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Andrew J. Knisely, Peter J. Collins, November 2016

RCS and Antenna measurement accuracy critically depends on the quality of the incident field. Both compact and far field ranges can suffer from a variety of contaminating factors including phenomena such as atmospheric perturbation, clutter, multi-path, as well as Radio Frequency Interference (RFI). Each of these can play a role in distorting the incident field from the ideal plane wave necessary for an accurate measurement. Methods exist to mitigate or at least estimate the measurement uncertainty caused by these effects. However, many of these methods rely on knowledge of the incident field amplitude and phase over the test region. Traditionally the incident field quality is measured directly using an electromagnetic probe antenna which is scanned through the test region. Alternately, a scattering object such as a sphere or corner reflector is used and the scattered field measured as the object is moved through the field. In both cases the probe/scatterer must be mounted on a structure to move and report the position in the field. This support structure itself acts as a moving clutter source that perturbs the incident field being measured. Researchers at the Air Force Institute of Technology (AFIT) have recently investigated a concept that aims to eliminate this clutter source entirely. The idea is to leverage the advances in drone technology to create a free flying field probe that doesn’t require any support structure. We explore this concept in our paper, detailing the design, hardware, and software developments required to perform a concept demonstration measurement in AFIT’s RCS measurement facility. Measured data from several characterization tests will be presented to validate the method. The analysis will include an estimate of the applicability of the technique to a large outdoor RCS measurement facility.

Serge Bories, Lama Ghattas, Dominique Picard, November 2016

Direction Finding (DF) Antennas are usually designed and tested in controlled environments. However, antenna far field response may change significantly in its operational environment. In such perturbing or not -controlled close context, the antennas calibration validity becomes a major issue which can lead to DF performance degradation and to a costly re-calibration process. Even if in-situ re-calibration is still complicated; the DF antenna response can be monitored, during the mission, in order to ensure the DOA accuracy. This paper presents an innovative design and the performance of a low-disturbing solution to detect the near field antenna response deviations from a nominal case. The proposed system is based on an array of transmitting miniature dipoles deployed all around the DF antennas. These probes are optically fed through a non-biased photodiode that carries the direct conversion into a RF signal at the desired frequency. The detection re-used the DF receiving RF chains to analyze any deviation (complex values) of the antennas array manifold. Compared to the Optically Modulated Scatterer (OMS) technique, the benefits of the proposed approach are demonstrated experimentally over a frequency decade (UHF band). First a better sensitivity is shown (higher than 80 dB on the monitored link), and secondly the phase detection is made really simple compared to the OMS technique. Finally, a relation between this in-situ diagnosis mode and the DF angular direction accuracy is established. Thus the capacity to detect, on the near field response, the presence of various types of closed obstacles (open trap on the carrier, additional antenna…) which perturb significantly the far field antenna response, is evaluated.

Abdul Sattar Kaddour, Essia Benabdallah, Serge Bories, Christophe Delaveaud, Anthony Bellion, November 2016

The radiated efficiency is a key performance indicator for multi-standards frequency agile electrically small antennas (ESA) that are mounted on wireless IoT sensors. One of the techniques to estimate it, consists to integrate, over all the angular directions, the gain measured in the far field condition. The gain-comparison method is usually implemented in the CEA LETI testbench ; which requires an accurate knowledge of the standard horn gain. The introduction of a new RF-optical link to remove coaxial cable perturbation on ESA radiation, in our test bench has raised the opportunity to proceed to an error budget analysis. This paper delivers the main results of this study where the impact of several parameters such as the optical fiber movement, the horn position, the received power level, chamber imperfection… have been evaluated. We have carried on the three antennas method (one Vivaldi and two TEM standard horns) to estimate the complex transfer function of the three antennas. The overall goal is to estimate the detailed uncertainty analysis of the ESA efficiency measurement over a large band of frequencies. This work aims to identify the most impacting effects on uncertainty and to initiate the discussion with the AMTA community how to decrease them.

Fabien Ferrero,Yoan Benoit, Laurent Brochier, Jerome Lanteri, Jean-Yves Dauvignac, Claire Migliaccio, Stuart Gregson, November 2015

A specific set-up for probe-fed antenna with an articulated arm has been developed by NSI with a 500mm AUT-probe distance. This paper will give an example of far-field measurement and highlight its limitations. A near field approach to filter the probe effect is investigated. First measurement results, including amplitude and phase, will be presented. Phase data will be leveraged to develop post-processing technique to filter probe and environmental effect.

Yahya Rahmat-Samii,Joshua Kovitz, Luis Amaro, Jeff Harrell, November 2015

Recently, the Rapid Scatterometer (RapidScat) instrument was developed to sense ocean winds while being housed onboard the International Space Station (ISS). This latest addition to the ISS, launched and mounted in September 2014, significantly improves the detection and sensing capabilities of the current satellite constellation. The dual-beam Ku-band reflector antenna autonomously rotates at 18 rpm and acquires scientific data over a circular scan during typical ISS operations. Mounting such an antenna on the ISS, however, gives rise to many engineering challenges. An important consideration for any antenna onboard the ISS is the interference generated towards nearby ISS systems, space vehicles and humans due to the possible exposure to high RF power. To avoid this issue, this work aimed to characterize the antenna's absolute near-field distribution, whose knowledge was required for a blanker circuit design to shut off the RF power for certain time slots during the scan period. Computation of these absolute near-fields is not a straightforward task and can require extensive computational resources. The initial computation of those fields was done using GRASP; however, an independent validation of the GRASP results was necessary because of safety concerns. A customized plane wave spectrum back projection method was developed to recover the absolute electric field magnitudes from the knowledge of the measured far-field patterns. The customized technique exploits the rapid computation of the Fast Fourier Transform alongside the proper normalization. The procedure starts by scaling the normalized (measured or simulated) far-field patterns appropriately to manifest the desired total radiated power. This was followed by transforming the vectors into the desired rectangular coordinate system and interpolating those components onto a regularized spectral grid. The FFT of the resulting Plane Wave spectrum was properly scaled using the sampling lengths to determine the absolute near-field distributions. The procedure was initially validated by comparing the results with analytical aperture distributions with known far-field patterns. The properly normalized PWS approach was subsequently applied to the RapidScat Antenna using measured patterns from JPL’s cylindrical near-field range. The resulting near-fields compare quite well between the plane wave spectrum technique and GRASP, thus validating the calculations. This work provided significant enabling guidelines for the safe operation of the ISS-RapidScat instrument.

Kazem Sabet,Richard Darragh, Ali Sabet, Sean Hatch, November 2015

The design of active electronically steered arrays (AESA) is a challenging, time-consuming and costly endeavor. The design process becomes much more sophisticated in the case of dual-band circularly polarized active phased arrays, in which CP radiating elements at two different frequency bands occupy a common shared aperture. A design process that takes into account various inter-element and intra-element coupling effects at different frequency bands currently relies solely on computer simulations. The conventional near-field scanning systems have serious limitations for quantifying these coupling effects mainly due to the invasive nature of their metallic probes, which indeed act as receiving antennas and have to be placed far enough from the antenna under test (AUT) to avoid perturbing the latter’s near fields. In recent years, a unique, versatile, near-field mapping/scanning technique has been introduced that circumvents most of such measurement limitations thanks to the non-invasive nature of the optical probes. This technique uses the linear Pockels effect in certain electro-optic crystals to modulate the polarization state of a propagating optical beam with the RF electric field penetrating and present inside the crystal. In this paper, we will present near-field and far-field measurement data for a dual-band circularly polarized active phased array that operates at two different S and C bands: 2.1GHz and 4.8GHz. The array uses probe-fed, cross-shaped, patch antenna elements at the S-band and dual-slot-fed rectangular patch elements at the C-band. At each frequency band, the array works both as transmitting and receiving antennas. The antenna elements have been configured as scalable array tiles that are patched together to create larger apertures.

Jose Luis Besada,Ana Ruiz, Carlo Rizzo, November 2015

In planar and cylindrical near-field antenna measurements the probe pattern correction is essential, since the used angular sector of the probe pattern extends over large part of the forward hemisphere. But in spherical near-field measurements, the probe is always looking towards an antenna under test (AUT) and the used angular sector of the probe pattern is relatively small: it usually does not exceed some ±30deg, but typically is much smaller, depending on the size of the AUT and the distance to the probe. For this reason, for low-directive probes with little pattern variation in the used angular sector, it is often said that the probe pattern correction can be omitted without introducing significant error in the calculated far-field AUT pattern. However, no specific guidelines on the value of the introduced error have been presented so far in the literature. In this paper, the error in the calculated far-field AUT pattern due to omitted probe pattern correction is investigated by simulations and confirmed by selected measurements. The investigation is carried out for two typical probes, an open-ended waveguide and a small conical horn, and for aperture-type AUTs of different electrical size with different distance to the probe. The obtained results allow making a justified choice on including or omitting the probe pattern correction in practical situations based on the estimated error at different levels of the AUT pattern.

This paper discusses the application of modern NF measurements and statistical analysis techniques to efficiently characterize the FF radiation pattern statistics of antennas and other EM emitters whose radiated EM fields vary erratically in a seemingly random manner. Such randomly-varying radiation has been encountered, for example, in measurements involving array antenna elements and reflector feed horn(s) containing active or passive devices that affect the relative phases and/or amplitudes of the pertinent RF signals in a non-deterministic manner [1-2]. In-Band (IB) as well as Out-Of-Band (OB) signals may be involved in some cases. Other possible randomly varying EM radiations include leakage from imperfectly-shielded equipment, connectors, cables, and waveguide runs [2- 4] Previous work at GTRI [5-7] has shown that computations of key FF radiation pattern statistics can be made based on NFFF transformations involving a) the sample average value of the complex electric field at each NF measurement point, b) the sample average value (a real number) of the standard deviation of the complex electric field at each NF measurement point, and c) the measured complex cross-covariance functions at all different NF measurement points. The key FF radiation pattern statistics of most interest are typically a) the statistical average FF radiation pattern, b) the standard deviation, c) the probability density function (p.d.f.), and d) the cumulative probability distribution (C.P.D.). Simulated data measurement protocols and the requisite statistical processing of the NF measured data will be presented and discussed in detail at the symposium. The NF cross-covariance functions introduce a new level of complexity in NF measurements and analysis that is absent for “deterministic” EM field measurements because the cross covariance functions must be measured and processed for all different NF measurement points on the NF surface to compute valid Pattern FF statistics. However, pairs of linear or circular probe arrays can be used to great advantage to achieve tolerable NF measurement times for the cross covariance functions and the aforementioned NF statistical quantities, thereby enabling valid computations of the FF pattern statistics. The use of dual probe arrays will be presented and discussed in detail and compared with mechanical scanning of two “single” probes over two NF measurement surfaces. A technique for estimating the cross-covariance functions will be presented and compared with exact values.

MIL STD 461 is the Department of Defense standard that states the requirements for the control of electromagnetic interference (EMI) in subsystems and equipment used by the armed forces. The standard requires users to measure the unintentional radiated emissions from equipment by placing a measuring antenna at one meter distance from the equipment under test (EUT). The performance of the antenna at 1m distance must be known for the antenna to measure objects located at this close proximity. MIL STD 461 requires the antennas to be calibrated at 1 m distance using the Society of Automotive Engineers (SAE) Aerospace Recommended Practice (ARP) 958. This SAE ARP 958 document describes a standard calibration method where two identical antennas are used at 1m distance to obtain the gain at 1m for each antenna. In this paper the authors show using simulations that the SAE ARP 958 approach introduces errors as high at 2 dB to the measured gain and AF. To eliminate this problem the authors introduce a new method for calibrating EMC antennas for MIL STD 461. The Method is based on the well-known extrapolation range technique. The process is to obtain the polynomial curve that is used to get the far field gain in the extrapolation gain procedure, and to perform an interpolation to get the gain at 1 m. The results show that some data in the far field must be collected during the extrapolation scan. When the polynomial is calculated the antenna performance values at shorter distances will be free of near field coupling. Measured results for a typical antenna required for emissions testing per the MIL STD 461 match well with the numerical results for the computed gain at 1 m distance. Future work is required to study the use of this technique for other short test distances used in other electromagnetic compatibility standards, such as the 3 m test distance used by the CISPR 16 standard. Keywords: Antenna Calibrations, EMC Measurements, Extrapolation Range Techniques

Jeffrey A. Fordham,Francesco D'Agostino, November 2015

Spherical spiral scanning involves coordinating the motion of two simultaneous axes to accomplish near-field antenna measurements along a line on a sphere that does not cross itself. The line would ideally start near a pole and trace a path along the sphere to the other pole. An RF probe is moved along this path in order to collect RF measurements at predefined locations. The data collected from these measurements is used along with a near-field to far-field transformation algorithm to determine the radiated far-field antenna pattern. The method for transforming data collected along spherical spiral scan has been previously presented [1]. Later laboratory measurement studies have shown the validity of the spherical spiral scanning technique [2]. Here, the authors present a review of the spherical scanning technique and present recent advances and the applicability of the method to testing antennas mounted on automobiles. The method has the advantages of a reduction of the overall number of data points required in order to meet a minimum sampling requirement determined using non-redundant sampling techniques. This reduction in the number of data points and the advantage of moving two axes simultaneously result in a significant reduction in the time required to collect a set of measured data. Keywords: Spherical Near-Field, Telematics, Automotive References: [1] F. D’Agostino, C. Gennarelli, G. Riccio, and C. Savarese, “Theoretical Foundations of near-field to far-field transformations with spiral scannings,” Prog. In Electromagn. Res., vol. PIER 61, pp 193-214, 2006. [2] F. D’Agostino, F. Ferrara, J. Fordham, C. Gennarelli, R. Guerriero, and M. Migliozzi, “An Experimental Validation of the Near-Field to Far-Field Transformation with Spherical Spiral Scan,” Proc. Of the Antenna Measurement Techniques Association, 2012.

Paula Irina Popa,Sergey Pivnenko, Olav Breinbjerg, November 2015

We previously demonstrated that 60 GHz planar near-field antenna measurements without external frequency conversion can provide far-field radiation patterns in good agreement with spherical near-field antenna measurements in spite of the cable flexing and thermal drift effects [P.I.Popa, S.Pivnenko, J.M.Nielsen, O.Breinbjerg, ”60 GHz Antenna Measurement Setup Using a VNA without External Frequency Conversion ”36thAnnual Meeting and Symposium of the Antenna Measurements Techniques Association, 12-17 October, 2014]. In this work we extend the validation of this 60 GHz planar near-field set-up to antenna diagnostics and perform a detailed systematic study of the extreme near-field of a standard gain horn at 60 GHz from planar and spherical near-field measurement data. The magnitude and phase of all three rectangular components of the electric and the magnetic aperture fields are calculated, as is the main component of the Poynting vector showing the power flow over the aperture. While the magnitude of the co-polar electric field may seem the obvious object for antenna diagnostics, we demonstrate that there is much additional information in those additional quantities that combine to give the full picture of the aperture field. The usefulness of the complete information is illustrated with an example where the horn aperture is disturbed by a fault. We compare the results of the planar and spherical near-field measurements to each other and to simulation results.

As millimeter-wave applications become more widely available technologies, there is a demand to know material properties for design and application purposes. However, many mass produced materials are either not specified at these frequencies or the price materials can be costly. Therefore the easiest method for characterization is by measurement. Traditional methods of this measurement type involve the reflectivity of a fabric sample placed on a flat metallic reference plate. However, this method has some major difficulties at these high frequencies. For example, the surface of the reference plate must be very flat and smooth and must be carefully oriented such that their surface is precisely facing the transmitting and receive and antennas. Furthermore the electrically large size of the reference plate of this setup makes it difficult to measure in far-field and anechoic range time is expensive. Resistive and conductive fabrics have applications such as shielding, anti-static, and radio wave absorption. Radio wave absorption and radar cross section engineering is currently of high interest to the automotive industry for testing newly emerging automotive radar systems. Such fabric measurement has already been utilized to accurately characterize artificial skin for radar mannequins to recreate the backscattering of human targets at 77 GHz. This paper presents a new and convenient method for measuring the reflective properties of conductive and resistive materials at millimeter wave frequencies by wrapping fabrics around a metallic reference cylinder. This new approach to fabric characterization method is able to obtain higher accuracy and repeatability despite the difficulties of measuring at high frequency.

Manuel Sierra Castañer,Pilar González-Blanco García, Manuel José López Morales, Francesco Saccardi, Lars J. Foged, November 2015

During the last years, new algorithms, based on time filtering, spatial or modal filtering, have been designed for echo reduction techniques applied to antenna measurements. These algorithms have been used for different applications where the effect of the echoes is important, as far field system, VHF or UHF applications, automotive systems, small antennas, etc. The authors, in previous papers, have analysed the effect of different algorithms: time filtering (fft, non uniform dft or matrix pencial), modal filtering based on Spherical modes (MV-Echo) and spatial filtering based on Integral Equations (Insight) and holographic techniques (fft and dft) to cancel the effect of the reflections. This comparison has been applied to the measurements of a dipole antenna (SD1900) using a StarLab system. It is observed that each of the algorithms is better for different situations, depending on the source of the echo. For instance, time filtering techniques are good for reflections coming from different distances with respect the direct ray, but not so good for close reflections. In addition hey need a large frequency band to work properly. Spatial algorithms can correct the effect of positioners or other structures close to the antenna under test, but they are better for planar near field acquisitions and worse for classical single probe spherical near field where the antenna is rotated and probe is fixed (e.g. roll-over-azimuths systems). Moreover, they require extra information of the AUT geometry. This paper presents first a comparison of each algorithm and then, a combination of time and spatial techniques based on uniform or non-uniform DFT to take advantage of the benefits of each algorithm for different origins of the reflections.

Brian Simakauskas,Maxim Ignatenko, Dejan Filipovic, November 2015

Unlike most antenna performance parameters (directivity, beamwidth, and efficiency, e.g.), phase center is not strictly defined and warrants further clarification when used. Put simply, the phase center is the point at which antenna radiation seems to emanate and is determined as the center of a spherical surface of constant phase in the far field. For practical antennas, however, such a point is fictional and can only be established by minimizing the phase variation on a portion of the spherical surface over a smaller angle of interest, generally where the radiation intensity is greatest (e.g. the 3dB beamwidth). Most commonly, the phase center is defined for a two dimensional planar cut parallel to the direction of propagation, for example the E or H plane of a horn. Knowledge of the phase center is particularly critical in the feeds of reflectors or lenses, where it is required to be located at the focal point of the reflecting or refracting structure to maximize aperture efficiency. Due to its electro-mechanical properties the horn antenna has often been used as the feed for the above mentioned configurations. For wideband applications, the stabilization of the phase center over the entire frequency band poses a significant challenge since this point generally tends from the mouth to the throat of a horn as frequency is increased. The design discussed in this paper involves a feed horn operated in conjunction with a Lunenburg Lens for increased directivity and gain over 18-45 GHz bandwidth. A design overview is discussed with the primary focus on phase stabilization considerations. Methods for determining the phase center of the design are also discussed and compared. These include analytical solutions using the aperture current approximation, simulations using method of moments and finite element method from FEKO and HFSS, respectively, as well as measurements taken in the anechoic chamber at the University of Colorado Boulder.

Josef Migl,Hans-Juergen Steiner, Juergen Habersack, Carsten Schmidt, Christian Hoetzel, November 2015

Compensated Compact Range Facilities are the state-of-the-art RF test facilities for spacecraft payload modules and/or antennas. The outstanding features of the compact range technique are the (a) real-time testing capability, (b) easy to use far-field measurement technique, (c) extremely high frequency capability, (d) end-to-end payload testing at multiple test zones due to scanning features, and last but not least the (e) considerable low cross-polar contribution over the full frequency band between 1 - 200 GHz which is one of the important parameters for telecommunication antenna testing. Upcoming spacecraft antennas with single feed per beam configuration and broadband transponder requirements (up to 500 MHz) need rapid test environments for antenna and payload (end-to-end) measurement campaigns. For the desired wide frequency spectrum the Ka-Band and even higher bands (U, and V) are of interest for the next generation of telecommunication spacecraft antennas. Compensated Compact Ranges provide an excellent test environment for such scenarios. Recent developments for the range feeds up to 200 GHz, a new heavy load and highly accurate specimen positioner design, and the easy enlargeable reflector system within the existing chamber complete the picture of a state-of-the-art test facility for present and future spacecraft testing. The paper will explain the advantages of the selected system design and preferred technology with its resulting features to optimally cover the future requests focusing to new developments in the high frequency range. For typical spacecraft antenna scenarios a comparison between Compact Range and Near-Field facilities will demonstrate the applicability in the frequency range from 1 to 200 GHz. Beside the developed test set-up for the required measurement parameters, typical measurement times and achievable performance with its related error budget will be depicted.

Highly accurate antenna measurements can require precise alignment and positioning of the probe antenna to the antenna under test. The positioning of the antenna during acquisition can involve the movement of several simultaneous axes of motion. This places a global positioning accuracy requirement on the positioning system. To achieve precision in global positioning and alignment, an understanding of dominant error factors such as load induced deflection/resonance, thermal deflection, positioning error sources and mechanical alignment tolerances is essential. This paper focuses on how global accuracy and stability were achieved, addressing these factors, on a recently delivered large far field antenna measurement system. The system involved eight axes of positioning with the ability to position 950 lbs antenna under test 19.5 ft above the chamber floor achieving 0.007 inch and 0.005 degrees positioning accuracy relative to the global range coordinate system. Stability of the probe antenna after motion was within 0.001 inch. Key Words: Global Position Accuracy, Far Field, Position Stability, Simultaneous Motion, Position Error Correction, High Accuracy, Precise Motion

Edward Szpindor,Per Iversen, Daniel Frey, James Stamm, November 2015

A multi-probe array (MPA) spherical near-field antenna measurement system, comprised of COTS equipment, has been developed for testing UHF antennas mounted in an aircraft rotodome. The spherical probe radius is 5 meters, which accommodates a 24 ft. diameter rotodome. The probe array, arranged in a circular arc about the test zone center, provides rapid time multiplexed samples of dual polarized spherical theta angle measurements. These measurements are collected at incremental steps of spherical phi angles, provided by a floor azimuth turntable. The rotodome is mounted on the azimuth turntable, and is rotated 360 degrees during a data collection. During one azimuth rotation, completed in a few minutes, a full set of 3D, dual polarized, multi-frequency near-field pattern data is collected. The data is transformed to full 3D far-field patterns in another few minutes, providing a complete rotodome test time within 15 minutes. The entire system is contained within a room 42’ x 42’ x 25’. This paper will describe the test requirements, physical requirements of the DUT, size constraints of the facility, and measurement speed goals. Alternate solutions and range geometries will be discussed, along with why the MPA solution is best given the requirements and size constraints. The system will be described in detail, including discussion of the room design, RF instrumentation, multi-probe array, positioning equipment, and controllers. Measurement results will be presented for test antennas of known pattern characteristics, along with other performance metrics, such as test times.

Serguei Matitsine,Tse-Tong Chia, Alexander Zubov, Rengasamy Kumaran, Hock-Kwee Oh, November 2015

We have successfully designed and developed an innovative “CLose-range Antenna Scanner System” (or CLASS) suitable for measuring the far-field radiation pattern of installed antennae at short distances. The system consists of three key components: (1) a uniquely designed lens horn antenna that generates plane waves in close proximity, (2) a mechanical x-y scanner to scan the antenna-under-test, and (3) a customized stitching software to compute the far-field antenna pattern from the measured field information. The developed system has a scan area of 4.6 x 4.6 m, with resolutions of ±0.1mm in both the x and y traverse directions. The scanner structure is designed in a scalable fashion to cater for measurement of antenna installed at various locations (e.g. front and sides) on a platform. The system is capable of measurement from 1 to 18 GHz and generates far-field radiation pattern with a gain accuracy of ±1 dB.

Yvonne Weitsch,Thomas. F. Eibert, Raimund Mauermayer, Leopold G. T. van de Coevering, November 2015

For today's sophisticated antenna applications, the accurate knowledge of 3D radiation patterns is increasingly important. To measure the antennas under far-field conditions over a broad frequency band is hereby hardly impossible. By near-field to far-field transformation, one can overcome the difficulties of limited measurement distances. In common spherical near-field antenna measurement software, the transformation based on spherical mode expansion is typically implemented. These software tools only provide to correct the influence of first order azimuthal probe modes. The influence of the probe’s higher order modes though increases with shorter measurement distances. To measure a broad frequency range in one measurement set-up and to save time, dual ridged horns are popular candidates since they operate over a wide frequency range. The drawback is that they are probes of higher order. In this contribution, we will present an investigation on near-field measurements which are transformed into the far-field deploying the transformation technique based on spherical modes which is extended by a higher order probe correction capability. The resulting diagrams comparing first and higher order probe correction show that a correction is important in particular for the cross polarization In addition, the near-field data is transformed with an algorithm which employs a representation by equivalent currents. In this method, a higher order probe correction based just on the probe’s far-field pattern is integrated. The equivalent currents supported by an arbitrary Huygens surface allows to reconstruct the current densities close to the actual shape of the AUT which is mandatory for precise antenna diagnostics. Another issue needs to be accounted for regarding limited measurement distances and spherical modal expansion. While representing the AUT and the probe in spherical modes the radii of the spheres grow the more modes are included which depends on the sizes of the TX and the RX antennas. It has to be ensured that both spheres do not interfere. All measurements were carried out in the anechoic chamber of our laboratory in which measurements starting at 1 GHz are practicable according to the dimension of the chamber and of the absorbers. Due to our restricted measurement distance of 0.57 m, all the above mentioned rules need to be considered. In conclusion, small anechoic chambers are also capable of delivering precise antenna measurements over a broad frequency range due to algorithms capable of higher order probe correction.

The spherical multipole based near-field far-field transformation is one of the most widespread algorithms for field transformation due to its very low computation time achieved by employing the fast Fourier transform (FFT) and imposing the utilization of first order probe antennas which obtain regularly distributed near-field samples on a spherical surface. Thus, huge efforts in highly accurate scanner system and antenna design are invested to fulfill the transformation algorithm requirements. In comparison, the recently developed inverse source reconstruction methods are very undemanding as they allow to use arbitrary probe antennas and arbitrarily shaped measurement surfaces as long as the probe’s relative position and orientation with respect to the device under test (DUT) is accurately known. Furthermore, the diagnostics capabilities of the algorithms give insight into the radiation mechanisms of the antenna. Although multilevel fast multipole boosted inverse source reconstruction algorithms such as the fast irregular antenna field transformation algorithm (FIAFTA) provide an excellent linearithmic complexity, their computation time is still higher than the one of the spherical transformation. The flexibility to process near-field samples on an irregular grid is yet only of interest for some challenging measurement scenarios where it is easier to determine the exact position and orientation of the probe than to accurately position it at certain grid points. Moreover, most antenna measurement facilities are already equipped with positioner systems for spherical scans. Therefore, a spherical multipole based transformation with higher order probe correction capability is proposed to perform a fast near-field far-field transformation. Once the far-fields and thus, the plane wave representation of the antenna has been obtained, a hierarchical plane wave representation is utilized to efficiently determine the equivalent sources of the antenna. For best sources localization and diagnostic features, equivalent surface currents on a Huygens’ surface enclosing the antenna are used. Their organization in a hierarchical octree is the key to a fast transformation from the antenna far-field to its equivalent sources. In this way, the blend of the spherical multipole based transformation and the hierarchical plane wave based field representation allows to profit from the benefits of both transformation approaches.

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