procedure, including pointwise probe correction, is presented. For a measurement sphere with constant radius, the additional calculation time is small. Furthermore, varying but known measurement distances can be corrected using the same technique. The procedure is tested with a dual-polarized SNF measurement and a simulated measurement with varying measurement distances.

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.

Near-Field Far-Field Transformation Utilizing 2-D Plane-Wave Expansion for Monostatic RCS Extrapolation

Near-field far-field transformation (NFFFT) is a common solution to the huge costs associated with the radar cross section (RCS) measurements. One such NFFFT technique for the monostatic RCS measurement has been proposed, which utilizes the 3-D plane-wave expansion. While the technique has the higher flexibility, its use of 3-D near-field scans is costly. In this letter, we propose a 2-D version of the NFFFT that utilizes the 2-D plane-wave expansion. Thus the one-cut-plane RCS can be obtained by measuring only on a plane with the higher flexibility.

Planar scanning measurement of monostatic/bistatic RCS by near-field far-field transformation based on fast multipole method

Planar scanning measurement of monostatic/bistatic RCS by near-field far-field transformation based on fast multipole method

Near-field scanning for EM emission characterization

This tutorial reviews a few important issues when using the near-field scanning technique for EM emission characterization. Calibration of field probes is introduced first to eliminate or reduce the errors in the measurement of EM field components. Then, methodologies to obtain the phase information in near-field scanning are discussed. For characterizing radiators in free space in terms of far-field emissions, different Near-Field Far-Field Transformation algorithms are introduced. Finally, radiated-emission models based on near-field scanning are presented for characterizing the radiators in a complex environment/system, and an example on interference estimation demonstrates the application of such models.

Fast near-field far-field transformation for phaseless and irregular antenna measurement data

Abstract. The characterization of antenna radiation patterns by transformed near-field measurements requires accurate amplitude and phase data. This represents a problem since expensive measurement equipment is required, especially at millimeter and submillimeter wavelengths (Isernia et al., 1996). Amplitude-only antenna field measurements are theoretically sufficient for the unique determination of antenna far-fields. Therefore, phaseless techniques are of special interest. However, the required field transformations are extremely challenging, since they are nonlinear and strongly ill-posed. In this work, the amplitude-only or phaseless near-field far-field transformation problem is formulated as a nonlinear optimization problem. The linear radiation operator within the nonlinear formulation is evaluated using the fast irregular antenna field transformation algorithm (FIAFTA). A hybrid solution procedure is described which combines a genetic algorithm with an iterative conjugate gradient (CG) search method. Numerical results prove the efficiency and flexibility of the formulation and it is shown that the algorithm remains stable when the noise level in the measurements is moderate. Nevertheless, regularization techniques might be beneficial to further improve the robustness of the algorithm.

Monostatic Radar Cross Section Near-Field Far-Field Transformations by Multilevel Plane-Wave Decomposition

Retrieving far-field radar cross-section information from near-field data is a well-established methodology. However, existing algorithms impose many restrictions on the underlying measurement procedure. In this paper, algorithms are presented which are based on plane-wave decompositions and hierarchical groupings. Consequently, arbitrarily located monostatic near-field samples with arbitrary polarization information can be processed with full consideration of the radar antenna characteristics, where the computational complexity is identical to other fast approaches. The method uses scattering coefficients based on a Cartesian plane-wave scattering matrix as unknowns for the solution of the transformation problem. With this matrix description, the complete polarimetric information is obtained with a single transformation. Numerical examples are given to prove the usefulness of the algorithm.

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.