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Planar near-field (PNF) acquisition always samples a limited or truncated subset of the infinite plane in front of an antenna under test (AUT). That truncation of the sampled field has two primary impacts: Power radiating to or from angles beyond the probing boundary is not fully captured and thus not included and erroneous ripple is injected throughout the pattern when the transformation algorithm sees by default a sudden drop to zero power beyond that boundary. The topic of truncation mitigation in the PNF geometry has been addressed with a variety of algorithms. This paper introduces a new algorithm that is similar to, yet distinct from, some that have come before. The new algorithm makes use of the recently introduced holographic PNF filter [1][2][3], treating the truncation effects like stray signals. Where the most common technique [2][4] uses the known planar-AUT bounds (2D) and a computed “valid region” of the plane-wave spectrum as truth through iterative transformations, this algorithm treats as truth the known AUT volume (3D) and the measured PNF data. The new algorithm is evaluated herein by retruncating a large set of measured PNF data.
In 1987 the author built the world's first Personal Near-field antenna measurement System (PNS). This led to the formation of Nearfield Systems Inc. (NSI) a company that became a major manufacturer of commercial near-field antenna measurement systems. After leaving NSI in 2015 several new personal antenna measurement tools were built including a modern updated PNS. The new PNS consists of a portable XY scanner, a hand held microwave analyzer and a laptop computer running custom software. The PNS was then further generalized into a modular electromagnetic field imaging tool called "Radio Camera". The Radio Camera measures electromagnetic fields as a n-dimensional function of swept independent parameters. The multidimensional data sets are processed with geometric and spectral transformations and then visualized. This paper provides an overview of the new PNS and Radio Camera, discusses operational considerations, and compares it with the technology of the original 1987 PNS. Today it is practical for companies, schools and individuals to build low-cost personal antenna measurement systems that are fully capable of meeting modern industry measurement standards. These systems can be further enhanced to explore and visualize electromagnetic fields in new and interesting ways.
The experimental validation of an accurate and fast near-field-far-field (NF-FF) transformation technique with spherical scan, suitable for long antennas under test (AUTs) mounted in offset configuration, is provided in this work. The main feature of such a NF-FF transformation is to require, unlike the traditional spherical (TS) one, an amount of NF samples, which is minimum and results to be practically the same in both cases of offset and onset mount-ings of the AUT. To this end, an optimal sampling interpolation formula , developed by properly exploiting the non-redundant sampling representations and modeling an offset mounted long AUT by a cylinder ended by two half-spheres, is employed to precisely recover the massive input NF data for the TS NF-FF transformation from the collected non-redundant samples. A considerable measurement time-saving can be so achieved. Experimental results assessing the validity and the practical feasibility of such a technique are shown.
The two scans phaseless technique is a well-known procedure for the characterization of antennas on near-field ranges without need of measuring the phase. Amplitude information over two surfaces compensates for the lack of phase reference. In this paper we propose the combination of spherical and planar surfaces for the application of the two scans technique, together with the application of Wirtinger Flow, a state-of-the art phase retrieval algorithm with high convergence guarantees. The use of different types of surface adds additional information about the field's degrees of freedom, allowing for smaller separation between acquisition surfaces as compared with the 2-sphere techniques. In addition, an initial estimation for the phase is not required. The phase retrieval process is formulated in terms of the Spherical Wave Expansion (SWE) of the antenna under test. The SWE-to-PWE (Plane Wave Expansion) is utilized in order to process the amplitude field on the planar surface. Results for simulated and measured near-field data are shown to demonstrate the potential capabilities of the proposed technique.
Non-destructive testing (NDT) is a fundamental step in the production chain of aircraft structural components since it can save both money and time in product evaluation and troubleshooting. This paper presents a reflection-based imaging technique for electromagnetic (EM) testing of composite panels, with the device under test (DUT) being metal backed and both the transmitting and receiving components of the NDT system situated on the same side of the DUT. One of the key properties of the presented technique is the complete redundancy of a reference measurement, thereby making it feasible to retrieve a high quality image of the DUT with only a single measurement. Data for both a proof-of-concept DUT and an industrially manufactured composite panel is provided, and the retrieved images show the applicability of both the measurement technique and the imaging algorithms.
Accurate in situ antenna manifolds are desired for performance evaluation of radio frequency systems, including communication, navigation, and radar among others. In situ antenna measurements are the most accurate way to obtain antenna manifolds on the platform of interest, but are often impractical or impossible to obtain. Instead, combinations of simulations and measurements are used to estimate antenna manifolds on platforms. First, the gain and phase of the target antenna are measured on a simple ground plane, over the frequencies and field of view of interest. The measurements are then imported into computational electromagnetics codes to simulate platform scattering from the platform of interest. However, the representation of the measured data is not unique, which leads to inaccuracies and/or a large run time in computational electromagnetics codes. This paper presents a new method to represent measured antenna data in electromagnetics codes through aperture current distributions of simulated cross-slots and monopoles. A weighted sum of far-fields from the simulated equivalent elements approximates the measured antenna far-fields, with weights determined by the minimization of the L2-norm difference between measured far-fields and equivalent element far-fields. However, the least square solution may place large, unrealizable currents on the aperture. A constraint is introduced to limit the amount of current on the aperture, by minimizing the length of the solution vector. In this paper, the details of the suggested method will be presented. We will also illustrate the accuracy of the method through example simulations, where good agreement is achieved between truth data and equivalent antennas on complex platforms.
This paper presents a time domain antenna measurement technique by using a low cost software defined radio receiver. The technique aims to resolve measurement challenges derived from antennas where the reference signal is not accessible. The phase reconstruction implemented in this work is based on calculating the Fast Fourier Transform of the time domain signal to estimate the power spectrum and the relative phase between measurement points. In order to do that a reference antenna is used to retrieve the phase, providing a full characterization in amplitude and phase of the electric field and allowing source reconstruction. The results demonstrate the potential of this technique for new antenna measurement systems and reveal some of the limitations of the technique to be optimized, like the undesired reflections due to the interactions between the probe and the reference antenna.
As modern antenna array systems for MIMO and 5G applications are deployed, there is increased demand for measurement techniques for timely calibration, at both research and commercial sites.[1] The desired measurement method must allow for the de-embedding of information about the closed digital signal chain and element alignment, and must be performed in the near-field. Current means of measuring large arrays cover a variety of methods. Single-element gain and pattern calibration must cover the parameter space of element weightings and is extremely time-consuming, to the point where the measurement may take longer than the duration over which the array response is stable.[4] Two other popular methods are the transmission of orthogonal codes and the use of holography to reconstruct a full-array pattern. The first of these methods again requires extremely long measurement time. For an array of N elements and weightings per element W_n, the matrix of orthogonal codes must be of an order greater than NW_n.[4][3]. This number varies with the form of W_n depending on whether the array is analog or digital, but in both cases for every desired beam configuration, an order-N encoding matrix must be used. The second method relies on illuminating subsets of elements within an array and reconstructing the full pattern.[2] Each illuminated subset, however, neglects some amount of coupling information inherent to the complete system, making this an imperfect method. In this work we explore the development of a sparse set of measurements for array calibration, relying on coherent multi-channel data acquisition of wideband signals at 75 GHz, and the hardware characterization and post-processing necessary to perform channel de-embedding at an elemental level for a 4x1 system. By characterizing the complete RF chain of our array and the differential skew and phase response of our measurement hardware, we identify crucial quantities for measuring closed commercial systems. Additionally, by combining these responses with precise elemental location information, we consider means of de-embedding elemental response and coupling effects that may be compared to conventional single-element calibration information and full-pattern array measurements. [1] C. Fulton, M. Yeary, D. Thompson, L. Lake, and A. Mitchell. Digital phased arrays Challenges and opportunities. Proceedings of the IEEE, 104(3):487–503, 2016. [2] E. N. Grossman, A. Luukanen, and A. J. Miller. Holographic microantenna array metrology. Proceedings of SPIE, Passive Millimeter-Wave Imaging Technology VIII, 5789(44), 2005. [3] E. Lier and M. Zemlyansky. Phased array calibration and characterization based on orthogonal coding Theory and experimental validation. 2010 IEEE International Symposium on Phased Array Systems and Technology (ARRAY), pages 271–278, 2010. [4] S. D. Silverstein. Application of orthogonal codes to the calibration of active phased array antennas for communication satellites. IEEE Transactions on Signal Processing, 45(1):206–218, 1997.
An innovative method for the diagnosis of large reflector antennas from far field data in radio astronomical application is presented, which is based on the optimization of the number and the location of the far field sampling points required to retrieve the antenna status in terms of feed misalignments. In these applications a continuous monitoring of the Antenna Under Test (AUT), and its subsequent reassessment, is necessary to guarantee the optimal performances of the radiotelescope. The goal of the method is to reduce the measurement time length to minimize the effects of the time variations of both the measurement setup and of the environmental conditions, as well as the issues raised by the complex tracking of the source determined by a prolonged acquisition process. Furthermore, a short measurement process helps to shorten the idle time forced by the maintenance activity. The field radiated by the AUT is described by the aperture field method. The effects of the feed misalignments are modeled in terms of an aberration function, and the relationship between this function and the Far Field Pattern is recast in the linear map by expanding on a proper set of basis functions the perturbation function of the Aperture Field. These basis functions are determined using the Principal Component Analysis. Accordingly, from the Far Field Pattern, assumed measured in amplitude and phase, the unknown parameters defining the antenna status can be retrieved. The number and the position of the samples is then found by a Singular Values Optimization (SVO).
For near-field antenna measurement it is sometimes desirable or necessary to measure only the magnitude of the near-field - to perform so-called phaseless (or amplitude-only or magnitude-only) near-field antenna measurements [1]. It is desirable when the phase measurements are unreliable due to probe positioning inaccuracy or measurement equipment inaccuracy, and it is necessary when the phase reference of the source is not available or the measurement equipment cannot provide phase. In particular, as the frequency increases near-field phase measurements become increasingly inaccurate or even impossible. However, for the near-field to far-field transformation it is necessary to obtain the missing phase information in some other way than through direct measurement; this process is generally referred to as the phase retrieval. The combined process of first measuring the magnitudes of the field and subsequently retrieving the phase is referred to as a phaseless near-field antenna measurement technique. Phaseless near-field antenna measurements have been the subject of significant research interest for many years and numerous reports are found in the literature. Today, there is still no single generally accepted and valid phaseless measurement technique, but several different techniques have been suggested and tested to different extents. These can be divided into three categories: Category 1 – Four magnitudes techniques, Category 2 – Indirect holography techniques, and Category 3 -Two scans techniques. This paper provides an overview of the different phaseless near-field antenna measurement techniques and their respective advantages and disadvantages for different near-field measurement setups. In particular, it will address new aspects such as probe correction and determination of cross-polarization in phaseless near-field antenna measurements. [1] OM. Bucci et al. “Far-field pattern determination by amplitude only near-field measurements”, Proceedings of the 11’th ESTEC Workshop on Antenna Measurements, Gothenburg, Sweden, June 1988.
Installing a large compact range reflector and electromagnetically qualifying the quiet zone is a major undertaking, especially for very large panelized reflectors. The approach taken to design the required rolled-edge reflector geometry for achieving a 5 meter quiet zone across a frequency range of 350 MHz to 40 GHz was previously presented [1]. The segmentation scheme, fabrication methodology, and intermediate qualification of panels using an NSI-MI developed microwave holography tool were also presented. This reflector has since been installed and the compact range qualified by direct measurement of the electromagnetic fields in the quiet zone using a large field probe. This paper presents the comparison and correlation between the holography predictions and the field probe measurements of the quiet zone. Installation and alignment techniques used for the multiple panel reflector are presented. Available metrology tools have inherent accuracy limitations leading to residual misalignment between the panels. NSI-MI has overcome this limitation by using its holography tool along with existing metrology techniques to predict the field quality in the quiet zone based on surface measurements of the panels. The tool was used to establish go/no-go criteria for panel alignment accuracy achieved on site. Correlation of the holography predictions with actual field probe measurements of the installed reflector validates the application of the holography tool for performance prediction of large, multiple-panel, rolled-edge reflectors. Keywords: Rolled-Edge Reflector, Compact Range, Field-Probing, Quiet Zone, Microwave Holography
The 3D reconstruction algorithm of DIATOOL, with its higher-order Method of Moments-based implementation, reconstructs extreme near fields and surface currents on arbitrary 3D surfaces enclosing the antenna under test (AUT) from its measured radiated field. This is a valuable analysis and diagnostics tool for the antenna engineer to speed up the antenna prototyping cycle and identify errors in the manufactured AUTs, since the 3D reconstruction can solve a number of problems which traditional microwave holography cannot handle, namely: Accurate and detailed identification of array malfunctioning due to the enhanced spatial resolution of the reconstructed fields and currents Filtering of the scattering from support structures and feed network leakage A number of papers published over the past four years have shown these features in detail. At the same time it was observed that the spherical wave expansion (SWE) of the field radiated by the currents reconstructed by DIATOOL always provides a SWE power spectrum that looks noise-free. This phenomenon was observed for all the antennas on which the 3D reconstruction was applied, and it was explained as being an effect of the 3D reconstruction algorithm, which uses the a-priori information that all sources are contained inside the reconstruction surface. However, since real measured data were always used as input, it was not possible to prove that the SWE power spectrum of the reconstructed currents coincided with the one that would be obtained from noise-free measurements. The purpose of the present paper is thus to investigate in detail the noise filtering capabilities of the 3D reconstruction algorithm of DIATOOL. Models of several antennas, differing in size and type, were set up in GRASP with noise at different levels added to the radiated field. The noisy field was then given as input to DIATOOL and the SWE coefficients and the power spectra of the reconstructed currents were compared with the noise-free results coming from GRASP. Moreover, the effect of the varying noise level on the obtainable resolution was investigated.
A three-step equiangular (120º) phase shifting holography (EPSH) technique is proposed for THz antenna near-field/far-field prediction. The method is attractive from the viewpoint of receiver sensitivity, phase accuracy over the entire complex plane, simplified detector array architecture, as well as reducing planarity requirements of the near-field scanner. Numerical modeling is presented for the holographic receiver performance, using expected phase shift calibrations errors and phase shift noise. The receiver model incorporates responsivity and thermal noise specifications of a commercial Schottky diode detector. Additionally, simulated near-field patterns at 372GHz demonstrate the convenience of the method for accurate and high dynamic range THz near-field/far-field predictions, using a phase-shifter calibrated to ±0.1°.
In this paper the inverse-source technique or source reconstruction technique has been applied as diagnostic tool to determine the complex excitation at sub array and single element level of a measured array antenna [1-5]. The inverse-source technique, implemented in the commercially available tool “INSIGHT” [5], allows to compute equivalent electric and magnetic currents providing exclusive diagnostic information about the measured antenna. By additional processing of the equivalent currents the user can gain insight to the realized excitation law at single element and sub-array level to identify possible errors. The array investigated in this paper is intended as part of the European Navigation System GALILEO and is a pre-development model flying on the In-Orbit Validation Element the GIOVE-B satellite. The antenna, developed by EADS-CASA Espacio, consists of 42 patch elements, divided into six sectors and is fed by a two level beam forming network (BFN). The BFN provide complex excitation coefficients of each array element to obtain the desired iso-flux shaped beam pattern [6-7]. The measurements have been performed in the new hybrid (Near Field and Compact Range) facility in the ESTEC CPTR as part of the installation and validation procedure [8]. The investigation has been performed without any prior information of the array and intended excitation. The input data for the analysis is the measured spherical NF data and the array topology and reference coordinate system. References [1] J. L. Araque Quijano, G. Vecchi. Improved accuracy source reconstruction on arbitrary 3-D surfaces. Antennas and Wireless Propagation Letters, IEEE, 8:1046–1049, 2009. [2] L. Scialacqua, F. Saccardi, L. J. Foged, J. L. Araque Quijano, G. Vecchi, M. Sabbadini, “Practical Application of the Equivalent Source Method as an Antenna Diagnostics Tool”, AMTA Symposium, October 2011, Englewood, Colorado, USA [3] J. L. Araque Quijano, L. Scialacqua, J. Zackrisson, L. J. Foged, M. Sabbadini, G. Vecchi “Suppression of undesired radiated fields based on equivalent currents reconstruction from measured data”, IEEE Antenna and wireless propagation letters, vol. 10, 2011 p314-317. [4] L. J. Foged, L. Scialacqua, F. Mioc,F. Saccardi, P. O. Iversen, L. Shmidov, R. Braun, J. L. Araque Quijano, G. Vecchi " Echo Suppresion by Spatial Filtering Techniques in Advanced Planar and Spherical NF Antenna Measurements ", AMTA Symposium, October 2012, Seattle, Washington, USA [5] http://www.satimo.com/software/insight [6] A. Montesano, F. Monjas, L.E. Cuesta, A. Olea, “GALILEO System Navigation Antenna for Global Positioning”, 28th ESA Antenna Workshop on Space [7] L.S. Drioli, C. Mangenot, “Microwave holography as a diagnostic tools: an application to the galileo navigation antenna”, 30th Annual Antenna Measurement Techniques Association Symposium, AMTA 2008, Boston, Massachusetts November 2008 [8] S. Burgos, M. Boumans, P. O. Iversen, C. Veiglhuber, U. Wagner, P. Miller, “Hybrid test range in the ESTEC compact payload test range”, 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements ESA/ESTEC, The Netherlands, September 2013
Measurement post-processing techniques based on spatial filtering have been presented as promising tools for the mitigation of echo’s deriving from the measurement environment in regular Near Field (NF) measurement scenarios [1]. The adaptation of these tools into standard measurement procedures depends on the possibility to demonstrate the real effectiveness in a given measurement scenario. The standard validation approach is to introduce a known disturbance into a measurement scenario and show the efficiency of the techniques in attenuating this disturbance. While highly effective as a functional demonstration of this approach the benefit of the echo reduction on an actual measurement scenario should still be evaluated on a case by case basis. A hybrid Near Field (NF) system has recently been installed in the existing dual reflector Compact Payload Test Range of ESTEC [2-3]. The installed system has been designed to perform spherical, cylindrical and planar NF measurements. Despite the design effort to optimize the NF system position in the chamber some interaction with the dual reflectors in the range were expected and for the PNF system in particular [4]. During the hybrid system acceptance measurements have been performed on the space array antenna intended as part of the European Navigation System GALILEO. The antenna is a pre-development model flying on the In-Orbit Validation Element, GIOVE-B satellite, developed by EADS-CASA Espacio [5-6]. This L-band antenna is particularly important test case for ESTEC since the PNF system will later be used in the final testing at space craft level on the GALILEO Satellites. This paper presents the preliminary finding of the MV-Echo post processing validation for PNF measurements in the hybrid range. The GALILEO array antenna has been measured in different configuration, with and without echo reduction processing and the results compared. The purpose of the activity was to quantify the benefits of the MV-Echo processing. Since the array is working in circular polarization it was possible to identify the major echo contributions as 2’nd order reflections. References [1] L. J. Foged, L. Scialacqua, F. Mioc, F. Saccardi, P. O. Iversen, L. Shmidov, R. Braun, J. L. Araque Quijano, G. Vecchi, “Echo Suppression by Spatial Filtering Techniques in Advanced Planar and Spherical NF antenna Measurements”, 34th Annual Symposium of the Antenna Measurement Techniques Association, AMTA, October 2012, Seattle, Washington, USA [2] S. Burgos, M. Boumans, P. O. Iversen, C. Veiglhuber, U. Wagner, P. Miller, “Hybrid test range in the ESTEC compact payload test range”, 35th ESA Antenna Workshop on Antenna and Free Space RF Measurements ESA/ESTEC, The Netherlands, September 2013 [3] S. Burgos, P. O. Iversen, T. Andersson, U. Wagner, T. Kozan, A. Jernberg, B. Priemer, M. Boumans, G. Pinchuk, R. Braun, L. Shmidov, “Near-Field Hybrid Test Range from 400 MHz to 50 GHz in the ESTEC Compact Payload Test Range with RF upgrade for high frequencies”, EUCAP 2014 [4] Paper on position of NF system in the range – was it astrium that did it? [5] L.S. Drioli, C. Mangenot, “Microwave holography as a diagnostic tools: an application to the galileo navigation antenna”, 30th Annual Antenna Measurement Techniques Association Symposium, AMTA 2008, Boston, Massachusetts November 2008 [6] A. Montesano, F. Monjas, L.E. Cuesta, A. Olea, “GALILEO System Navigation Antenna for Global Positioning”, 28th ESA Antenna Workshop on Space [7] J. E. Hansen, Spherical Near-Field Antenna Measurements, Peter Peregrinus Ltd. On behalf of IEE, London, United Kingdom, 1988. [8] F. Jensen, A. Frandsen, “On the number of modes in spherical wave expansion”, AMTA Symposium, October 2004, Stone Mountain, GA, USA.
We present exact solutions to antenna holography problems based on planar, spherical, or cylindrical nearfield data. Full field distribution information in the source region is determined exactly, from two tangential field components over a planar, spherical, or cylindrical surface. Stated in so many words, all three components of both electric and magnetic fields in the antenna aperture are obtained exactly from two-component near-field data. Conventional antenna holography relies upon back transformation for planar near-field data, and upon optimization schemes for both spherical and cylindrical near-field data. It is both acknowledged and accepted that the back transform is only an approximate solution due to its far-field nature, whereas optimization algorithms are vulnerable to convergence instability and, moreover, are computationally intensive. Our approach tackles holography by solving an inverse scattering problem, with exact solutions derived on the basis of three common types of near-field data. A mapping algorithm is proposed herein which determines the field everywhere, in both interior and exterior regions, based on a single-slice nearfield data capture. It provides exact antenna holography solutions analytically, with the full electric and magnetic fields disclosed throughout the source region. The field mapping algorithm is a direct, closed-form solution which is numerically straightforward and efficient. Verification is carried out and demonstrated by analytic examples and numerical simulations, as well as by hardware measurements. Nine test examples are given. Analytic examples include dipole arrays deployed across planar, spherical, and cylindrical regions, and a narrow azimuthal slot on a conducting sphere. The simulation example exposes the structure of a slotted array antenna based upon its near-field data as generated by a commercial software package. The hardware measurements address themselves to a concrete embodiment of that same slotted array antenna, an elongated sector antenna, and to a patch antenna. Excellent agreement is found in all test cases.
This paper validates the sub-reflectarray technique for main reflector antenna distortion compensation through simulations and measurements. First, axial defocusing of the feed creates spherical aberration distortion and it is corrected using sub-reflectarray by conjugate field matching method. Then, a ring-type distortion is created on the main reflector and it is also compensated using a similar approach. A hybrid HFSS/PO simulation approach was used for the design and analysis. Bipolar planar near-field measurements are performed to validate the compensation technique and back projection holography is used to locate the position of distortions and to study the effects of the distortion on the antenna performance.
This paper presents a new approach to the inversion of boundary value (BV) problems in an infinite conductive, homogeneous media. Our interest is to investigate the possibility of imaging underwater electromagnetic sources from remote electromagnetic sensor data. Specifically, given two polarizations of the electric/magnetic fields on a cylindrical surface exterior to the electric and magnetic sources, we develop a frequency domain, back-projection technique that allows for the complete determination of the electric and magnetic fields in the region between the BV surface and the sources. This is an inverse problem and Tikhonov regularization is used to obtain an accurate filtered, back-propagated solution. In this approach two components of the measured field yield the six components of the field closer to the source. Of particular interest is the active part of the Poynting vector that is constructed from the back-projected fields, providing the power per unit area radiated from the sources. We believe it may be of immense practical use in diagnosis of electromagnetic sources underwater. We test the theory with a numerical experiment using a linear array of either magnetic or electric dipole sources excited in a frequency range of 1 to 1000 Hz in seawater that generate two cylindrical holograms (30m radius) of the axial polarization of the magnetic and electric fields, respectively. The complete (all polarizations) electric and magnetic fields are predicted along with the real and imaginary parts of the Poynting vector on a cylindrical back-propagation surface (20m radius). These simulations show that very accurate results are obtained even with low signal-to-noise levels. Work supported by the Office of Naval Research.
This paper presents the methodology to generate a pseudo time domain holography from frequency swept measurements. This is an approximation to the time domain holography (TDH) invented by the authors [1,2], which opens a new possibility for antenna diagnostics using conventional instrumentation and in the absence of time domain measurements. Practical examples using two spaceborne antennas are provided and discussed.
This paper describes an application of well known microwave holography to the practical case of the space antenna for the European Navigation System GALILEO. The antenna consists in an array of 45 patch elements, divided into six sectors, fed by a two level beam forming network. In fact, the procedure described in this paper has been used in the frame of the development of the GALILEO Navigation antenna to identify element feeding errors. A planar hologram on the aperture plane of the array has been obtained by a set of spherical near field measurements. Sampling the resulting aperture field distribution (in amplitude and phase) allowed reconstructing the excitation law and identifying errors. The developed procedure was validated with a number of test cases assessing numerical errors introduced by the process. Applying the back-projection to the measured far-field led to discover that some sectors of the array were overfed and that errors were present in the central power divider responsible of the first power distribution in the antenna. A new power divider was then manufactured and integrated into the array leading to a well performing antenna.