Localization and litigation of radio frequency interference for interferometric arrays

Thesis (PhD)--Stellenbosch University, 2018.ENGLISH ABSTRACT: Radio telescopes have increased exponentially in sensitivity ever since the first single dish radio telescopes were built in the 1930's. This trend continues with the development of next generation telescopes such as the Square Kilometre Array (SKA). Parallel to the development of radio telescopes, has been the rapid expansion of telecommunication technologies. Consequently, radio telescopes are becoming more sensitive in an environment with ever increasing radio frequency interference (RFI). The ideal solution to RFI that is detected by a radio telescope is to locate its source and then have it removed. Removal of the source is usually only possible if it is occurring in a protected band or the radio telescope is in a radio quiet zone. Unfortunately, most of the radio spectrum has been allocated to active communication services and not all radio telescopes are in radio quiet zones. The alternative is to mitigate its effect using methods such as spatial RFI mitigation. The contributions of this PhD dissertation are twofold: firstly, a source localization algorithm that takes into account the constraints and advantages of the arrays used for radio astronomy has been developed; and secondly, existing spatial RFI mitigation techniques have been adapted to take into account the bandwidth of the RFI signals. The computationally efficient localization algorithm that was developed is best suited for interferometric arrays with low array beam sidelobes. Two variants of the algorithm were developed, one that works for sources in the near-field and the other for far-field sources. In the near-field, the computational complexity of the algorithm is linear with search grid size compared to cubic scaling of the state-of-the-art 3-D MUSIC method. The trade-off is that the proposed algorithm requires a once-off a priori calculation and storing of weighting matrices. In an experiment using a station of the Low Frequency Array (LOFAR) a hexacopter was flown around the array, at a mean radial distance of 190 m, broadcasting a signal. The mean error in distance between the estimated position of the hexacopter and the GPS position of the hexacopter was 2 m for a wavelength of 6.7 m. The non-narrowband RFI mitigation method developed consists of a second order filter that is used to mitigate powerful RFI with bandwidth sufficient to cause aberrations that are below the noise, but with power that competes with the astronomical sources. The second order filter consists of a first order subspace subtraction filter combined with a flat frequency response model for the RFI source. Taking into account mutual coupling as well as a calibration step to account for unknown complex gains, the algorithm was found to process approximately 1.6 times more bandwidth than using just a first order subspace subtraction filter.AFRIKAANSE OPSOMMING: Sedert die eerste enkelskottel radioteleskope in die 1930's gebou is, het die sensitiwiteit van radioteleskope eksponensieël toegeneem. Hierdie tendens gaan voort met die ontwikkeling van volgende generasie teleskope, soos byvoorbeeld die Square Kilometer Array (SKA). In parallel met die ontwikkeling van radioteleskope, het telekommunikasietegnologieë ook vinnig uitgebrei. Gevolglik word radioteleskope meer sensitief in 'n omgewing met toenemende radiofrekwensie-inmenging (RFI). Die optimale oplossing vir RFI is om die bron daarvan op te spoor en te verwyder. Verwydering van die bron is gewoonlik net moontlik as dit teenwoording is in 'n beskermde band of as die radio teleskoop in 'n radio-stil gebied is. Ongelukkig is meeste van die radio spectrum toegeken aan kommunikasiedienste en nie alle radio teleskope is in radio-stil gebiede nie. Die alternatief om die effek daarvan te mitigeer deur middel van metodes soos ruimtelike RFI-mitigasie. Die bydraes van hierdie doktorale proefskrif is tweeledig: eerstens, die ontwikkeling van 'n bronlokaliseringsalgoritme wat die beperkings en voordele van die skikkings wat gebruik word vir radio astronomie in ag neem en tweedens, die aanpassing van bestaande ruimtelike RFI mitigeringstegnieke om die bandwydte van die RFI seine in ag te neem. Die berekeningsdoeltreffende lokaliseringsalgoritme wat ontwikkel is, is die beste geskik vir interferometriese skikkings met lae samestelling-bundel sylobbe. Twee weergawes van die algoritme is ontwikkel, die eerste hanteer bronne in die nabyveld en die ander hanteer vêrveld bronne. In die nabyveld is die berekeningskompleksiteit van die algoritme lineêr met soektogroostergrootte in vergelyking met die kubieke skalering van die 3-D MUSIC-metode. Die nadeel is dat die voorgestelde algoritme 'n eenmalige a priori berekening en stoor van gewigsmatrikse vereis. In 'n eksperiment by 'n stasie van die Low Frequency Array (LOFAR), het 'n heksakopter oor die skikking gevlieg met 'n gemiddelde radiale afstand van 190 m en 'n sein uitgesaai. Die gemiddelde fout in die afstand tussen die beraamde posisie van die heksakopter en die GPS-posisie van die heksakopter was 2 m vir 'n golflengte van 6.7 m. Die nie-smalband RFI mitigasie metode wat ontwikkel is, fasiliteer die de-finieering van 'n tweede-orde filter wat gebruik word om kragtige RFI met bandwydte verwante krag onder die geruis, maar met krag wat met die astronomiese bronne kompeteer, te mitigeer. Die tweede order filter bestaan uit 'n eerste orde subruimte verminderingsfilter gekombineer met 'n plat frekwensie responsmodel vir die RFI bron. Met inagneming van wedersydse koppeling asook 'n kalibrasie stap om vir onbekende komplekse antenna aanwinste voorsiening te maak, is gevind dat die algoritme ongeveer 1.6 meer bandwydte kan verwerk as 'n eerste orde subruimte verminderingsfiter

Microwave Radiometry at Frequencies From 500 to 1400 MHz: An Emerging Technology for Earth Observations

icrowave radiometry has provided valuable spaceborne observations of Earth’s geophysical properties for decades. The recent SMOS, Aquarius, and SMAP satellites have demonstrated the value of measurements at 1400 MHz for observ- ing surface soil moisture, sea surface salinity, sea ice thickness, soil freeze/thaw state, and other geophysical variables. However, the information obtained is limited by penetration through the subsur- face at 1400 MHz and by a reduced sensitivity to surface salinity in cold or wind-roughened waters. Recent airborne experiments have shown the potential of brightness temperature measurements from 500–1400 MHz to address these limitations by enabling sensing of soil moisture and sea ice thickness to greater depths, sensing of temperature deep within ice sheets, improved sensing of sea salinity in cold waters, and enhanced sensitivity to soil moisture under veg- etation canopies. However, the absence of significant spectrum re- served for passive microwave measurements in the 500–1400 MHz band requires both an opportunistic sensing strategy and systems for reducing the impact of radio-frequency interference. Here, we summarize the potential advantages and applications of 500–1400 MHz microwave radiometry for Earth observation and review recent experiments and demonstrations of these concepts. We also describe the remaining questions and challenges to be addressed in advancing to future spaceborne operation of this technology along with recommendations for future research activities

Advanced RFI detection, RFI excision, and spectrum sensing : algorithms and performance analyses

Because of intentional and unintentional man-made interference, radio frequency interference (RFI) is causing performance loss in various radio frequency operating systems such as microwave radiometry, radio astronomy, satellite communications, ultra-wideband communications, radar, and cognitive radio. To overcome the impact of RFI, a robust RFI detection coupled with an efficient RFI excision are, thus, needed. Amongst their limitations, the existing techniques tend to be computationally complex and render inefficient RFI excision. On the other hand, the state-of-the-art on cognitive radio (CR) encompasses numerous spectrum sensing techniques. However, most of the existing techniques either rely on the availability of the channel state information (CSI) or the primary signal characteristics. Motivated by the highlighted limitations, this Ph.D. dissertation presents research investigations and results grouped into three themes: advanced RFI detection, advanced RFI excision, and advanced spectrum sensing. Regarding advanced RFI detection, this dissertation presents five RFI detectors: a power detector (PD), an energy detector (ED), an eigenvalue detector (EvD), a matrix-based detector, and a tensor-based detector. First, a computationally simple PD is investigated to detect a brodband RFI. By assuming Nakagami-m fading channels, exact closed-form expressions for the probabilities of RFI detection and of false alarm are derived and validated via simulations. Simulations also demonstrate that PD outperforms kurtosis detector (KD). Second, an ED is investigated for RFI detection in wireless communication systems. Its average probability of RFI detection is studied and approximated, and asymptotic closed-form expressions are derived. Besides, an exact closed-form expression for its average probability of false alarm is derived. Monte-Carlo simulations validate the derived analytical expressions and corroborate that the investigated ED outperforms KD and a generalized likelihood ratio test (GLRT) detector. The performance of ED is also assessed using real-world RFI contaminated data. Third, a blind EvD is proposed for single-input multiple-output (SIMO) systems that may suffer from RFI. To characterize the performance of EvD, performance closed-form expressions valid for infinitely huge samples are derived and validated through simulations. Simulations also corroborate that EvD manifests, even under sample starved settings, a comparable detection performance with a GLRT detector fed with the knowledge of the signal of interest (SOI) channel and a matched subspace detector fed with the SOI and RFI channels. At last, for a robust detection of RFI received through a multi-path fading channel, this dissertation presents matrix-based and tensor-based multi-antenna RFI detectors while introducing a tensor-based hypothesis testing framework. To characterize the performance of these detectors, performance analyses have been pursued. Simulations assess the performance of the proposed detectors and validate the derived asymptotic characterizations. Concerning advanced RFI excision, this dissertation introduces a multi-linear algebra framework to the multi-interferer RFI (MI-RFI) excision research by proposing a multi-linear subspace estimation and projection (MLSEP) algorithm for SIMO systems. Having employed smoothed observation windows, a smoothed MLSEP (s-MLSEP) algorithm is also proposed. MLSEP and s-MLSEP require the knowledge of the number of interferers and their respective channel order. Accordingly, a novel smoothed matrix-based joint number of interferers and channel order enumerator is proposed. Performance analyses corroborate that both MLSEP and s-MLSEP can excise all interferers when the perturbations get infinitesimally small. For such perturbations, the analyses also attest that s-MLSEP exhibits a faster convergence to a zero excision error than MLSEP which, in turn, converges faster than a subspace projection algorithm. Despite its slight complexity, simulations and performance assessment on real-world data demonstrate that MLSEP outperforms projection-based RFI excision algorithms. Simulations also corroborate that s-MLSEP outperforms MLSEP as the smoothing factor gets smaller. With regard to advanced spectrum sensing, having been inspired by an F–test detector with a simple analytical false alarm threshold expression considered an alternative to the existing blind detectors, this dissertation presents and evaluates simple F–test based spectrum sensing techniques that do not require the knowledge of CSI for multi-antenna CRs. Exact and asymptotic analytical performance closed-form expressions are derived for the presented detectors. Simulations assess the performance of the presented detectors and validate the derived expressions. For an additive noise exhibiting the same variance across multiple-antenna frontends, simulations also corroborate that the presented detectors are constant false alarm rate detectors which are also robust against noise uncertainty

Characterising Spatial and Temporal Ionospheric Variability with a Network of Oblique Angle-of-arrival and Doppler Ionosondes

Ionospheric variability exists on a broad range of scales, and routinely impacts skywave propagation modes of high frequency radio waves, to the detriment of radar and communication systems. In order to better understand the electron density structures associated with such variability at mid-latitudes, a network of oblique angle-of-arrival (AoA) and Doppler ionosondes were installed in central and northern Australia as part of the ELOISE campaign in 2015. This thesis analyses observations from the ELOISE AoA ionosondes, with a focus on characterising the influence of medium- to large- scale gradients and signatures of travelling ionospheric disturbances (TIDs). Following an overview of the experiment, the design and calibration of the new ionosonde system is described. With multi-channel receivers connected to each element of two twin-arm arrays, a total of eleven AoA paths of between 900 and 2700 km were collected, including nine with interleaved Doppler measurements using a special channel scattering function (CSF) capability. On-board signal processing was developed to perform real-time clear channel evaluation and CSF scheduling, and generate the AoA ionograms and delay-Doppler images with fitted electron density profiles. In further offline analysis, peak detection and mode classification was carried out, to support reflection point mapping and tilt estimation. Significant testing and validation of the new ionosonde before and after the experiment revealed AoA uncertainties on the scale of 0.2–0.5° in bearing and 0.4–0.9° in elevation. Having identified a low-elevation bias, models of tropospheric refraction and antenna mutual coupling effects were considered as possible correction strategies, but ultimately an empirical approach based on aggregated ionospheric returns was implemented. Small-scale (intra-dwell) ionospheric variability also has the potential to compromise results, through unresolved multi-mode mixing, and this has been investigated using a combination of spatial and temporal variability metrics derived from the CSF data. The analysis of large quantities of F2 peak data shows persistent diurnal patterns in the oblique AoA observables that are also well-captured by a conventional data-assimilative ionospheric model, even without the benefit of AoA and Doppler inputs. Furthermore, Doppler measurements are reproduced remarkably well using just the midpoint fitted profiles. A statistical study has quantified the level of consistency between observations and model, to provide greater confidence in the results. Many of the geophysical features can be interpreted as ionospheric gradients, as evident in the tilt estimates, and horizontally moving structures such as TIDs, using a form of Doppler-based drift analysis. While signatures of TIDs vary considerably, two simple wave-like perturbation models have been evaluated to help classify quasi-periodic behaviour in the AoA observations, as well as understand the directional filtering effect imposed by the path geometry. In some cases, a set of TID parameters can be determined by eye, but in others automatic parameter inversion techniques may be more viable. Two such techniques were implemented but results using both real and synthetic data demonstrated some significant limitations. Finally, attempts to relate TID signatures across multiple paths shows promise, but there still appears to be a strong dependence on path geometry that is difficult to eliminate.Thesis (Ph.D.) -- University of Adelaide, School of Physical Sciences, 202

RFI Mitigation for VLBI and Arrays - Water Megamasers in Active Galaxies

This thesis studies the central parsec in active galaxies via spectral line observations of OH and water megamasers and millimeter-wave interferometry. The aims are four-fold: 1) measure the mass of the supermassive black hole in active galactic nuclei (AGN) through circumnuclear water maser observations, 2) measure the Hubble constant through circumnuclear water maser observations, 3) mitigate the radio frequency interference that degrades spectral line observations, and 4) probe the innermost regions of AGN by expanding a mm-wavelength interferometer. The current paradigm conjectures that AGN contain a supermassive black hole The high spatial resolution of very long baseline radio interferometry (VLBI) allows to track AGN-launched jets over pc to kilo-pc scales outside an AGN. Within AGN, water megamaser emission mapped by VLBI is an excellent tracer of the sub-pc structure, in particular of the accretion disk. Its rotation curve, traced by water masers, allows an accurate SMBH mass measurement, important for constraining the empirical relation between black hole mass and stellar velocity dispersion in the galactic bulge – current evidence suggest that this MBH–sigma -relation is not universal, indicating differences in SMBH feeding, accretion history and AGN evolution. Disk masers further yield accurate distances to nearby maser galaxies by an almost purely geometric means. This allows measuring the current rate of expansion of the Universe, described by the Hubble constant, H0, an important cosmological parameter. To constrain DE models the key goal of the Megamaser Cosmology Project (MCP; Braatz, NRAO) is to measure H0 to at least 3% precision. Relatively few (~5%) active galaxies have been detected in water masers. In this thesis I carried out a water maser survey in nearby galaxies, some with AGN, some also detected in the dissociation product of water, the neutral hydroxyl radical (OH). Four new water masers were detected, including OH-detected galaxies, such as NGC 4261 famous for its dusty torus. The MCP project by J. Braatz et al. conducts 22 GHz VLBI and single-dish observations of disk maser galaxies. I analyzed the data of three quite different maser galaxies with putative AGN (NGC 23, UGC 3193 and IC 2560). The maser data for NGC 23 suggest either an association with a possibly truncated low-luminosity jet, or exceptionally luminous nuclear /extranuclear star formation masers. The AGN disk water masers in UGC 3193 reveal a large accretion disk with two rings suggestive of a disrupted disk around a low central SMBH mass of about 0.6+-0.2 x 10^6 Msun The disk masers in IC 2560 on the other hand indicate a SMBH mass of 5.4^+0.9_-0.6 x 10^6 Msun, and undermassive in the common MBH-sigma -relation, consistent the trend seen in other water maser galaxies. The IC 2560 disk masers also allowed the Hubble constant to be measured, resulting in an H0 of 67.7^+11.6_-8:9 km/s/Mpc. Combined with recent MCP results (UGC 3789, NGC 6264) this yields a new maser-based Hubble constant of 68.4+-5.3 km/s/Mpc (8%). Spectral lines observations are often degraded by man-made radio frequency interference (RFI). Thus I also discuss two techniques for mitigating RFI. The first was implemented in a popular VLBI software correlator. I evaluate the theoretical and practical performance, also in a VLBI search for 1.6 GHz OH in tori of Cygnus A and NGC 1068. I find the mitigation method to be effective but limited in practice due to the particular software correlator architecture. The second method improves over two existing approaches for antenna arrays, including focal plane arrays. While current instrumentation did not allow an immediate application, e.g., in the maser survey, I find that the method shows great potential for future observations in presence of RFI. Lastly, our recent work on expanding a global sub-millimeter VLBI array has enabled extreme angular resolution, suffcient to resolve the SMBH/disk system and the jet launching region. I present the first 230 GHz VLBI observation of the core region of blazar 3C 279. The work allows extreme-resolution observations of, e.g., Sgr A* and the SMBHs in M87 that will lead to a better understanding of SMBH spin, accretion, and jet launching

Extended diffuse radio emission in galaxy clusters

Galaxy clusters are the most massive gravitationally bound systems in the universe which grow through mergers with other clusters, galaxy groups, and accretion of gas. The mergers generate shocks and turbulence in the intra-cluster medium (ICM). Along the shock edges, particles are accelerated to relativistic energies through multiple crossings at the shock front. The extended diffuse emission sources formed as a result are commonly classified as radio halos and radio relics. The precise nature and origin of the relativistic particles is nevertheless not well understood. We study the nature of the radio relic candidate in Abell 115. We obtain it's spectral properties using radio continuum observations at 150\,MHz with LOFAR, 610\,MHz with the GMRT, and 1.5\,GHz with the VLA. We confirm it's nature as a radio relic. Polarization analyses suggest that part of the large scale synchrotron source is embedded in a region of high ICM density. We show that the galaxy cluster A1430 hosts a two-component radio halo using observations at 150\,MHz with LOFAR. We obtain the spectral index of the radio halo and derive estimates of the radio power at 1.4 GHz. We also show that a part of the radio halo could be produced via turbulence and the rest lies in a region compressed by the merger via adiabatic compression. Using a 100-m single dish radio telescope, we observe the galaxy clusters PSZ1-G108, Abell 746, 0809+39, and Abell 1367. We detected the polarised flux at 4.85 GHz in all the sources that were previously labelled as radio relics. The radio spectra of the integreted emission below 4.85 GHz can be well fitted with a single power law for all the radio relics. Polarisation observations of radio synchrotron sources offer a method of measuring the strength and geometry of the shock front. The observations of the galaxy clusters PSZ1-G108, Abell 746, 0809+39, and Abell 1367 show that radio relics' spectral properties are well represented by a single power-law below 5GHz.Synchrotronstrahlungsquellen, die in bisher 100 verschmelzenden Galaxienhaufen beobachtet worden sind, werden als Radiorelikte und Radiohalos klassifiziert. Viele Details der Beschleunigung von Elektronen im Haufengas auf relativistische Energien und der Ursache der Magnetfelder in Galaxienhaufen sind noch unverstanden. In dieser Arbeit stellen wir Beobachtungen mehrerer verschmelzender Galaxienhaufen mit dem 100-m-Radioteleskop in Effelsberg bei 4,85 GHz, dem Very Large Array (VLA) bei 1,5 GHz, dem Giant Metrewave Telescope (GMRT) bei 610 MHz und dem Low Frequency Array (LOFAR) bei 150 MHz vor. Die Untersuchungen wurden mit Archivdaten des Röntgensatellits Chandra ergänzt. Ziel der Arbeit ist es, die Eigenschaften und den Ursprung solcher großräumiger Synchrotronemission in Galaxienhaufen besser zu verstehen. Wir bestätigen das Radiorelikt in Abell 115 anhand seiner Spektralindex- und Polarisationseigenschaften. Unsere Analyse weist darauf hin, dass dieses Radiorelikt durch eine nicht-axiale Verschmelzung erzeugt wurde und dass ein Teil des Radiorelikts in einer Region des Haufengases mit sehr geringer Dichte liegt. Wir zeigen auch zum ersten Mal, dass der Galaxienhaufen Abell 1430 einen Radiohalo mit mindestens zwei Komponenten beherbergt. Die Morphologie der Röntgenemission im Vergleich zur Radiohaloemission zeigt, dass die westliche Komponente des Radiohalos durch Turbulenz erzeugt werden kann. Die östliche Komponente befindet sich zwischen den Haufenzentren und könnte durch Kompression des Haufengases im Zuge der Verschmelzung des Galaxienhaufens erzeugt worden sein. Wir haben Polarisation in den Radiorelikten in PSZ1-G108, Abell 746, Abell 1367 und 0809+39 bei 4,85 GHz entdeckt. Die Spektren aller Radiorelikte unterhalb von 4,85 GHz zeigen ein Potenzgesetz. Unsere Polarisationsbeobachtungen erlauben auch die Messung der Stärke und Geometrie der für Radiorelikte mutmaßlich ursächlichen Stoßfronten

Elevation and Deformation Extraction from TomoSAR

3D SAR tomography (TomoSAR) and 4D SAR differential tomography (Diff-TomoSAR) exploit multi-baseline SAR data stacks to provide an essential innovation of SAR Interferometry for many applications, sensing complex scenes with multiple scatterers mapped into the same SAR pixel cell. However, these are still influenced by DEM uncertainty, temporal decorrelation, orbital, tropospheric and ionospheric phase distortion and height blurring. In this thesis, these techniques are explored. As part of this exploration, the systematic procedures for DEM generation, DEM quality assessment, DEM quality improvement and DEM applications are first studied. Besides, this thesis focuses on the whole cycle of systematic methods for 3D & 4D TomoSAR imaging for height and deformation retrieval, from the problem formation phase, through the development of methods to testing on real SAR data. After DEM generation introduction from spaceborne bistatic InSAR (TanDEM-X) and airborne photogrammetry (Bluesky), a new DEM co-registration method with line feature validation (river network line, ridgeline, valley line, crater boundary feature and so on) is developed and demonstrated to assist the study of a wide area DEM data quality. This DEM co-registration method aligns two DEMs irrespective of the linear distortion model, which improves the quality of DEM vertical comparison accuracy significantly and is suitable and helpful for DEM quality assessment. A systematic TomoSAR algorithm and method have been established, tested, analysed and demonstrated for various applications (urban buildings, bridges, dams) to achieve better 3D & 4D tomographic SAR imaging results. These include applying Cosmo-Skymed X band single-polarisation data over the Zipingpu dam, Dujiangyan, Sichuan, China, to map topography; and using ALOS L band data in the San Francisco Bay region to map urban building and bridge. A new ionospheric correction method based on the tile method employing IGS TEC data, a split-spectrum and an ionospheric model via least squares are developed to correct ionospheric distortion to improve the accuracy of 3D & 4D tomographic SAR imaging. Meanwhile, a pixel by pixel orbit baseline estimation method is developed to address the research gaps of baseline estimation for 3D & 4D spaceborne SAR tomography imaging. Moreover, a SAR tomography imaging algorithm and a differential tomography four-dimensional SAR imaging algorithm based on compressive sensing, SAR interferometry phase (InSAR) calibration reference to DEM with DEM error correction, a new phase error calibration and compensation algorithm, based on PS, SVD, PGA, weighted least squares and minimum entropy, are developed to obtain accurate 3D & 4D tomographic SAR imaging results. The new baseline estimation method and consequent TomoSAR processing results showed that an accurate baseline estimation is essential to build up the TomoSAR model. After baseline estimation, phase calibration experiments (via FFT and Capon method) indicate that a phase calibration step is indispensable for TomoSAR imaging, which eventually influences the inversion results. A super-resolution reconstruction CS based study demonstrates X band data with the CS method does not fit for forest reconstruction but works for reconstruction of large civil engineering structures such as dams and urban buildings. Meanwhile, the L band data with FFT, Capon and the CS method are shown to work for the reconstruction of large manmade structures (such as bridges) and urban buildings

1-D broadside-radiating leaky-wave antenna based on a numerically synthesized impedance surface

A newly-developed deterministic numerical technique for the automated design of metasurface antennas is applied here for the first time to the design of a 1-D printed Leaky-Wave Antenna (LWA) for broadside radiation. The surface impedance synthesis process does not require any a priori knowledge on the impedance pattern, and starts from a mask constraint on the desired far-field and practical bounds on the unit cell impedance values. The designed reactance surface for broadside radiation exhibits a non conventional patterning; this highlights the merit of using an automated design process for a design well known to be challenging for analytical methods. The antenna is physically implemented with an array of metal strips with varying gap widths and simulation results show very good agreement with the predicted performance