Reflector design stemmed from the need to shape the light emitted by candles or lamps. Over 2,000 years ago people realized that a mirror shaped as a parabola can concentrate light, and thus significantly boosts its intensity, to the point where objects can be set afire. Nowadays many applications require an accurate control of light, such as automotive headlights, streetlights, projection displays, and medical illuminators. In all cases light emitted from a light source can be shaped into a desired target distribution with a reflective surface. Design methods for systems with rotational and translational symmetry were devised in the 1930s. However, the freeform reflector shapes required to illuminate targets with no such symmetries proved to be much more challenging to design. Even when the source is assumed to be a point, the reflector shape is governed by a set of second-order partial non-linear differential equations that cannot be solved with standard numerical integration techniques. An iterative approach to solve the problem for a discrete target, known as the method of supporting ellipsoids, was recently proposed by Oliker. In this research we report several efficient implementations of the method of supporting ellipsoids, based on the point source approximation, and we propose new reflector design techniques that take into account the extent of the source. More specifically, this work has led to three major achievements. First, a thorough analysis of the method of supporting ellipsoids was performed that resulted in two alternative implementations of the algorithm, which enable a fast generation of freeform reflector shapes within the point source approximation. We tailored the algorithm in order to provide control over the parameters of interest to the designers, such as the reflector scale and geometry. Second, the shape generation algorithm was used to analyze how source flux can be mapped onto the target. We derived the condition under which a given source-target mapping can be achieved with a smooth continuous surface, referred as the integrability condition. We proposed a method to derive mappings that satisfy the integrability condition. We then use these mappings to quickly generate reflector shapes that create continuous target distributions as opposed to reflectors generated with the method of supporting ellipsoids that create discrete sets of points on the target. We also show how mappings that do not satisfy the integrability condition can be achieved by introducing step discontinuities in the reflector surface. Third, we investigated two methods to design reflectors with extended sources. The first method uses a compensation approach where the prescribed target distribution is adjusted iteratively. This method is effective for compact sources and systems with rotational or translational symmetry. The second method tiles the source images created by a reflector designed with the method of supporting ellipsoids and then blends the source images together using scattering in order to obtain a continuous target distribution. This latter method is effective for freeform reflectors and target distributions with no sharp variations. Finally, several case studies illustrate how these methods can be successfully applied to design reflectors for general illumination applications such as street lighting or luminaires. We show that the proposed design methods can ease the design of freeform reflectors and provide efficient, cost-effective solutions that avoid unnecessary energy consumption and light pollution.

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Yes / A Novel design of a curved single-layered frequency selective surface with an 11 × 11 array of a 13 × 13 mm-sized unit cell has been merged with a miniaturized, CPW-fed ultra-wideband monopole of dimensions (20 × 25 mm2) for gain enhancement. The suggested prototype, crafted on an FR-4 dielectric substrate and demonstrates a very broad bandwidth starting from 2.66 to 17.98 GHz (148%), which covers the entire UWB frequency band. The combined antenna-curved FSS reflector shows a very important gain improvement from 0.2–5.4 dB to 8.8–14.9 dB, having a peak gain increase of 10 dB at 10.6 GHz. Basic design features were studied and discussed through simulations, yielding promising results The proposed structure can be used in UWB and GPR applications. / The full-text of this article will be released for public view at the end of the publisher embargo on 31 Oct 2024.

The U.S. Evolutionary Power Reactor (EPR) is a new, large-scale pressurized water reactor made by AREVA NP Inc. Surrounding the core of this reactor is a steel wall structure sitting inside called the heavy reflector. The purpose of the heavy reflector is to reduce the neutron flux escaping the core and thus increase the efficiency of the reactor while reducing the damage to the structures surrounding the core as well. The heavy reflector is heated due to absorption of the gamma radiation, and this heat is removed by the water flowing through 832 cooling channels drilled through the heavy reflector. In this project, the temperature distribution in the heavy reflector was investigated to ascertain that the maximum temperature does not exceed the allowable temperature of 350 C, with the intent of modifying the flow distribution in the cooling channels to alleviate any hot spots. The analysis was conducted in two steps. First, the flow distribution in the cooling channels was calculated to test for any maldistribution. The temperature distribution in the heavy reflector was then calculated by simulating the conjugate heat transfer with this flow distribution as the coolant input. The turbulent nature of the flow through the cooling channels made the calculation of the flow distribution computationally expensive. In order to resolve this problem, a simplification method using the "equivalent flow resistance" was developed. The method was validated by conducting a few case studies. Using the simplified model, the flow distribution was calculated and was found to be fairly uniform. The conjugate heat transfer calculation was conducted. The same simplification method used in the flow distribution analysis could not be applied to this calculation; therefore, the computational cost of this model was reduced by lowering the grid density in the fluid region. The results showed that the maximum temperature in the heavy reflector is 347.7 C, which is below the maximum allowable temperature of 350 C. Additional studies were conducted to test the sensitivity of the maximum temperature with change in the flow distribution in the cooling channels. Through multiple calculations, the maximum temperature did not drop more than 3 C; therefore, it was concluded that the flow distribution in the cooling channels does not have significant effect on the maximum temperature in the heavy reflector. / Master of Science

This thesis presents methods for modeling the pattern of large axisymmetric paraboloidal focus-fed reflector antenna systems. The intended application of these methods is to improve the performance of time-domain interference canceling (TDC) in radio astronomy. The first method yields a closed-form expression for the antenna pattern with parameters accounting for the focal ratio and feed pattern. In subsequent adaptive methods, parameters of this model are calculated using measurements of interference signals. The corrected pattern model improves the prediction of the change in the true pattern for future times. The methods are compared by (1) comparing the error in the pattern model with respect to the true pattern and (2) comparing the pattern value update period required to achieve a specified level of residual interference when used in TDC. The efficacy of the pattern modeling methods is demonstrated by showing that the error in the pattern model decreases and the pattern value needs to be updated at a much slower rate for effective TDC. / Master of Science / Radio astronomy is the study of astronomical objects at radio frequencies. Radio telescopes, employing large reflector antennas, are often used to detect and measure extremely weak signals received from distant astronomical bodies. A growing problem for radio astronomy is that human-made communication satellites, orbiting around the earth, interfere with the radio signals. A satellite traversing the antenna pattern interferes with the signal of interest and contaminates it. Presently, this interference is managed by scheduling (avoidance) or by deleting the afflicted data. However, satellite interference is expected to become worse in the future with the increase in the number of satellites in orbit. Therefore, it will become increasingly difficult to avoid the interference by scheduling observations, and there may be too much afflicted data to delete. Hence, more sophisticated techniques may soon be required. One possible method for interference mitigation is Time Domain Canceling (TDC), which is the method addressed in this thesis. This method involves generating an estimate of the interference signal from the interfering satellite. This estimated interference signal is then subtracted from the measured signal contaminated with the interference signal. Ideally, this process should completely remove the interference while preserving the signal of interest and the noise (important in radio astronomy). To improve the accuracy of estimation of the interference signal, we require precise knowledge of the antenna pattern because the interference signal is seen through the antenna pattern. However, the pattern for large reflector antennas employed in radio telescopes is not precisely known and is often difficult to measure or analyze. In this work, we address this problem of lack of pattern knowledge by developing methods for modeling the pattern of large axisymmetric paraboloidal focus-fed reflector antenna systems. We have shown that the pattern model can be significantly improved using measurements of the interference signal in real time. We have also demonstrated that the performance of TDC improves with the incorporation of the developed pattern models.

Surface errors on parabolic reflector antennas degrade the overall performance of the antenna. They cause amplitude and phase errors in the aperture field which lower the gain, raise the side lobes, and fill in the nulls. These are major problems in large ->space reflector antenna systems. F or example, future multiple beam antenna systems requiring spatial isolation to allow frequency reuse could be rendered useless if high side lobes are present. Space antenna structures are difficult to build. They must maintain a nearly perfect parabolic shape in a harsh environment while remaining lightweight. The restrictions on the structure become more severe as science and technology requirements demand electrically large antennas. Mechanically, there are technologies [4)r building antennas with adaptive surfaces that can compensate for many of the larger distortions caused by thermal and gravitational forces. However, as the frequency and size of the reflectors increase, the subtle surface errors become significant and degrade the overall radiation pattern. It is for this reason that another method must be used to further improve the radiation pattern. Electromagnetic compensation for surface errors in large apace reflector antennas has been the topic of several research studies. Most of these studies try to correct the focal plane fields of the reflector near the radiation pattern. The compensation is implemented by weighting the elements of an array feed. In most of the studies, a precise knowledge of the reflector surface is required. An alternative approach to electromagnetic compensation is presented in this study. The proposed technique uses pattern synthesis to compensate for the surface errors. It differs from previous methods in two major respects. The previous studies used global algorithms that try to correct the entire focal plane field near the focal point or the aperture plane field and, hence, modify the entire radiation pattern. The pattern synthesis approach uses a localized algorithm in which pattern corrections are directed specifically towards portions of the pattern requiring improvement. The second major difference is that the pattern synthesis technique does not require knowledge of the reflector surface, but instead uses radiation pattern data to perform the compensation. / Ph. D.

The Log-Periodic Loop Antenna with Ground Reflector (LPLA-GR) is investigated as a new type of antenna, which provides wide bandwidth, broad beamwidth, and high gain. This antenna has smaller transverse dimensions (by a factor of 2/pi) than a log-periodic dipole antenna with comparable radiation characteristics. Several geometries with different parameters are analyzed numerically using ESP code, which is based on the method of moments. A LPLA-GR with 6 turns and a cone angle of 30* offers the most promising radiation characteristics. This antenna yields 47.6 % gain bandwidth and 12 dB gain according to the numerical analysis. The LPLA-GR also provides linear polarization and unidirectional patterns. Three prototype antennas were constructed and measured in the Virginia Tech Antenna Laboratory. Far-field patterns and input impedance were measured over a wide range of frequencies. The measured results agree well with the calculated results. Because of its wide bandwidth, high gain, and small size, the LPLA is expected to find applications as feeds for reflector antennas, as detectors in EMC scattering range, and as mobile communication antennas. / Master of Science

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Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: Utilising future radio interferometer arrays, such as the Square Kilometre Array (SKA), to their full potential will require calibrating for various direction- dependent effects, including the radiation pattern (or primary beam in the parlance of radio astronomers) of each of the antennas in such an array. This requires an accurate characterisation of the radiation patterns at the time of observation, as changing operating conditions may cause substantial variation in these patterns. Furthermore, fundamental imaging limits, as well as practical time constraints, limit the amount of measurement data that can be used to perform such characterisation. Herein three techniques are presented which aim to address this requirement by providing pattern models that use the least amount of measurement data for an accurate characterisation of the radiation pattern. These methods are demonstrated through application to the MeerKAT Offset Gregorian (OG) dual-reflector antenna. The first technique is based on a novel application of the Jaco bi-Bessel series in which the expansion coefficients are solved directly from the secondary pattern. Improving the efficiency of this model in the desired application leads to the development of a different set of basis functions, as well as two constrained solution approaches which reduce the number of pattern measurements required to yield an accurate and unique solution. The second approach extends the application of the recently proposed Characteristic Basis Function Patterns (CBFPs) to compensate for non-linear pattern variations resulting from mechanical deformations in a reflector antenna system. The superior modelling capabilities of these numerical basis functions, which contain most of the pattern features of the given antenna design in a single term, over that of analytic basis functions are demonstrated. The final method focusses on an antenna employing a Phased Array Feed (PAF) in which multiple beam patterns are created through th e use of a beam-former. Calibration of such systems poses a difficult problem as the radiation pattern shape is susceptible to gain variations. Here we propose a solution which is based on using a Linearly Constrained Minimum Varia nce (LCMV) beamformer to conform the realised beam pattern to a physics-based analytic function. Results show that the LCMV beamformer successful ly produces circularly symmetric beams that are accurately characterised with a single-term analytic function over a wide FoV. / AFRIKAANSE OPSOMMING: Die volle benutting van toekomstige radio interferometersamestellings, soos die Square Kilometre Array (SKA), benodig die kalibrering van verskeie rigting-afhanklike effekte, insluitend die stralingspatroon (bekend as die primêre bundel onder radio astronome) van elke antenne in só ’n samestelling. Hierdie benodig ’n akkurate karakterisering van die stralingspatrone op die waarnemingstydstip, aangesien veranderende bedryfskarakteristieke ’n beduidende afwyking in hierdie patrone veroorsaak. Verder, weens fund amentele perke in beeldverwerking, asook praktiese tydbeperkinge, bestaan daar ’n limiet op die hoeveelheid gemeetde data wat benut kan word om die nodige karakterisering mee te doen. Hierin word drie tegnieke ten toon gestel wat gemik is daarop om aan hierdie behoefte te voorsien deur die gebruik van modelle wat ’n minimum hoeveelheid metingdata benodig om ’n akkurate beskrywing van die stralingspatroon te lewer. Die verskeie metodes word aangebied aan die hand van die MeerKAT afset-Gregorian dubbelreflektorantenne. Die eerste tegniek is gebasseer op ’n nuwe toepassing van die Jacobi- Besselreeks waarin die sekondêre stralingspatroon direk gebruik word om die uitsettingskoëffisiënte op te los. Die doelmatigheidsverbetering van hierdie model in die huidige toepassing lei na die ontwikkeling van ’n nuwe versameling van basisfunksies, asook twee voorwaardelike oplossings wat die nodige aantal metings vir ’n akkurate, unieke oplossing verminder. In die tweede tegniek word die toepassing van die onlangs voorgestelde Karakteristieke Basisfunksie Patrone uitgebrei om te vergoed vir die nie-lineêre stralingspatroonafwykings wat teweeggebring word deur meganiese vervormings in die reflektorantenne. Die superieure modelleringsvermoëns van hierdie numeriese basisfunksies, wat meeste van die patroonkenmerke vasvang in ’n enkele term, bo dié van analitiese basisfunksies word gedemonstreer. Die laaste metode fokus op die gebruik van ’n gefaseerde samestellingvoer waarin veelvoudige bundelpatrone geskep word deur die gebruik van ’n bundelvormer. Die kalibrering van sulke instrumente word bemoeilik daardeur dat die patroonvorm gevoelig is vir aanwinsafwykings. Hier stel ons ’n oplossing voor waarin ’n lineêrbegrensde minimumstrooiing bundelvormer gebruik word om die stralingspatroon te pas op ’n fisika-gebasseerde analitiese funksie. Resultate toon dat hierdie bundelvormer sirkelsimmetriese bundels kan skep wat akkuraat beskryf word deur ’n een-term analitiese funksie oor ’n wye gesigsveld.

Dans cette thèse, nous nous intéressons à la résolution de nombreux problèmes d’optique anidolique. Plus précisément, il s’agit de construire des composants optiques qui satisfont des contraintes d’illumination à savoir que l’on veut que la lumière réfléchie(ou réfractée) par ce composant corresponde à une distribution fixée en avance. Comme applications, nous pouvons citer la conception de phares de voitures ou de caustiques. Nous montrons que ces problèmes de conception de composants optiques peuvent être vus comme des problèmes de transport optimal et nous expliquons en quoi cette formulation permet d’étudier l’existence et la régularité des solutions. Nous montrons aussi comment, en utilisant des outils de géométrie algorithmique, nous pouvons utiliser une méthode numérique efficace, la méthode de Newton amortie, pour résoudre tous ces problèmes. Nous obtenons un algorithme générique capable de construire efficacement un composant optique qui réfléchit (ou réfracte)une distribution de lumière prescrite. Nous montrons aussi la convergence de l’algorithme de Newton pour résoudre le problème de transport optimal dans le cas où le support de la mesure source est une union finie de simplexes. Nous décrivons également la relation commune qui existe entre huit différents problèmes de conception de composants optiques et montrons qu’ils peuvent tous être vus comme des équations de Monge-Ampère discrètes. Nous appliquons aussi la méthode de Newton à de nombreux problèmes de conception de composants optiques sur différents exemples simulés ainsi que sur des prototypes physiques. Enfin, nous nous intéressons à un problème apparaissant en transport optimal numérique à savoir le choix du point initial. Nous développons trois méthodes simples pour trouver de “bons” points initiaux qui peuvent être ensuite utilisés comme point de départ dans des algorithmes de résolution de transport optimal. / In this thesis, we are interested in solving many inverse problems arising inoptics. More precisely, we are interested in designing optical components such as mirrors andlenses that satisfy some light conservation constraints meaning that we want to control thereflected (or refracted) light in order match a prescribed intensity. This has applications incar headlight design or caustic design for example. We show that optical component designproblems can be recast as optimal transport ones for different cost functions and we explainhow this allows to study the existence and the regularity of the solutions of such problems. Wealso show how, using computational geometry, we can use an efficient numerical method namelythe damped Newton’s algorithm to solve all these problems. We will end up with a singlegeneric algorithm able to efficiently build an optical component with a prescribed reflected(or refracted) illumination. We show the convergence of the Newton’s algorithm to solve theoptimal transport problem when the source measure is supported on a finite union of simplices.We then describe the common relation between eight optical component design problemsand show that they can all be seen as discrete Monge-Ampère equations. We also apply theNewton’s method to optical component design and show numerous simulated and fabricatedexamples. Finally, we look at a problem arising in computational optimal transport namelythe choice of the initial weights. We develop three simple procedures to find “good” initialweights which can be used as a starting point in computational optimal transport algorithms.