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The planar wide-mesh scanning (PWMS) methodology is based on Non-redundant scanning schemes allowing faster measurements than classical Nyquist-compliant acquisitions based on denser, regular, equally spaced Near Field (NF) sampling. The methodology has no accuracy loss and has been validated at different bands and with different antennas [1]. The effectiveness of the PWMS technique has always been proven in error-free (or quasi-error-free) scenarios, assuming that possible errors introduced by the technique itself are independent of the typical source of measurement uncertainty. In this paper, we investigate for the first time the sensibility of the method wrt one of this error source included in the 18-terms lists [2], considered by the measurement community as an exhaustive list of the NF errors: X and Y probe positioning errors. Such errors are unknown and random and are associated to the mechanical vibrations and/or backlash of the system. The investigation has been done considering actual measurements of a multi-beam reflector antenna with approximately 35 dBi gain (MVG SR40 fed by two MVG SH5000 dual ridge horn). The AUT has been measured in planar geometry emulated by a 6-axis Staubli robot. The test was performed at 22-33 GHz. A set of measurements has been performed introducing a uniformly distributed random error in the range [0-1] mm, corresponding to ?/10 at 30 GHz. Errors are considered unknown. In the paper it will be shown that both in the classical and PWMS approaches the main beam is basically not affected by the introduced errors. The sidelobes are instead affected by such errors especially in the pattern cut where the beam is tilted. Such error levels obtained with the classical approach are comparable to those obtained with the PWMS approach, meaning that the latter is stable and against such type of perturbations.
NF-FF transformations have proven to be a convenient tool to accurately reconstruct the antenna pattern from NF measurements. In this framework, a very hot issue is the reduction of the time required to perform the measurements. To obtain a remarkable reduction of this time, nonredundant (NR) NF-FF transformations with planar spiral scannings have been developed in [1], by applying the NR representations of electromagnetic fields [2]. Optimal sampling interpolation (OSI) formulas have been used to efficiently reconstruct the massive NF data for the classical plane-rectangular (PR) NF-FF transformation from the NR spiral samples. The drastic measurement time-saving is due to the reduced number of needed NF samples acquired on fly, by adopting continuous and synchronized motions of the linear positioner of the probe and of the turntable of the AUT. However, such a time-saving is obtained at the expense of a nonuniform step of the spiral. Therefore, the linear positioner velocity is not constant, but must vary according to a not trivial law to trace the spiral, and this implies a complex control of the linear positioner. This work aims to develop an effective NF-FF transformation with planar spiral scanning for volumetric AUTs, wherein the spiral step is uniform and, hence, the linear positioner velocity becomes constant. To this end, the AUT is considered as enclosed in a sphere, the spiral is chosen in such a way that its step coincides with the sampling spacing needed to interpolate along a radial line according to the spatial band-limitation properties, and the NR representation along such a spiral is determined. Then, an OSI algorithm is developed to recover the NF data needed by the PR NF-FF transformation from the spiral samples. Numerical simulations assessing the accuracy of the developed NF-FF transformation will be shown.
Spherical near-field systems installed in shielded anechoic chambers are typically involved in modern automotive antenna measurements [1-3]. Such systems are often truncated at or close to the horizon to host the vehicle under test while limiting the size/cost of the chamber. The vehicle is usually placed on a metallic floor [4] or on a floor covered by absorbers [5]. The latter solution is intended to emulate a free space environment and is a key factor to perform accurate measurements down to 70 MHz. The availability of the free-space response also enables easy emulation of the car's behaviour over realistic grounds [6-7] while such emulations are more complex when a conductive ground is considered [8]. Conductive ground measurements also suffer from a strong interaction between the conductive floor and the measurement system and only in a limited number of situations such types of floor are a good approximation of realistic grounds (such as asphalts). However, the main advantage of conductive floor systems is the ease of accommodation of the vehicle under test which is simply parked in the center of the system. In absorber-based systems, instead, more time is generally needed to remove/place the absorber around the vehicle. Moreover, at low frequencies (70-400 MHz), large and bulky absorbers are normally used to ensure good reflectivity levels and the vehicle needs to be raised to avoid shadowing effect of absorbers. In this paper we investigate whether the measurement setup phase in absorber-based systems can be simplified by using smaller absorbers at low frequencies and/or not using them at all but considering conductive floors. The loss of accuracy in such scenarios will be studied considering a scaled vehicle and an implemented scaled automotive system where it is possible to access the full-spherical, real free-space scenario which is used as reference. The analysis is carried out considering (scaled) frequencies relevant to automotive applications in the 84-1500 MHz range. Two types of scaled absorbers, of different size and reflectivity, are considered to emulate the behaviour of the realistic full-scale 48-inch and 18-inch height absorbers. Measurements over metallic floor are included also in the analysis.
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.