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Near Field
Nearfield Antenna Measurements over Seawater  Challenges and Prospects
The question of how to perform a nearfield antenna measurement in the presence of the airsea interface is one that has been raised previously by the author[1]. When discussing spherical near field measurements various approaches have been proposed for addressing this problem, that are also applicable to measurements taken over a conducting ground plane. In this paper we shall discuss some of the practical challenges involved in data collection and measurement methods when performing this type of measurement. Examples shall be taken from both spherical nearfield measurements of simple sources along with singlepoint athorizon measurements to examine the challenges associated with these approaches. A notional approach for measuring realized power gain at the horizon will also be discussed.
Polyhedral Sampling Structures for Phaseless Spherical NearField Antenna Measurements
In conventional Spherical NearField (SNF) antenna measurements, both amplitude and phase are necessary to obtain the Far Field (FF) of the Antenna Under Test (AUT) from the NearField (NF) measurements. However, phase measurements imply the use of expensive equipment, e.g., network analyzer, and rely on the assumption of having access to the reference phase, which is, for example, not the case in Over The Air (OTA) measurement scenarios. For these reasons, phaseless approaches gain attention and different methods have been investigated such as twosphere techniques, indirect holography, or the use of different probes. Recent research on twosphere techniques introduces algorithms originally developed for solving the socalled phase retrieval problem like PhaseLift or WirtingerFlow. Applied to SNF, the phase retrieval problem corresponds to obtaining the phase of the Spherical Mode Coefficients (SMCs) from amplitude NF measurements only. It has been shown that WirtingerFlow benefits from taking measurements over different structures, decreasing the redundancy. First investigations examined the combination of two spheres resp. a sphere and a plane and showed better reconstruction of the FF with the second combination. Furthermore, it has been shown that increasing the distance between both structures improves the reconstruction of the FF. Note that so far investigations have been based on the plane wave expansion.
We currently deepen the knowledge presented above in a framework solely based on the spherical wave expansion. From a mathematical point of view, planes can be seen as spheres of infinite radius, i.e., a plane combined with a sphere may be interpreted as a special case of combining two spheres. This interpretation goes hand in hand with the observation that an increased radius difference between both spheres leads to better reconstruction performance. Consequently, we analyze different polyhedral sampling structures composed of planes (such as tetrahedrons or cubes), mimicking several spheres of infinite radius in different spatial directions. For the mathematical analysis of nonspherical structures in the basis of spherical waves, pointwise probe correction is used. First experiments show a better reconstruction of the FF compared to the standard twospheres/sphereplane sampling.
Measuring G/T with a Spherical NearField Antenna Measurement System via the CWAmbient Technique
In modern systems where RF front ends are tightly integrated, the parameters of passive aperture gain and active electronics noise figure become difficult to obtain, and, in many cases, impossible to measure directly. Instead, the parameter referred to as Gain over Noise Temperature, or G/T, becomes the performance metric of interest. Recently, the antenna measurement community has seen an increased demand to use nearfield measurement systems for determining G/T values. Papers presented at AMTA over the past few years have shown that it is possible to determine G/T values using measurements taken in planar nearfield antenna ranges. The CWAmbient technique was one of the techniques proposed for computing G/T values by utilizing planar nearfield measurements [1,2].
In this paper, we show how the CWAmbient technique can also be applied to calculate G/T values in spherical nearfield antenna measurement systems. This paper provides a brief summary of the CWAmbient technique, and then presents the procedure and equations required for computing G/T using a spherical nearfield system.
To validate the recommended procedure, we compare predicted and measured G/T values for a separable unit under test (UUT). Since the passive aperture for this UUT is separable from the backend active electronics, we measure the aperture gain of the UUT and the noise figure of the backend electronics individually, and then compute the composite G/T value for this assembly. We then compare these composite values against G/T measurements from a spherical nearfield antenna measurement system. We summarize these comparisons and provide conclusions regarding the validity of using a spherical nearfield system to measure G/T.
Reduced Azimuthal Sampling for Spherical NearField Measurements
This paper investigates on the use of undersampling over the azimuthal dimension to reduce measurement time on spherical nearfield scanning. This means that the number of angular phi samples is reduced, which allows to reduce the number of positioner steps, obtaining measurement time savings virtually proportional to the number of samples reduction. Of course this undersampling introduces an error, which can be interpreted as an aliasing term over the retrieved Spherical Wave Expansion of the Antenna Under Test (AUT). The axial symmetry of the vast majority of antennas allows the application of significant undersampling ratios with little aliasing errors. However, this information is not a priori known due to the lack of a reference AUT radiation pattern, or in the case of malfunctioning antennas with degraded symmetry.
Here we proposed a measurement procedure for the exploitation of the AUT axial symmetry. The procedure consists on an iterative AUT measurement with increasing number of azimuthal cuts. As the number of cuts increases, the aliasing error decreases, thus obtaining the final radiation pattern with a lower uncertainty. We will introduce an aliasing error estimator, which estimates the error caused by the undersampling without any a priori knowledge of the AUT. This estimator can be used as a stopping criterion of the iterative measurement procedure when the desired accuracy is achieved.
The proposed technique will be demonstrated using different antennas, showing considerable reductions in measurement time with low errors in the transformed farfield pattern, and with the guarantee that the error is below a given threshold thanks to the derived estimator.
Nearfield testing with a 8.9x1.6 m2 planar scanner at Christiaan Huygens Laboratory (CHL)
A nearfield scanner has been upgraded, maintaining mechanical hardware more than 65 years old and extending it with suitable computer control to enable an 8.9x1.6m^2 scanplane. Already in 1957 Xband phase accuracies within 3 degrees were reported (ref.1). The facility is computer controlled, with servo's to enable position and polarisation control and a Rohde and Schwartz network analyser in the loop. It is positioned in an area near the main workshop and runs proprietary software for control, acquisition and transformation. An old satellite antenna has been aligned as Antenna Under Test (AUT) and measured near 12 GHz. It was measured before as reported in (ref.2). The antenna is an engineering model of an antenna used on the OTS satellite in mid 80's. It has a few properties which are worthwhile to use for inspection, to enable to get insight into scanner properties and transformation results. Deviation between electrical and mechanical axis, low cross polarisation, orthogonal channels and specific input impedance can be mentioned as points to verify and to control with verification measurements exploiting symmetries and fliptests, rather than ticking off in an 18term error budget usually adopted. Direct gain measurements have been established. The probe can be selected, either an openended waveguide or a circular waveguide with annular corrugation as probe for instance. It involves related discussion of probe correction.
The first results show acceptable information for the facility, with initial comparison to previous results for pattern and absolute gain. It has allowed to survey alignment, assess scanner control properties and assess microwave component properties  with interest into direct gain measurements.
A short historical description for the facility (ref.1) and antenna precedes a main discussion of the followed procedures and obtained results for the AUT with related discussion.
Definition, Implementation, and Evaluation of a Novel SpiralSampling Technique
Building on the theory of spiral nearfield acquisitions, the authors present a novel spiral acquisition implemented in a spherical nearfield (SNF) chamber for a large automotive application. This new spiral permits the relaxation of certain restrictions associated with the standard spiral. Specifically, it allows us to eliminate extra or redundant rings beyond the poles, allows for greater control of the angular velocity ratio (i.e. gear ratio) between the theta and phi physical positioning axes, and does not require that the theta axis retrace between acquisitions.
In this paper, we describe the new spiral?s motivations, implementation, advantages, and measurement results. We first discuss the new spiral sampling, its mathematical definition, and its comparison to a standard spiral. Next, we describe the practical considerations and implementation of the coordinated motion between theta and phi for spiral sampling over a spherical surface. Next, we present the results showing good pattern agreement between conventional SNF and the new spiral method. We also discuss the reductions in nearfield acquisition time and total test time that were achieved using the new spiral.
Adaptive Sampling for Compressed Spherical NearField Measurements
One of the main disadvantages of Spherical NearField (SNF) measurements is their acquisition time. This is due to the need of sampling a whole sphere around the Antenna Under Test (AUT) to perform the NearFieldtoFarField Transformation (NFFFT). A step of the NFFFT is to decompose the measured signal in each one of the spherical waves it consists of, thus retrieving the Spherical Mode Coefficients (SMCs) associated to the AUT. Under typical measurement conditions, the SMCs of most physical AUTs prove sparse, i.e., most of their terms are zero or neglectable. Using this assumption, the system of linear equations with the SMCs as variables can be solved with fewer equations, that is, fewer measurement samples. This is done by applying an l1minimization solver, following classical methodology from the field of compressed sensing. However, the location of the measurement points that generate nonredundant equations is not trivial. In typical compressedsensing applications, a random sampling matrix is taken. Since a random matrix is inefficient for the acquisition with mechanical rolloverazimuth positioner systems, a recent approach is to take an equidistant distribution of points on elevation and to calculate their corresponding pair on azimuth that delivers the minimum coherence of the sampling matrix. However, the number of sampling points M required for a successful reconstruction depends on the sparsity level of the SMCs of the unknown AUT, making its choice critical and based on a pessimistic approach.
A method for the adaptive choice of M is suggested. After the acquisition of a starting set of M_0 measurement points, chosen using phase transition diagrams, the SMCs are estimated online with few iterations of an l1minimization algorithm. Afterwards, further points are acquired, and the SMCs are estimated again using them. Following the evolution and the decrease of the variation between estimates, it is possible to truncate the measurement at a point where a successful reconstruction is guaranteed. The method for the construction of a minimumcoherent sampling matrix for adaptive acquisition and the truncation criteria for a specific accuracy are discussed with a focus onimplementation, and supported with numerical experiments, performed with measurementdata.
Revising the Theory and Practice of Electrical Alignment Procedures for Spherical Nearfield Antenna Measurement Facilities
The electrical alignment of the positioner of the Antenna Under Test (AUT) is an important issue to be accounted for before any antenna measurement can take place in a spherical nearfield measurement facility. This is because the spherical transmission formula requires the AUT to be scanned on the surface of a sphere. Typically, the tower has been aligned by optical means but, usually, it is necessary to translate it along some axis to place the AUT in the center of the measurement sphere. Furthermore, mounting the AUT can alter the alignment due to its gravitational load. Therefore, alignment of the tower after mounting the AUT is a critical step, which is accomplished with the socalled flip tests [1].
These flip tests, which can detect only the axis intersection and zero? errors of a roll over azimuth system, have been discussed in the past, for example [12], but not as extensively as their importance would require. Moreover, there were no analytical proofs provided for the error formulas given, which forces the interested researcher to derive them again in order to comprehend them and adapt them to his measurement facility.
This paper starts with a concise and thorough presentation of how the fliptests are performed in practice, as well as their theoretical justification.
In the second part, the paper presents a novel idea regarding the interdependence of the alignment errors. It has been observed experimentally that two linear coupled equations can model their behavior. Consequently, they can be fully corrected simultaneously with only two fliptests, without the need of correcting each one in small steps. Simulation tests were performed validating these results.
Finally, the paper concludes with addressing a few miscellaneous issues that are inevitably risen by the nature of this procedure, such as the effect of the antenna gain, the positioning of the probe and the distance between the AUT and the probe.
Sensitivity analysis of Fast NonRedundant NF Sampling Methodologies with Probe Positioning errors
The planar widemesh scanning (PWMS) methodology is based on Nonredundant scanning schemes allowing faster measurements than classical Nyquistcompliant 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 errorfree (or quasierrorfree) 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 18terms 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 multibeam 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 6axis Staubli robot. The test was performed at 2233 GHz. A set of measurements has been performed introducing a uniformly distributed random error in the range [01] 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.
NFFF TRANSFORMATION WITH UNIFORM PLANAR SPIRAL SCANNING FOR VOLUMETRIC ANTENNAS
NFFF 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) NFFF 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 planerectangular (PR) NFFF transformation from the NR spiral samples. The drastic measurement timesaving 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 timesaving 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 NFFF 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 bandlimitation 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 NFFF transformation from the spiral samples. Numerical simulations assessing the accuracy of the developed NFFF transformation will be shown.
Experimental Investigation of Different Floor Materials in Automotive Near Field Antenna Testing
Spherical nearfield systems installed in shielded anechoic chambers are typically involved in modern automotive antenna measurements [13]. 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 freespace response also enables easy emulation of the car's behaviour over realistic grounds [67] 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 absorberbased systems, instead, more time is generally needed to remove/place the absorber around the vehicle. Moreover, at low frequencies (70400 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 absorberbased 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 fullspherical, real freespace scenario which is used as reference. The analysis is carried out considering (scaled) frequencies relevant to automotive applications in the 841500 MHz range. Two types of scaled absorbers, of different size and reflectivity, are considered to emulate the behaviour of the realistic fullscale 48inch and 18inch height absorbers. Measurements over metallic floor are included also in the analysis.
Near Field Measurements with Radically reduced Sampling requirement through Numerically defined expansion Functions
We present an antenna measurement methodology requiring a radically lower number of field samples than the standard Nyquistbased 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 Nyquistcomplaint 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 matrixvector 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 multifeed configurations (using several SH5000) at 18 and 30 GHz. Patterns obtained with downsampled fast approach are compared to standard measurements. Downsampling factors up to 8 are achieved maintaining very high correlation levels with standard techniques.
Using HighAccuracy Swing Arm Gantry Positioners in Spherical NearField Automotive Measurement Systems
Spherical NearField (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 8meter 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.
Correction of Nonideal Probe Orientations for Spherical NearField Antenna Measurements
Positioning in nearfield 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 nearfield to farfield 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 nonideal 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 nonideal probe orientations has been neglected due to the assumption that the probe receiving pattern is broad.
In this paper, nonideal probe orientations will be investigated and a spherical wave expansion procedure which corrects nonideal 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 higherorder 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 Fourierbased 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.
Determination of the FarField Radiation Pattern of a Vehicle Mounted VHF Antenna From a Set of Sparse NearField Measurements
The paper summarizes the performance of a new nearfield to farfield (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 nearfield 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 NearField to FarField Transformation, Electromagnetic Inverse Problems.
Radiation Center Estimation from NearField Data Using a Direct and an Iterative Approach
Spherical NearField (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 farfield case, analyzing its error at different nearfield 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 nearfield to farfield 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.
Nearfield Antenna Measurements over Seawater – Some Preliminary Thoughts
The principles of nearfield 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 nearfield 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 nearfield 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 airsea 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 nearfield 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.
Nearfield Antenna Measurements over Seawater – Some Preliminary Thoughts
The principles of nearfield 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 nearfield 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 nearfield 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 airsea 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 nearfield 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.
Cost Functions in NearField Spherical Scanning Data Processing Algorithms
Spherical wave coefficients are chosen to minimize a cost function that is a norm of the residual of the fit. For example, in standard orthogonalitybased 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, “NearField 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, “Nearfield, sphericalscanning 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, “Nearfield antenna measurements with nonideal measurement locations,”IEEE Antennas and Propagat., vol. 46, pp. 716 – 722, May 1998.
Assessment of a 3DPrinted Aluminum Corrugated Feed Horn at 118.7503 GHz
We investigate allmetal 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 farfield pattern results obtained with the NIST robotic antenna range CROMMA are presented. Farfield pattern data were obtained from a spherical nearfield scan over the front hemisphere of the feed horn. The quasiGaussian 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 nearfield measurements using the robotic arm in CROMMA. The consistency in parameters between extrapolation and nearfield measurements allowed the extrapolation data to be used insitu as a diagnostic. Optimal nearfield scan radius was determined by observing the reflection coefficient S11 during the extrapolation measurement. The feed horntoprobe antenna separation for which S11 was reduced to 0.1 dB peaktopeak was taken as the optimal nearfield 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.

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