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We present an antenna measurement methodology requiring a radically lower number of field samples than the standard Nyquist-based theory maintaining a comparable accuracy. simulations and partial knowledge of the geometry of the Antenna Under Test are combined to build a set of numerically defined expansion functions: the method uses basic knowledge of the antenna and the assumption that scattering from large surfaces can be predicted accurately by numerical tools; areas of the antenna such as feeding structures are treated as unknown and represented by equivalent electric and magnetic currents on a conformal surface. In this way, the complexity, and thus the number of unknowns, is dramatically reduced wrt the full problem for most antennas. The basis functions representing the full antenna are used to interpolate a radically reduced set of measured samples to a fine regular grid of Near Field (NF) samples in standard geometries. Regular NF to Far Field (FF) transformation techniques are then employed to determine the FF. The sampling reduction is evaluated compared to a regular sampling on standard Nyquist-complaint grids. The method can be employed in standard sampling ranges. In [1] asymptotic simulation tools were used to build the numerical basis. In this paper, methods based on Surface Integral Equations (SIEs) are used to compute currents and fields. The currents induced on the antenna structure by each elementary source are computed and used to evaluate the radiated field. Both electric and magnetic elementary sources are placed around the antenna and the SIE problems use a fast algorithm to evaluate matrix-vector products. The methodology is validated with planar and spherical acquisitions on a reflector antenna (MVG SR40) fed by a dual ridge horn SH4000 and in a multi-feed configurations (using several SH5000) at 18 and 30 GHz. Patterns obtained with down-sampled fast approach are compared to standard measurements. Down-sampling factors up to 8 are achieved maintaining very high correlation levels with standard techniques.
Spherical Near-Field (SNF) systems using a swing arm gantry configuration have been the go to solution for automotive measurement systems. Recent advances in the automotive industry have warranted a need for SNF systems with high mechanical positioning accuracy supporting measurements up to 40 GHz and beyond. This paper presents the design and implementation of a new swing arm gantry positioner having an 8-meter radius and a radial axis to support high frequency SNF measurements. We first define the relation of the gantry axis to the global coordinate system and discuss primary sources of errors. Next, a robust mechanical design is presented including design considerations and implementation. We then present errors measured using a tracking laser interferometer for probe position through the range of gantry axis travel. Static corrections for probe positioning errors are implemented in the control system using the radial axis. The resultant residual error for the swing arm gantry is then shown to have the accuracy required for high frequency SNF measurements.
Positioning in near-field antenna measurements is crucial and often an absolute position accuracy of ?\50 is required. This can be difficult to achieve in practice, e.g. for robotic arm measurement systems and/or high frequencies. Therefore, optical measurement devices are used to precisely measure the position and orientation. The information can be used to correct the position and orientation during the measurement or in the near-field to far-field transformation. The latter has the benefit that the measurement acquisition is typically faster because no additional correction movements are needed. Different methods for correction of non-ideal measurement positions in r, ? and f have been presented in the past. However, often not only the relative position but also the orientation between the antenna under test (AUT) and the probe coordinate system is not perfect. So far, correction and investigation of the related non-ideal probe orientations has been neglected due to the assumption that the probe receiving pattern is broad. In this paper, non-ideal probe orientations will be investigated and a spherical wave expansion procedure which corrects non-ideal probe orientations and positions will be presented. This is achieved by including an arbitrary probe pointing in the probe response calculation by additional Euler rotations of the probe receiving coefficients. The introduced pointwise higher-order probe correction scheme allows an exact spherical wave expansion of the radiated AUT field. The transformation is based on solving a system of linear equations and, thus, has a higher complexity compared to Fourier-based methods. However, it will be shown that most of the calculations can be precomputed during the acquisition and that solving the linear equation system can be accelerated by using iterative techniques such as the conjugate gradient method. The applicability of the proposed method is demonstrated by measurements where an intentional misalignment is introduced. Furthermore, the method can be used to include full probe correction in the translated spherical wave expansion algorithm. In conclusion, the proposed procedure is a beneficial extension of spherical wave expansion methods and can be applied in different measurement scenarios.
The paper summarizes the performance of a new near-field to far-field (NF/FF) transform approach for a VHF vehicle mounted AUT test case, and compares the approach with the spherical measurement approach. The NF/FF transformation is based on the solution of an inverse problem in which the measured NF and predicted FF values are attributed to a set of equivalent electric and magnetic surface currents which lie on a convex arbitrary surface that is conformal to the antenna under test (AUT). The NF points are conformal to the AUT, reducing the number of samples and relaxing positioning requirements used in conventional spherical, NF/FF geometries. A pseudo inversion of the matrix representing the mapping of the equivalent sources into the near-field samples is obtained by using the singular value decomposition (SVD), which is used to form an approximation of the inverse of the matrix. This inverse, when multiplied by the NF measurement vector, solves for the efficiently radiating components of the current, which are used to compute the FF in a straightforward manner. Keywords—Antenna Near-Field to Far-Field Transformation, Electromagnetic Inverse Problems.
Spherical Near-Field (SNF) measurements are an established technique for the characterization of an Antenna Under Test (AUT). The normal sampling criterion follows the Nyquist theorem, taking equiangular samples. The sampling step size depend on the smallest sphere that, centered in the measurement’s coordinate system, encloses the AUT, i.e. the global minimum sphere. In addition, a local minimum sphere can be defined as the sphere with minimum radius which, centered in the AUT, encloses it alone. The local minimum sphere is always equal or smaller than the global minimum sphere, being equal when the AUT is centered in the measurement’s coordinate system. It is assumed that the local minimum sphere’s center coincides with the radiation center. Furthermore, it is possible to compute a Translated Spherical Wave Expansion (TSWE) centered in the local minimum sphere, thus needing less measurement points, as long as the relative position of its center is known. Due to practical reasons, it is not always possible to easily locate the radiation center. In this paper, the relative position of the radiation center of an AUT with respect to the measurement's coordinate system’s center is estimated from SNF data using two approaches. The first approach takes the phase center as an estimation of the radiation center and is based on the method of moving reference point, strictly valid for the far-field case, analyzing its error at different near-field distances. The second approach is based on a spherical modes' spectrum analysis: the closer the AUT’s radiation center is to the coordinate system's center, the larger the power fraction in the lower modes will be. The proposed algorithm iteratively displaces the SWE and checks the power in a predefined number of modes until the convergence criterion is fulfilled. It is important to note that no near-field to far-field transformation is used, for the less measurement points taken do not allow it. A thorough analysis of the estimation error is done by simulation for different cases and antennas. The estimation error of both methods is compared and discussed, highlighting the convenience of each method depending on the requirements.
The principles of near-field antenna measurements and scanning in Cartesian and spherical coordinates are well established and documented in the literature, and in standards used on antenna ranges throughout government, industry, and academic applications. However the measurement methods used and the mathematics that are applied to compute the gain and radiation of the pattern of the test antenna from the near-field data assume typically that the antenna is operating in free space. This leaves several questions open when dealing with antennas operating over a lossy ground plane, such as the ocean damp soil, etc. In this paper, we shall discuss some of the motivation behind an examination of the physics and mathematics involved in performing a near-field antenna measurement over a seawater ground plane. Examples of past work in this are shall be discussed along with some of the challenges of performing far field antenna measurements in the presence of the air-sea interface. These discussions lead to some fundamental questions about how one defines gain in this environment and whether or not a near field approach could be beneficial. This will lead to some discussion of when and how the existing modal field expansions used in near-field measurements may need to be adjusted to account for the presence of the ground plane created by the ocean surface. An example of the limiting case of an antenna operating over a metallic ground plane will be discussed as a stepping stone to the more general problem of an antenna operating over a lossy ground plane.
The principles of near-field antenna measurements and scanning in Cartesian and spherical coordinates are well established and documented in the literature, and in standards used on antenna ranges throughout government, industry, and academic applications. However the measurement methods used and the mathematics that are applied to compute the gain and radiation of the pattern of the test antenna from the near-field data assume typically that the antenna is operating in free space. This leaves several questions open when dealing with antennas operating over a lossy ground plane, such as the ocean damp soil, etc. In this paper, we shall discuss some of the motivation behind an examination of the physics and mathematics involved in performing a near-field antenna measurement over a seawater ground plane. Examples of past work in this are shall be discussed along with some of the challenges of performing far field antenna measurements in the presence of the air-sea interface. These discussions lead to some fundamental questions about how one defines gain in this environment and whether or not a near field approach could be beneficial. This will lead to some discussion of when and how the existing modal field expansions used in near-field measurements may need to be adjusted to account for the presence of the ground plane created by the ocean surface. An example of the limiting case of an antenna operating over a metallic ground plane will be discussed as a stepping stone to the more general problem of an antenna operating over a lossy ground plane.
Spherical wave coefficients are chosen to minimize a cost function that is a norm of the residual of the fit. For example, in standard orthogonality-based processing algorithms [1], the cost function is an integral (over 4 p steradians) of the squared amplitude of the difference between actual measurements and predicted values. Some recent work [2,3] at NIST has led to the use of discrete norms where the integral is replaced by a weighted sum. We explore issues regarding the choice of these weights, the relative performance of different weighting schemes, and the relation between the continuous and discrete cases. These norms are mathematically equivalent if there is a solution with zero residual. In practice, we have observed noticeable variation due to the presence of measurement errors, including multiple reflections, room reflections… Also, different weighting schemes are associated with widely varying condition numbers. When the condition number is large, small measurement errors can lead to large errors in the result. Additionally, we show that the integral cost function mentioned above can be reduced to a discrete quadrature. M.H. Francis and R.C. Wittmann, Chp. 19, “Near-Field Scanning Measurements: Theory and Practice” in Modern Antenna Handbook, ed. C.A. Balanis, John Wiley & Sons, 2008. R.C. Wittmann, B.K. Alpert, M.H. Francis, “Near-field, spherical-scanning antenna measurements with nonideal probe locations,”IEEE Antennas and Propagat., vol. 52, pp. 2184 – 2186, August 2004. R.C. Wittmann, B.K. Alpert, M.H. Francis, “Near-field antenna measurements with nonideal measurement locations,”IEEE Antennas and Propagat., vol. 46, pp. 716 – 722, May 1998.
We investigate all-metal 3D printing as a viable option for millimeter wave applications. 3D printing is finding applications across many areas and may be a useful technology for antenna fabrication. The ability to rapidly fabricate custom antenna geometries may also help improve cub satellite prototyping and development time. However, the quality of an antenna produced using 3D printing must be considered if this technology can be relied upon. Here we investigate a corrugated feed horn that is fabricated using the powder bead fusion process for use in the PolarCube cube satellite radiometer. AlSi10Mg alloy is laser fused to build up the feed horn, including the corrugated structure on the inner surface of the horn. The intricate corrugations, and tilted waveguide feed transition of this horn made 3D printing a compelling and interesting process to explore. We will discuss the fabrication process and present measurement data at 118.7503 GHz. Gain extrapolation and far-field pattern results obtained with the NIST robotic antenna range CROMMA are presented. Far-field pattern data were obtained from a spherical near-field scan over the front hemisphere of the feed horn. The quasi-Gaussian HE11 hybrid mode supported by this antenna results in very low side lobe levels which poses challenges for obtaining good SNR at large zenith angle during spherical near field measurements. This was addressed through using a single alignment and electrical calibration while autonomously changing between extrapolation and near-field measurements using the robotic arm in CROMMA. The consistency in parameters between extrapolation and near-field measurements allowed the extrapolation data to be used in-situ as a diagnostic. Optimal near-field scan radius was determined by observing the reflection coefficient S11 during the extrapolation measurement. The feed horn-to-probe antenna separation for which |S11| was reduced to 0.1 dB peak-to-peak was taken as the optimal near-field scan radius for the highest measurement SNR. A comparison of these measurements to theoretical predictions is presented which provides an assessment of the performance of the feed horn.
We investigate all-metal 3D printing as a viable option for millimeter wave applications. 3D printing is finding applications across many areas and may be a useful technology for antenna fabrication. The ability to rapidly fabricate custom antenna geometries may also help improve cub satellite prototyping and development time. However, the quality of an antenna produced using 3D printing must be considered if this technology can be relied upon. Here we investigate a corrugated feed horn that is fabricated using the powder bead fusion process for use in the PolarCube cube satellite radiometer. AlSi10Mg alloy is laser fused to build up the feed horn, including the corrugated structure on the inner surface of the horn. The intricate corrugations, and tilted waveguide feed transition of this horn made 3D printing a compelling and interesting process to explore. We will discuss the fabrication process and present measurement data at 118.7503 GHz. Gain extrapolation and far-field pattern results obtained with the NIST robotic antenna range CROMMA are presented. Far-field pattern data were obtained from a spherical near-field scan over the front hemisphere of the feed horn. The quasi-Gaussian HE11 hybrid mode supported by this antenna results in very low side lobe levels which poses challenges for obtaining good SNR at large zenith angle during spherical near field measurements. This was addressed through using a single alignment and electrical calibration while autonomously changing between extrapolation and near-field measurements using the robotic arm in CROMMA. The consistency in parameters between extrapolation and near-field measurements allowed the extrapolation data to be used in-situ as a diagnostic. Optimal near-field scan radius was determined by observing the reflection coefficient S11 during the extrapolation measurement. The feed horn-to-probe antenna separation for which |S11| was reduced to 0.1 dB peak-to-peak was taken as the optimal near-field scan radius for the highest measurement SNR. A comparison of these measurements to theoretical predictions is presented which provides an assessment of the performance of the feed horn.
One of the keys to developing new science and technologies is to have sound metrology tools and techniques. Whenever possible, we would like these metrology techniques to make absolute measurements of the physical quantity. Furthermore, we would like to make measurements directly traceable to the International System of Units (SI). Measurements based on atoms provide such a direct SI traceability path and enable absolute measurements of physical quantities. Atom-based measurements have been used for several years; most notable are time (s), frequency (Hz), and length (m). There is a need to extend these atom-based techniques to other physical quantities, such as electric (E) fields. We are developing a fundamentally new atom-based approach for that will lead to a self-calibrated, SI traceable E-field measurement and has the capability to perform measurements on a fine spatial resolution in both the far-field and near-field. This new approach is significantly different from currently used field measurement techniques in that it is based on the interaction of radio-frequency (RF) E-fields with Rydberg atoms (alkali atoms placed in a glass vapor-cell that are excited optically to Rydberg states). The Rydberg atoms act like an RF-to-optical transducer, converting an RF E-field strength to an optical-frequency response. In this new approach, we employ the phenomena of electromagnetically induced transparency (EIT) and Autler-Townes splitting. This splitting is easily measured and is directly proportional to the applied RF E-field amplitude and results in an absolute SI traceable measurement. The technique is very broadband allowing self-calibrated measurements over a large frequency band including 500 MHz to 500 GHz (and possibly up to 1 THz and down to 10's of megahertz). We will report on the development of this new metrology approach, including the first fiber-coupled vapor-cell for E-field measurements. We also discuss key applications, including self-calibrated measurements, millimeter-wave and sub-THz measurements, field mapping, and sub-wavelength and near-field imaging. We show results for mapping the fields inside vapor cells, for measuring the E-field distribution along the surface of a circuit board, and for measuring the near-field at the aperture in a cavity.
A technique of visualizing a surface current or a near-field equivalent source distribution is required for an antenna evaluation and its failure diagnostic. An inverse problem reconstructs the equivalent wave source distribution inside the measurement region by solving the propagation coefficient of the electromagnetic wave inversely from the near-field measured electromagnetic field the antenna under test (AUT) Since this method can set an arbitrary shape surface enclosing the AUT as a estimation surface, it is effective to visualize the internal equivalent source distribution. However under interference wave environments, the inverse source technique reconstructs the equivalent currents, including interference wave component as a part of internal source distribution. The estimation accuracy is particularly deteriorated under interference wave conditions. We propose a method of 2-step source reconstruction on arbitrary 3-D surface using dual measured electromagnetic surface, for reconstruct internal equivalent source accurately. First step, we set a shape of estimation surface similar to the shapes of measurement surface, to estimate the internal distribution accurately under well-posed conditions. Not only the shape of the estimation surface but also the sampling density is made same to the density of the measurement surfaces. In second step, to reconstruct an arbitrary shape surface from reconstructed internal field distribution in previous step. Since the inverse problem in this step is generally under ill-posed conditions, the regularization is applied to improve the accuracy of the solution. By this 2-step reconstruction, the interference wave is eliminated and the internal equivalent source on arbitrary surface is reconstructed. For example, we apply the proposed method to a 4-element linear patch array antenna, and the effectiveness of the proposed method is clarified. We also showed that the internal source distribution accurately reconstructed on an arbitrary surface even in the interference wave environments and identify the defective operation part of the AUT.
Among the near-field – far-field (NF-FF) transformation techniques, the one employing the bi-polar scanning is particularly interesting, since it retains all the advantages of that using the plane-polar one, while requiring a mechanically simple, compact, and cheaper measurement facility [1]. In fact, in this scan, the antenna under test (AUT) rotates axially, while the probe is mounted at the end of an arm that rotates around an axis parallel to the AUT one. An effective probe voltage representation on the scanning plane requiring a minimum number of bi-polar NF data has been developed in [2], by properly exploiting the nonredundant sampling representations of electromagnetic (EM) fields [3] and considering the AUT as enclosed in an oblate ellipsoid. A 2-D optimal sampling interpolation (OSI) formula is then employed to efficiently recover the NF data required by the traditional plane-rectangular NF-FF transformation [4] from the acquired nonredundant bi-polar samples. It is so possible to considerably reduce the number of the needed NF data and corresponding measurement time with respect to the previous approach [1], which did not exploit the nonredundant sampling representations. However, due to an imprecise control of the positioning systems and their finite resolution, it may be impossible to exactly locate the probe at the points fixed by the sampling representation, even though their position can be accurately read by optical devices. Therefore, it is very important to develop an effective algorithm for an accurate and stable reconstruction of the NF data needed by the NF-FF transformation from the acquired irregularly spaced ones. A viable and convenient strategy [5] is to retrieve the uniform samples from the nonuniform ones and then reconstruct the required NF data via an accurate and stable OSI expansion. In this framework, two different approaches have been proposed. The former is based on an iterative technique, which converges only if there is a biunique correspondence associating at each uniform sampling point the nearest nonuniform one, and has been applied in [5] to the uniform samples retrieval in the case of cylindrical and spherical surfaces. The latter, based on the singular value decomposition (SVD) method, does not exhibit this constraint and has been applied to the nonredundant bi-polar [6] scanning technique based on the oblate ellipsoidal modeling. However, it can be conveniently used only when the uniform samples recovery can be split in two independent one-dimensional problems. The goal of this work is not only to provide the experimental validation of the SVD based technique [6], but also to develop the approach using the iterative technique and experimentally assess its effectiveness. [1] L.I. Williams, Y. Rahmat-Samii, R.G. Yaccarino, “The bi-polar planar near-field measurement technique, Part I: implementation and measurement comparisons,” IEEE Trans. Antennas Prop., vol. 42, pp. 184-195, Feb. 1994. [2] F. D’Agostino, C. Gennarelli, G. Riccio, C. Savarese, “Data reduction in the NF-FF transformation with bi-polar scanning,” Microw. Optic. Technol. Lett., vol. 36, pp. 32-36, 2003. [3] O.M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Prop., vol. 46, pp. 351-359, March 1998. [4] E.B. Joy, W.M. Leach, Jr., G.P. Rodrigue, D.T. Paris, “Application of probe-compensated near-field measurements,” IEEE Trans. Antennas Prop., vol. AP-26, pp. 379-389, May 1978. [5] O.M. Bucci, C. Gennarelli, G. Riccio, C. Savarese, “Electromagnetic fields interpolation from nonuniform samples over spherical and cylindrical surfaces,” IEE Proc. Microw. Antennas Prop., vol. 141, pp. 77-84, April 1994. [6]F. Ferrara, C. Gennarelli, M. Iacone, G. Riccio, C. Savarese, “NF–FF transformation with bi-polar scanning from nonuniformly spaced data,” Appl. Comp. Electr. Soc. Jour., vol. 20, pp. 35-42, March 2005.
Millimeter wave vehicular radar operating in the 77 GHz band for automatic emergency breaking (AEB) applications in detecting vehicles, pedestrians, and bicyclists, test data has shown that the radar cross section (RCS) of a target decreases significantly with distance at short range distances typically measured by automotive radar systems, where the reliable detection is most critical. Some attribute this reduction to a reducing illumination spot size from the antenna beam pattern. Another theory points to the spherical phase front due to measurement in the Fresnel region of the target, when the distance for the far-field zone is not met. The illumination of the target depends on the antenna patterns of the radar, whereas the Fresnel region effects depend on the target geometry and size. Due to fluctuations in measured data for RCS as a function of range in the near-field, upper and lower bounds for the target RCS versus range have been determined empirically as a method for describing the expected RCS of target. So far, the range-dependent RCS bounds used in AEB test protocols have been determined empirically. The study discussed in this paper aims to study the underlying physics that produces range-dependent RCS in near field and provide analytical model of such behavior. The resultant analytical model can then be used to objectively determine the RCS upper and lower bounds according to the radar system parameters such as antenna patterns and height. A comparison of the analytically predicted model and empirical near-field RCS as a function of range data will be presented for pedestrian, bicyclist, and vehicle targets.
Millimeter wave vehicular radar operating in the 77 GHz band for automatic emergency breaking (AEB) applications in detecting vehicles, pedestrians, and bicyclists, test data has shown that the radar cross section (RCS) of a target decreases significantly with distance at short range distances typically measured by automotive radar systems, where the reliable detection is most critical. Some attribute this reduction to a reducing illumination spot size from the antenna beam pattern. Another theory points to the spherical phase front due to measurement in the Fresnel region of the target, when the distance for the far-field zone is not met. The illumination of the target depends on the antenna patterns of the radar, whereas the Fresnel region effects depend on the target geometry and size. Due to fluctuations in measured data for RCS as a function of range in the near-field, upper and lower bounds for the target RCS versus range have been determined empirically as a method for describing the expected RCS of target. So far, the range-dependent RCS bounds used in AEB test protocols have been determined empirically. The study discussed in this paper aims to study the underlying physics that produces range-dependent RCS in near field and provide analytical model of such behavior. The resultant analytical model can then be used to objectively determine the RCS upper and lower bounds according to the radar system parameters such as antenna patterns and height. A comparison of the analytically predicted model and empirical near-field RCS as a function of range data will be presented for pedestrian, bicyclist, and vehicle targets.
Among the near-field - far-field (NF-FF) transformations, that with spherical scan [1] is the most appealing due to its feature to allow the whole radiation pattern reconstruction of the antenna under test (AUT). To get a considerable measurement time saving, spherical NF-FF transformations for AUTs with one or two predominant dimensions, requiring a minimum number of NF data, have been developed in [2], by using the nonredundant sampling representations of the electromagnetic (EM) fields [3] and adopting a prolate or oblate ellipsoid to shape the AUT. Another effective possibility to save the measurement time is to make faster the scan by collecting the NF data through continuous and synchronized movements of the probe and AUT. To this end, NF-FF transformations with spherical spiral scan have been recently proposed. They rely on the nonredundant representations and use optimal sampling interpolation (OSI) formulae [3] to effectively recover the NF data needed by the traditional spherical NF-FF transformation [1] from the acquired ones. The nonredundant sampling representation on the sphere from spiral samples and the related OSI expansion have been developed in [4-6] by adopting a spherical AUT model and choosing the spiral pitch equal to the sample spacing needed to interpolate along a meridian. Then, NF-FF transformations with spherical spiral scan for long or quasi-planar AUTs [7] have been obtained by applying the unified theory of spiral scans for non-volumetric AUTs [8]. Unfortunately, due to practical constraints, it is not always possible to mount the AUT in such a way that it is centered on the scanning sphere centre. In this case, the number of NF data required by the NF-FF transformation [1] and the related measurement time can remarkably increase, due to the corresponding grow of the minimum sphere radius. Aim of this work is the development of a fast and accurate nonredundant NF-FF transformation with spherical spiral scan suitable for quasi-planar antennas, which requires practically the same number of NF data both in the centered and offset mountings of the AUT. To this end, an offset mounted quasi-planar AUT is modeled as contained in a oblate ellipsoid, and an effective representation of the probe voltage over the scanning sphere, using a minimum number of samples collected on a proper spiral wrapping it, is developed by applying the unified theory of spiral scans for non-volumetric AUTs [8] in the spherical coordinate system having the origin coincident with the AUT centre at distance from the scanning sphere one. The related OSI expansion allows to accurately reconstruct the NF data required for the NF-FF transformation. [1] J. Hald, J.E. Hansen, F. Jensen, F.H. Larsen, Spherical near-field antenna measurements, J.E. Hansen, (ed.), London, Peter Peregrinus, 1998. [2] O.M. Bucci, C. Gennarelli, G. Riccio, C. Savarese, “Data reduction in the NF–FF transformation technique with spherical scanning,” Jour. Electr. Waves Appl., vol. 15, pp. 755-775, June 2001. [3] O.M. Bucci, C. Gennarelli, C. Savarese, “Representation of electromagnetic fields over arbitrary surfaces by a finite and nonredundant number of samples,” IEEE Trans. Antennas Prop., vol. 46, pp. 351-359, March 1998. [4] O.M. Bucci, F. D’Agostino, C. Gennarelli, G. Riccio, C. Savarese, “NF–FF transformation with spherical spiral scanning,” IEEE Antennas Wireless Prop. Lett., vol. 2, pp. 263-266, 2003. [5] J F. D’Agostino, F. Ferrara, J.A. Fordham, C. Gennarelli, R. Guerriero, M. Migliozzi, “An experimental validation of the near-field - far-field transformation with spherical spiral scan,” IEEE Antennas Prop. Magaz., vol. 55, pp. 228-235, Aug. 2013. [6] F. D’Agostino, C. Gennarelli, G. Riccio, C. Savarese, “Theoretical foundations of near-field–far-field transformations with spiral scannings,” Prog. in Electr. Res., vol. 61, pp. 193-214, 2006. [7] R. Cicchetti, F. D’Agostino, F. Ferrara, C. Gennarelli, R. Guerriero, M. Migliozzi, “Near-field to far-field transformation techniques with spiral scannings: a comprehensive review,” Int. Jour. Antennas Prop., vol. 2014, ID 143084, 11 pages, 2014. [8] F. D’Agostino, F. Ferrara, C. Gennarelli, R. Guerriero, M. Migliozzi, “The unified theory of near–field–far–field transformations with spiral scannings for nonspherical antennas,” Prog. in Electr. Res. B, vol. 14, pp. 449-477, 2009.
Modern cars are equipped with a large number of antennas which are strongly integrated with the car. A full characterization of the radiating properties of the entire vehicle is thus typically required. In order to characterize the radiating properties of the installed antennas, large measurement systems accommodating the full vehicle are required. As in standard antenna measurements, a full spherical near field (NF) scanning around the car is desirable in order to perform an accurate NF/FF transformation. However, due to size and weight of the Device Under Test (DUT) and/or economic factors a full spherical scan is often unfeasible. For this reason, truncated spherical scanners (such as hemispherical) are typically involved. A classic solution is to combine hemispherical scanning with a metallic ground plane which is assumed to be a Perfect Electric Conductor (PEC) in the NF/FF transformation. However, the PEC ground-plane is less representative of realistic automotive environments such as asphalt that is strongly dielectric. A further drawback is the strong scattering from the large metallic ground-plane which highly compromises the NF measurements at low frequencies. In many situations, it is thus desirable to perform the NF measurements in a condition similar to free-space by using absorber materials on the floor. It is well-known that standard NF/FF transformations applied to partial spherical acquisitions generates the so called truncation errors. Such errors are stronger at lower frequencies due to the lower number of spherical modes for fixed DUT size. Moreover, typical antennas for automotive applications are generally low directive thus, the impact of the truncation on the measured pattern is often non-negligible. In such cases advanced post-processing techniques must be involved to mitigate the effect of the truncation errors. In this paper two truncation error mitigation techniques will be compared when applied to automotive measurements performed in free-space conditions. The first technique is an iterative process which at each iteration applies a modal filtering based on the size of the DUT. The second technique is based on the computation of the equivalent currents of the DUT over an equivalent surface which acts as spatial filter. Both techniques give excellent mitigation performance with different computational effort. The good agreement between two different techniques effectively defining the lower bound for what can be successfully mitigated by post processing techniques.
The Translated Spherical Wave Expansion (Translated-SWE) has been recently proposed as a powerful Near Field to Far Field (NF/FF) transformation tool which allows to reduce the number of samples in offset spherical NF measurements. The algorithm is based on the definition of a new reference system located on the Device Under Test (DUT) rather than on the center of the measurement sphere. The translation of the measurement system on the DUT allows to represent it with a minimum number of spherical modes (smaller minimum sphere) thus the reduction of the NF sampling points (down-sampling). The validation of the Translated-SWE have been presented in previous publications in case of DUT offset displaced along the Z-axis. This may occur in case of mechanical constraints of the measurement system such as mast or stand-offs of fixed length, used to handle the DUT. Similarly, in other measurement situations, the DUT is intentionally displaced offset wrt the center of rotation to enhance the echo reduction capabilities of the modal filtering performed on the SWE spectrum. It has been also shown that in such measurement scenarios the Translated-SWE can be effectively used allowing a significant reduction of the sampling points and thus of the testing time. Antennas installed on complex structure, like cars, is another example of offset radiating devices. In many practical case, the currents induced by the fed antenna on the structure have only a localized effect (e.g. higher directive antennas and/or antennas working at higher frequencies). In such situations a down-sampled acquisition can be performed taking advantage of the Translated-SWE which is run moving the reference system on the fed antenna so that only the portion of structure surrounding that antenna is taken into account. The size of the measured portion of the structure will of course depend on the density of the applied sampling while the remaining part will be neglected. In this paper the Translated-SWE algorithm will be applied to antenna installed on cars in generic offset position. To this purpose the algorithm has been updated in order to be able to deal with generic XYZ-offsets.
The portable antenna measurement system PAMS was developed for arbitrary and irregular near-field scanning. The system utilizes a crane for positioning of the near-field probe. Inherent positioning inaccuracies of the crane mechanics are handled with precise knowledge of the probe location and a new transformation algorithm. The probe position and orientation is tracked by a laser while the near-field is being sampled. Far-field patterns are obtained by applying modern multi-level fast multipole techniques. The measurement process includes full probe pattern correction of both polarizations and takes into account channel imbalances. Because the system is designed for measuring large antennas the RF setup utilizes fiber optic links for all signals from the ground instrumentation up to the gondola, at which the probe is mounted. This paper presents results of the Ka-band test campaign in the scope of an ESA/ESTEC project. First, the new versatile approach of characterizing antennas in the near-field without precise positioning mechanics is briefly summarized. The setup inside the anechoic chamber at Airbus Ottobrunn, Germany is shown. Test object was a linearly polarized parabolic antenna with 33dBi gain at 33GHz. The near-fields were scanned on a plane with irregular variations of over a wavelength in wave propagation. Allowing these phase variations in combination with a non-equidistant grid gives more degree of freedom in scanning with less demanding mechanics at the cost of more complex data processing. The setup and the way of on-the-fly scanning are explained with respect to the crane speed and the receiver measurement time. Far-fields contours are compared to compact range measurements for both polarizations to verify the test results. The methodology of gain determination is also described under the uncommon near-field constraint of coarse positioning accuracy. Finally, the error level assessment is outlined on the basis of the classic 18-term near-field budgets. The assessment differs in the way the impact of the field transformation on the far-field pattern is evaluated. Evaluation is done by testing the sensitivity of the transformation with a combination of measured and synthetic data.
Antenna measurements above a material half-space are becoming an interesting aspect of near-field measurements especially for automotive antenna tests. Upcoming measurement facilities will be equipped with a dielectric or metallic ground. The near-field is sampled on a measurement surface in the vicinity of the device under test (DUT) above the ground, e.g. on a hemisphere. Thus, the effect of the ground has to be considered in the subsequent near-field to far-field transformation in order to obtain the far-field of the DUT above the ground plane. Assuming the metallic ground of the facility to be perfectly conducting, the ground effects are considered by introducing image sources below the ground plane in addition to the primary sources of the DUT above the ground plane. If coupling effects between the DUT and the ground plane are negligible, the primary sources correspond to the sources of the DUT in free-space. As a consequence, by separating the primary sources from the image sources, the free-space far-field of the DUT can be obtained from near-field measurements above ground. This means that measurement ranges with a ground plane can also be used to obtain free-space far-fields. In electromagnetic simulations, the primary sources can be placed in arbitrary environments, e.g. for communication channel evaluations. The quality of the primary sources extraction process mainly depends on the distance of the DUT sources from the ground plane as well as on the localization property of the employed equivalent sources which e.g. can be electric and/or magnetic surface currents or spherical modes. In this contribution, the numerical properties of the forward operator describing the relation between the DUT sources and the signal of the probe antenna above ground are analyzed in detail. The requirements for the unique determination of the primary sources from the near-field observations by inverting the operator are identified. Based on numerical investigations and real measurements obtained in a hemispherical near-field measurement facility, it will be shown that dependent on the ratio of the geometrical extensions of the DUT and its height above the ground as wells as on the strength of the coupling between the DUT and the ground, the free-space DUT far-field can be extracted with high quality.