Near-field Far-field Transformation Research Articles

A Near-Field to Far-Field Transformation for Spheroidal Geometry Utilizing an Eigenfunction Expansion

This work presents a near-field to far-field (NF-FF) transformation for antenna and scatterer radiation evaluation. The transformation allows practical computation by making use of a sampling surface in the near-field that is spheroidal in shape: namely a prolate or oblate spheroid. The resulting vector wave equation does not support orthogonal vector solutions in spheroidal coordinates and instead rectangular field components are solved for using the scalar wave equation in spheroidal coordinates. The new transformation only requires knowledge of the completely-specified near-field electric field along the spheroidal transformation surface and does not need any information associated with the corresponding magnetic field. The benefit of using a spheroidal near-field geometry is its ability to closely conform to both linear and planar radiating structures while still permitting evaluation of the full far-field radiation pattern. Our approach makes use of an eigenfunction expansion of spheroidal wave-harmonics to develop two distinct, yet closely related, NF-FF transformation algorithms for each type of spheroidal surface. The spheroidal NF-FF transformation is validated and performance assessed using a well-characterized radiation structure. By applying the prolate and oblate algorithms to a radiating structure with known analytical near- and far-field electric fields, viz., a filament dipole with sinusoidal current distribution, we are able to setup and conduct multiple numerical tests that serve as a proof-of-concept for the spheroidal NF-FF transformation.

Data reduction in the NF‐FF transformation with bi‐polar scanning

AbstractAn efficient near‐field–far‐field transformation with bi‐polar scanning, which compensates for the effects of the measurement probe, is proposed in this paper. It is based on the theoretical results relevant to the nonredundant sampling representation of electromagnetic fields and, as a consequence, it requires a number of data—remarkably lower than that needed by the standard bi‐polar technique. Numerical examples assessing the accuracy and the stability of the far‐field reconstruction process are presented. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 32–36, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10662

Analysis of the effect of the truncated scan plane in time-domain near-field measurements

The thought and formulation for near-field far-field transformation based on the direct time-domain computation scheme are given. The effect of the truncated scan plane is investigated by simulating time-domain measurement of an open-ended waveguide antenna, and a simple and effective criterion is derived for removing the truncation errors in the practical time-domain near-field measurements.

Nonredundant Nf-Ff Transformation With Helicoidal Scanning

A probe compensated near-field-far-field (NF-FF) transformation technique with helicoidal scanning, which makes use of a minimum number of probe output voltage samples, is developed in this paper. This target is achieved by using a nonuniform helix as scanning curve, i.e., a circular helix with a constant angular elevation step, and by developing an efficient sampling representation over it. Then, by choosing the step coincident with the spacing needed to interpolate the probe voltage along a generatrix, it is possible to reconstruct such a voltage at any point over the cylinder. This allows the recovering of the data required by the standard probe compensated NF-FF transformation technique with cylindrical scanning. As compared with the previous technique employing a uniform helix with a constant linear elevation step, it allows one to reduce remarkably the number of needed samples without affecting the numerical efficiency. Numerical examples assess the accuracy and the stability of the FF reconstruction process.

A two probes scanning phaseless near-field far-field transformation technique

An innovative and effective technique to determine the far-field of a radiating system from near-field intensity data is introduced, analyzed, and tested. The approach is based on the simultaneous measurement of the amplitude of the voltages received by two different probe antennas moving over a single scanning surface in the near zone and performs the phase retrieval of the near-field by assuming as unknown the plane wave spectrum of the field. The radiated field is then straightforwardly evaluated. As compared to the existing phaseless measurement techniques, the use of two different probes makes it possible to avoid the need for a second scanning surface and thus allows the use of smaller (and cheaper) anechoic chambers. Furthermore, the measurement time is essentially equal to that required by conventional techniques based on the measurement of the complex near-field. The reliability and the effectiveness' of the approach are investigated and discussed and the key factors affecting its behavior are highlighted. In particular, the relevance of the difference between the plane wave spectra (PWS) of the two probe antennas in ensuring an acceptable reliability of the solution, with respect to the starting point of the procedure, is outlined. Finally, the effectiveness of the approach is confirmed by an extensive numerical analysis, which also shows the stability of the solution against data noise.

An effective near-field far-field transformation technique from truncated and inaccurate amplitude-only data

A general approach to the near-field far-field transformation from amplitude only near-field data is presented. The estimation of the far field is stated as an intersection finding problem and is solved by the minimization of a suitable functional. The difficulties related to the possible trapping of the algorithm by a false solution (common to any nonlinear inverse problem) are mitigated by setting the problem in the space of the squared field amplitudes (as already done in a number of existing papers) and by incorporating all the a priori knowledge concerning the system under test in the formulation of the problem. Accordingly, the a priori information concerning the far field, the near field outside the measurement region and the accuracy of the measurement setup and its dynamic range are properly taken into account in the objective functional. The intrinsic ill conditioning of the problem is managed by adopting a general, flexible, and nonredundant sampling representation of the field, which takes into account the geometrical characteristics of the source. As a consequence, the number of unknowns is minimized and a technique is obtained, which easily matches the available knowledge concerning the behavior of the field. The effectiveness of the approach is shown by reporting the main results of an extensive numerical analysis, as well as an experimental validation performed by using a very low cost near field facility available at the Electronic Engineering Department, University of Napoli, Italy.

Near-field far-field transformation in time domain from optimal plane-polar samples

This paper presents a new approach to the time-domain near-field far-field transformation technique introduced by Hansen and Yaghijan (1994) and is based either on a time-domain or frequency-domain scheme. The approach presented here attempts to overcome the main drawbacks of this technique related to the computer time and memory requirements, which could make unrealistic the application of the technique to cases of practical interest. To this end, the advanced representation of the (time and frequency domain) near field previously introduced by the authors, which requires a minimum number of nonequispaced field samples, are exploited. This leads to new relationship between the near-field measured samples and the far field, which requires a minimal set of time-space measurements. Various computational schemes are considered and compared showing that the presented algorithm requires a reduced measurement effort, computer time, and memory occupancy, while allowing a lower far-field reconstruction error for a fixed number of measurements.

Far-field computation from amplitude near-field data on two surfaces: cylindrical case

A near-field far-field transformation technique involving the amplitude of the measured data has been recently proposed. It requires two sets of near-zone amplitude measurements and relies upon a mean-square fitting of the measured amplitude by an iterative projection algorithm. In the paper the method is applied to the case of cylindrical scanning, for which all the details are explicitly worked out. Furthermore the probe effect is accounted for and the relative correction procedure is considered. The relevance of a rough phase estimate and/or a general knowledge of the source is also discussed to overcome the difficulties related to the presence of local minima which can trap the procedure. Numerical examples validating the effectiveness of the technique are provided.

Near-field far-field transformations using spherical-wave expansions

Spherical-wave expansions are a well-known technique of expressing electromagnetic field data. However, most previous work has been restricted to idealized cases in which the expansion coefficients are obtained analytically. In this paper spherical-wave expansions are used as a numerical technique for expressing arbitrary fields specified by analytical, experimental, or numerical data. Numerical results on the maximum wave order needed to expand fields arising from a source of a given size are given for two practical cases, and it is found that the generally accepted wave order cutoff value corresponds to 99.9 percent or more of the power in the input pattern. Near-field patterns computed from far-field data are compared to measured data for the two cases, demonstrating the excellent numerical accuracy of the technique.