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Analysis of Time and Direction of Arrival (TADOA) Data using Basis Pursuit in the AFRL One-RY Antenna Measurement Range
Brian Fischer, Ivan LaHaie, Michael Blischke, Brian Kent, Brittany Wells, James Stewart, October 2017
Time and Direction of Arrival (TADOA) analysis of field probe data has been an accepted method for characterizing stray signals in an antenna measurement range for many years ([1], [2]). Recent uncertainty investigations at the OneRY range have shown a need for increased resolution to isolate and characterize energy in TADOA images so that resources can be carefully applied to reduce the uncertainty from these stray signals. This is accomplished by modeling the TADAO image as the solution to a Basis Pursuit (BP) l1 minimization problem. This paper outlines the model development and shows concrete examples from OneRY field probe data where BP allows for the identification of stray energy which was previously difficult to find. We also show how the BP optimization context can be using to remove contamination from the data through the inclusion of additional basis functions ([3]). I.J. Gupta, E.K. Walton, W.D. Burnside, “Time and Direction of Arrival Estimation of Stray Signals in a RCS/Antenna Range,” Proc. of 18th Annual Meeting of the Antenna Measurement Techniques Association (AMTA '96), Seattle WA, September 30-October 3, 1996, pp. 411-416. I.J. Gupta, T.D. Moore, “Time Domain Processing of Range Probe Data for Stray Signal Analysis,” Proc. of 21st Annual Meeting of the Antenna Measurement Techniques Association (AMTA '99), Monterey Bay CA, October 4-8, 1999, pp. 213-218. B.E. Fischer, I.J. LaHaie, M.H. Hawks, T. Conn, “On the use of Basis Pursuit and a Forward Operator Dictionary to Separate Specific Background Types from Target RCS Data,” Proc. of 36th Annual Meeting of the Antenna Measurement Techniques Association (AMTA '14), Tucson AZ, October 12-17, 2014, pp. 85-90.
RCS Measurements and Imaging on Arrays of Retro-reflectors
Pax Wei, October 2017
For features of very weak scattering while masked by background and clutter, care must be taken in the measurement design as well as data processing, in order to extract the true RCS values. A good example of flush-mounted fasteners for a low-observable (LO) aircraft, arranged in an array, was reported by Lutz, Mensa, and Vaccaro [1]. In the Boeing 9-77 range, retro-reflectors (called retros) were routinely taped on a test-body for monitoring its 3-D locations and angles during measurements. Though the retro’s RCS may be several orders below that of a test-body, a challenge was to discover their exact values. In the millimeter wave range (MMWR), we measured 2-D arrays of retros arranged in both square and hexagonal lattices taped onto a flat metal surface pitched 20o down. RCS measurements were made as a function of frequency and aspect angle. From the 2-D FFT images, the nominal RCS for a retro in VV polarization was found to be -75 dBsm, independent of the geometry and number of retros even down to one unit-cell [2]. But for the HH polarization, there is no backscattering from such a flat metal surface. References [1]. J. Lutz, D. Mensa, and K. Vaccaro, "RCS measurements of LO features on a test body," Proc. 21st AMTA, pp. 320-325 (1999). [2]. P. S. P. Wei and J. P. Rupp, " RCS measurements on arrays of weak scatterers enhanced by diffraction," Proc. 26th AMTA, pp. 263-268 (2004). ---------------------------------------------- ** Sam Wei is at: 4123 - 205th Ave. SE, Sammamish, WA 98075-9600. Email:, Tel. (425) 392-0175
An RCS-based Wall-reflectivity Technique - The First On-site Test Results
Amin Enayati, Joachim Wesemael, October 2017
Among different measurement techniques for the wall reflectivity, an RCS_based technique has been implemented and test results are reported. For most of the anechoic chambers, the factory acceptance test and a quality-control check is sufficient for the customers to be sure that the absorbers used to line their chamber are good enough. In some cases, a quiet-zone reflectivity measurement will certify that the chamber yields the quietness as needed for the specific application of the customer. This last technique is mostly used in the far-filed ranges. However, in some anechoic chambers, e. g. some compact ranges, the customer wants to know the effect of the installation and the shipment on the final absorber installed in the room. That is why, they ask for a wall reflectivity measurement to see the reflectivity of the absorbers after being installed. The main problem to be solved when talking about wall reflectivity is the un-wanted clutter in the room which needs to be compensated for. Last year at AMTA 2016, we have introduced a clutter-removal technique to reduce the unwanted shattering levels. That was supported by some lab implementations and accordingly some limitations in the implementation. This paper, explains the result of the first practical on-site test done in an anechoic chamber. Many different points in the chamber have been tested and a detailed discussion of the results are brought to view.
Analysis of Near-Field RCS Behavior for mm-Wave Automotive Radar Testing Procedures
Domenic Belgiovane, Chi-Chih Chen, October 2017
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.
Additive manufacturing metallic sphere as a RCS measurement standard
Pierre Massaloux, October 2017
RCS measurements are usually performed in 3 steps in an anechoic chamber. First, the reflectivity of the target is measured. Then a reference measurement (generally without the target) is performed. Finally, a calibration standard of known RCS is used as a reference target. The main goal of the calibration phase is to transform raw measurements of reflectivity (S11 parameter in dB) into RCS (in dBsm) through the determination of the inverse transfer function of the entire RCS measurement layout. This calibration process indirectly converts the received electric field into a complex scattering coefficient. Moreover, it establishes a phase reference relatively to the rotation center of the target positioning system. The most frequently used standards are metallic spheres which have advantageous characteristics: monostatic RCS is well known by Mie-Series and independent of azimuth and elevation. However, manufacturing a perfect metallic lightweight sphere using conventional techniques include many issues that can generate defects in the spherical shape. The purpose of this paper is to evaluate the geometric and RCS performances of metallic spheres obtained from metal additive manufacturing systems using Selective Laser Melting (SLM) solutions. SLM is a fast prototyping technique designed to melt and fuse metallic powders together. On the one hand, these metallic spheres were checked by a 3D scanner in order to quantify the potential shape defects and on the other hand, RCS measurements were performed in an anechoic chamber. All these results will be presented in the final paper and compared with theoretical RCS data.
Advances in SAR-ISAR Blending
Christer Larsson, Johan Jersblad, October 2017
Radar signature measurements of targets with or without camouflage in different backgrounds using airborne SAR is complicated and expensive. Measurements at many orientations as well as illumination angles have to be performed for each target for completeness. A more efficient solution is to use ground based ISAR measurements of the desired targets and then blend these images into measured SAR scenes. We are developing a SAR-ISAR blending method where the target and background are modelled by point scatterer representations. This can be formulated as an inverse problem described by the equation Ax = y, (1) where A is a forward operator describing the model, x is the image and y is the measured RCS data. The point scatterer representations for the target and the SAR background are determined by solving (1). The main contribution of this paper is that we use a combination of L1 and L2 regularization methods to solve the inverse problem. The target measured by ISAR is sparse in the image domain and (1) is therefore solved efficiently using a L1 regularization method. However, the SAR background is not sparse in the image domain and (1) is therefore solved using a L2 regularization method. We use the following procedure: Define the operators A and At, where At is the conjugate transpose of A. The same operators are used for both the target and the background. Solve (1) using L1 regularization for the target measured using ISAR. Edit the target point scatterers so that only target related scatterers are included. Solve (1) using L2 regularization for the SAR background. Edit the background point scatterers by removing the shadowed region, alternatively attenuate if there is a camouflage net. Combine the edited point scatterers for the target and background and calculate the RCS for the combination. Add estimated system noise. Create a blended SAR-image. The method is demonstrated with ISAR measurements of a full-scale target, with and without camouflage, signature extraction and blending into a SAR background. We find that the method provides an efficient way of evaluating measured target signatures in measured backgrounds.
On the Disadvantages of Tilting the Receive End-Wall of a Compact Range for RCS Measurements
Vince Rodriguez, October 2017
Abstract— Tilting the receive end wall of a compact range anechoic chamber to improve Radar Cross-Section (RCS) measurements has been a tool of the trade used since the earliest days of anechoic chambers. A preliminary analysis using geometrical optics (GO) validates this technique. The GO approach however ignores the backscattering modes from the reflected waves from a field of absorber. In this paper, a series of numerical experiments are performed comparing a straight wall and a tilted wall to show the effects on both the quiet zone and the energy reflected back towards the source antenna. Two Absorber covered walls are simulated. Both walls are illuminated with a standard gain horn (SGH). The effects of a wall tilted back 20° are computed. The simulations are done for 72-inch long absorber for the frequency range covering from 500 MHz to 1 GHz. The ripple on a 10 ft (3.05 m) quiet zone (QZ) is measured for the vertical wall and the tilted wall. In addition to the QZ analysis a time-domain analysis is performed. The reflected pulse at the excitation antenna is compared for the two back wall configurations Results show that tilting the wall improves measurements at some frequencies but causes a higher return at other frequencies; indicating this method does not provide a broadband advantage. Keywords: Anechoic Chamber Design, Radar Cross Section Measurements, Geometrical Optics
Automating RCS Measurements for High Speed Production Line In-Process Verification
Roger Richardson, Brett Haisty, October 2017
In June of this year, DSC completed the installation of a turnkey RCS measurement system that is used for in-process verification (IPV) and final component validation using standard near field QC techniques in an echoic chamber. The delivered system included a radar, antennas, shroud, ogive pylon, foam column, elevators for each – column and pylon, automated pit covers, test bodies, target transport carts, and calibration targets. The system automatically loads test objects on the correct target support system, requiring no action by the operator to connect a target onto the azimuth over elevation “tophat” positioner – it is all automatic. The user interface is designed to be operated by production line workers, greatly reducing the need for experienced RCS test engineers. Simple pass/fail indicators are shown to the test technicians, while a full detailed data set is stored for engineering review and analysis. A wall display guides users through a test sequence for target handling and starting the radar. Radar data collection of all azimuth and elevation angles and target motion are initiated from a single button push. This is followed by all data processing necessary to conduct the ATP on the parts providing a pass/fail report on dozens of parameters. The application of production line quality automation to RCS measurements improves the repeatability of the measurements, greatly reduces both measurement time as well as overhead time, and allows systems operators to become more interchangeable. This highly successful project, which was completed on-time and on-budget, will be discussed. This discussion will include radar performance, antenna and shroud design, target handling, data processing and analysis software, and the control system that automates all the functions that are required for RCS measurements.
Geometric Effects on Radar Echoes from a Corner Reflector
P S P Wei, November 2018
Radar data on the complete polarimetric responses from a 4" dihedral corner reflector from 4 to 18 GHz have been collected and studied. As a function of the azimuth, the vertically suspended object may present itself to the radar as a dihedral, a flat plate, an edge, a wedge, or combinations of these. A two-dimensional method-of-moment (2-D MOM) code is used to model the perfectly electrical conducting (PEC) body, which allows us to closely simulate the radar responses and to provide insight for the data interpretation. Of particular interest are the frequency and angular dependences of the responses which yield information about the downrange separation of the dominant scattering centers, as well as their respective odd-or even-bounce nature. Use of the corner reflector as a calibration target is discussed.
Evaluation of the Monostatic-Bistatic theorem applied to the radar signature of aerial platforms in low frequency
J C Castelli, S Langlet, November 2018
In this paper, we explore the capabilities of the Monostatic-Bistatic Theorem (MBT) applied to Radar Cross Section (RCS) in low frequency. Originally, the validity of this theorem has been shown in high frequency for targets whose RCS is produced by elementary interactions (specular reflection in particular). We are interested in aerial platforms and in particular some Low Observable targets that have relatively "pure" geometries limiting the presence of complex interactions. Several variants of the MBT from the field of electromagnetism [1][2][3] and acoustics [4] are used. Their performances are compared from data obtained from a MoM method that is recognized to produce accurate scattering data. To highlight the discrepancies produced by the different variants, we use both a metric to compare the quality of the bistatic holograms obtained and also radar imaging which allows locating the areas of the target where the echoes are not correctly restored.
Conex Antenna, Radar, and Measurement Equipment Lab
Gregory Kiesel, Daniel Dykes, Eric Brown, Edward Garcia Iii, Ryan Buchanan, Tim Conn, November 2018
The Conex Antenna, Radar, and Measurement Equipment Lab (CARAMEL) is a ten-element VHF antenna array that operates from 30 MHz-120 MHz with an attached lab space. This array was developed for use in low frequency Radar Cross Section (RCS) measurements. The antenna elements support both vertical and horizontal polarizations. The antenna was designed using a genetic algorithm, employing the fragmented aperture technique; measured and modeled data will be presented. The attached lab space is air conditioned and provisioned for rack mounted equipment. The structure uses a modified 20' Conex shipping container where an entire sidewall has been replaced with a reinforced composite radome for the antennas. The overall mechanical frame design included a Finite Element Analysis to ensure structural integrity. The system is intended for long-term standalone use as an outdoor measurement radar system but can be moved using standard shipping container methods. The structure was shipped using a standard cargo carrier from Atlanta, Georgia to White Sands, New Mexico.
Validation of Additive Manufacturing for Broadband Choked Horns at X/Ku Band by Extensive Antenna Measurements
A Giacomini, R Morbidini, V Schirosi, F Saccardi, L J Foged, B Jun Gerg, D Melachrinos, M Boumans, November 2018
Additive manufacturing has become a popular alternative to traditional CAM techniques, as it has reached a suitable maturity and accuracy for microwave applications. The main advantage of the additive technologies is that the manufacturing can be performed directly from the 3D CAD model, available from the numerical simulation of the antenna, without significant modifications. This is a highly desirable feature, in particular for time and cost critical applications such as prototyping and manufacturing of small quantities of antennas. Different 3D-printing/additive manufacturing technologies are available in industry today. The purpose of the paper is an investigation on the accuracy and repeatability of the Selective Laser Melting (SLM) manufacturing technique applied to the construction of a batch of 15 broad band fully metallic chocked horns, operating at X/Ku band, manufactured in parallel. Manufacturing accuracy and repeatability has been evaluated using RF parameters as performance indicators comparing measured data and high accuracy simulations. The radiation patterns have been correlated to the numerical reference using the Equivalent Noise Level, while manufacturing repeatability is quantified on input matching by defining an interference level. These indicators have also been compared to state-of-the-art values commonly found for traditional manufacturing.
Modeling of Tapered Anechoic Chambers
Zubiao Xiong, Zhong Chen, November 2018
A hybrid method that combines the finite element method (FEM), the Floquet mode analysis and the shooting and bouncing ray method (SBR) is presented to solve the quiet-zone field in large tapered anechoic chambers. In the method, the field equivalence principle is employed to replace the throat of the tapered chamber by a set of equivalent electric and magnetic currents. The Floquet mode analysis is employed to approximate the rest of the absorber lined walls by virtual surfaces with equivalent reflection coefficients. The total quiet-zone field then becomes the superposition of the field radiated by the equivalent currents, and the field scattered by the virtual reflective surfaces. The scattered field is calculated from the SBR method. The required equivalent currents of the throat and the reflection coefficients of absorber array walls are computed with the use of the FEM, which allows the considerations of the complex structure and near-field interaction. Numerical examples are presented to demonstrate the feasibility of the proposed method.
Measurements of the dynamic pattern of an electronically steerable phased antenna array with circular polarization in Ka-band
Matthias Tebbe, Georg Strauss, November 2018
This paper presents two methods for measuring dynamic antenna patterns of phased arrays in a compensated compact range. The first method uses the turntable of the compact range to counter steer the antenna beam. The dynamic pattern is created by measuring single points of the pattern over time. This method is successfully tested, and the measurement results show the effect of phase jumps during the steering process. The second method extends the range of application to fast steering phased arrays by decoupling the antenna scan angle and the azimuth angle of the turntable.
2D RCS Prediction from Multistatic Near-Field Measurements on a Plane by Single-Cut Near-Field Far-Field Transformation and Plane-Wave Synthesis
Shuntaro Omi, Michitaka Ameya, Masanobu Hirose, Satoru Kurokawa, October 2019
A near-field far-field transformation (NFFFT) technique with a plane-wave synthesis is presented for predicting two-dimensional (2D) radar cross sections (RCS) from multistatic near-field (NF) measurements. The NFFFT predicts the FF of the OUT illuminated by each single source, then the plane-wave synthesis predicts the FF of the OUT each illuminated by each plane-wave by synthesizing the FFs given in the NFFFT step. The both steps are performed in the similar computational procedure based on a single-cut NFFFT technique that has been proposed previously. The method is performed at low cost computation because the NF and source positions are required only on a single cut plane. The formulation and validation of the method is presented.
Measurements of Non-Metallic Targets for the Austin RCS Benchmark Suite
Jon T Kelley, Ali E Yilmaz, David A Chamulak, Clifton C Courtney, October 2019
A simulation-supported measurement campaign was conducted to collect monostatic radar cross section (RCS) data as part of a larger effort to establish the Austin RCS Benchmark Suite, a publicly available benchmark suite for quantifying the performance of RCS simulations. In order to demonstrate the impact of materials on RCS simulation and measurement, various mixed-material targets were built and measured. The results are reported for three targets: (i) Solid Resin Almond: an almond-shaped low-loss homogeneous target with the characteristic length of ~10-in. (ii) Open Tail-Coated Almond: the surface of the solid resin almond's tail portion was coated with a highly conductive silver, effectively forming a resin-filled open cavity with metallic walls. (iii) Closed Tail-Coated Almond: the resin almond was manufactured in two pieces, the tail piece was coated completely with silver coating (creating a closed metallic surface), and the two pieces were joined. The measured material properties of the resin are reported; the RCS measurement setup, data collection, and post processing are detailed; and the uncertainty in measured data is quantified with the help of simulations.
Personal Near-field System
Dan Slater, October 2019
In 1987 the author built the world's first Personal Near-field antenna measurement System (PNS). This led to the formation of Nearfield Systems Inc. (NSI) a company that became a major manufacturer of commercial near-field antenna measurement systems. After leaving NSI in 2015 several new personal antenna measurement tools were built including a modern updated PNS. The new PNS consists of a portable XY scanner, a hand held microwave analyzer and a laptop computer running custom software. The PNS was then further generalized into a modular electromagnetic field imaging tool called "Radio Camera". The Radio Camera measures electromagnetic fields as a n-dimensional function of swept independent parameters. The multidimensional data sets are processed with geometric and spectral transformations and then visualized. This paper provides an overview of the new PNS and Radio Camera, discusses operational considerations, and compares it with the technology of the original 1987 PNS. Today it is practical for companies, schools and individuals to build low-cost personal antenna measurement systems that are fully capable of meeting modern industry measurement standards. These systems can be further enhanced to explore and visualize electromagnetic fields in new and interesting ways.
Indoor 3D Spherical Near Field RCS Measurement Facility: A new high resolution method for 3D RCS Imaging
Pierre Massaloux, Thomas Benoudiba-Campanini, Pierre Minvielle, Jean-François Giovannelli, October 2019
Indoor RCS measurement facilities are usually dedicated to the characterization of only one azimuth cut and one elevation cut of the full spherical RCS target pattern. In order to perform more complete characterizations, a spherical experimental layout has been developed at CEA for indoor Near Field monostatic RCS assessment [3]. This experimental layout is composed of a 4 meters radius motorized rotating arch (horizontal axis) holding the measurement antennas while the target is located on a polystyrene mast mounted on a rotating positioning system (vertical axis). The combination of the two rotation capabilities allows full 3D near field monostatic RCS characterization. 3D imaging is a suitable tool to accurately locate and characterize in 3D the main contributors to the RCS. However, this is a non-invertible Fourier synthesis problem because the number of unknowns is larger than the number of data. Conventional methods such as the Polar Format Algorithm (PFA), which consists of data reformatting including zero-padding followed by an inverse fast Fourier transform, provide results of limited quality. We propose a new high resolution method, named SPRITE (for SParse Radar Imaging TEchnique), which considerably increases the quality of the estimated RCS maps. This specific 3D radar imaging method was developed and applied to the fast 3D spherical near field scans. In this paper, this algorithm is tested on measured data from a metallic target, called Mx-14. It is a fully metallic shape of a 2m long missile-like target. This object, composed of several elements is completely versatile, allowing any change in its size, the presence or not of the front and / or rear fins, and the presence or not of mechanical defects, … Results are analyzed and compared in order to study the 3D radar imaging technique performances.
Bandwidth response of a reflectarray antenna working as a Compact Antenna Test Range probe
A F Vaquero, M Arrebola, M R Pino, October 2019
A reflectarray antenna working at 28 GHz is proposed to replace the reflector antenna of a Compact Antenna Test Range (CATR) system. As a first approach, the quiet zone obtained using a far-field collimated reflectarray is analysed. Due to the size of this area is not large enough, the generalized Intersection Approach is employed to carry out an optimization of the near-field for both phase and amplitude in order to maximize the size of the quiet zone at one plane. Simulations are compared for the near-field before and after the optimization process, showing an important enhancement of the size of the quiet zone, especially in the main cuts. From the obtained phase distribution a design is carried out. The unit cell chosen is based on a two-layer stacked patch, having good agreement between optimization and design results. Finally, the bandwidth response of the designed reflectarray is analysed, in order to assess its performances as probe in a CATR system.
Measurements on extended objects for radar field probes
P S P Wei, October 2019
An extended long object usually gives rise to a bright reflection (a glint) when viewed near its surface normal. To take advantage of this phenomenon and as a new concept, a discrete Fourier transform (DFT) on the RCS measurements, taken within a small angular range of broadside, would yield a spectrum of incident wave distribution along that object; provided that the scattering is uniform per unit length, such as from a long cylinder [1, 2]. In this report, we examine the DFT spectra obtained from three horizontal long objects of different lengths (each of 60, 20, and 8 feet). Aside from the end effects, the DFT spectra looked similar and promising as an alternative to the conventional field probes by translating a sphere across a horizontal path. Keywords: RCS measurements, compact range, field probes, extended long objects 1. The Boeing 9-77 compact range The Boeing 9-77 indoor compact range was constructed in 1988 based on the largest Harris model 1640. Figure 1 is a schematic view of the chamber, which is of the Cassigranian configuration with dual-reflectors. The relative position of the main reflector and the upper turntable (UTT) are as shown. The inside dimensions of the chamber are 216-ft long, by 80-ft high, and 110-ft wide. For convenience, we define a set of Cartesian coordinates (x: pointing out of the paper, y: pointing up, z: pointing down-range), with the origin at the center of the quiet zone (QZ). The QZ was designed as an ellipsoidal volume of length 50-ft along z, height 28-ft along y, and width 40-ft along x. The back wall is located at z = 75 ft, whereas the center of the roll-edged main reflector (tilted at 25 o from vertical) is at z =-110 ft. It is estimated that the design approach controls the energy by focusing 98% of it inside the QZ for target measurements. The residual field spreading out from the main reflector was attenuated by various absorbers arranged in arrays and covering the chamber walls.-, Tel. (425) 392-0175 2. Anechoic chamber In order to provide a quiet environment for RCS measurements, the inside surfaces of an anechoic chamber are typically shielded by various pyramidal and wedged-shaped absorbers, which afford good attenuation at near-normal incidence for frequencies higher than ~2 GHz. At low frequencies and oblique angles [3], however, Figure 1. A schematic view of the Boeing 9-77 compact range with dimensions as noted. insufficient attenuation of the radar waves by the absorbers may give rise to appreciable backgrounds. Figure 2 shows a panorama view inside the compact range, as viewed from the lower rear toward the main reflector and the UTT. With the exception of the UTT, all other absorbers are non-moving or stationary. A ring of lights on the floor shows the rim around the lower turntable (LTT), prior to the installation of absorbers. In order to minimize the target-wall interactions, the surfaces facing the QZ from the ceiling, floor, and two sidewalls are covered with the Rantec EHP-26 type of special pyramidal absorbers.

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