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Dissertations / Theses on the topic 'Modern optics'
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Paolini, Aaron Louis. "A real-time super resolution implementation using modern graphics processing units." Access to citation, abstract and download form provided by ProQuest Information and Learning Company; downloadable PDF file, 88 p, 2009. http://proquest.umi.com/pqdweb?did=1821542441&sid=7&Fmt=2&clientId=8331&RQT=309&VName=PQD.
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Weiss, Thomas. "Advanced numerical and semi-analytical scattering matrix calculations for modern nano-optics." Thesis, Clermont-Ferrand 2, 2011. http://www.theses.fr/2011CLF22150.
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Les propriétés optiques des nanomatériaux, tels que les cristaux photoniques ou les métamatériaux, ont reçu beaucoup d’attention dans les dernières années [1–9]. La dérivation numérique de ces propriétés se révèle pourtant très compliquée, en particulier dans le cas des structures métallo-diélectriques, qui comportent des résonances plasmoniques. C’est pourquoi des méthodes numériques avancées et des modèles semi-analytiques sont nécessaires. Dans cette thèse, nous montrerons que le formalisme de la matrice de diffraction peut satisfaire ces deux aspects. La méthode de la matrice de diffraction est un concept très général en physique. Dans le cas des structures périodiques, on peut dériver la matrice de diffraction à l’aide de la méthode modale de Fourier [10]. Pour la description exacte des géométries planes, nous avons développé la méthode des coordonnées adaptées [11], qui nous donne un nouveau système de coordonnées, dans lequel les interfaces des matériaux sont des surfaces de coordonnées constantes. En combinaison avec la méthode de la résolution spatiale adaptative, la méthode des coordonnées adaptées permet d’améliorer considérablement la convergence de la méthode modale de Fourier, de telle sorte qu’on peut calculer des structures métalliques compliquées très efficacement. Si on utilise la matrice de diffraction, il est non seulement possible de dériver les propriétés optiques en illumination de champ lointain, comme la transmission, la réflexion, l’absorption, et le champ proche, mais aussi de décrire l’émission d’un objet à l’intérieur d’une structure et d’obtenir les résonances optiques d’un sytème. Dans cette thèse, nous présenterons une méthode efficace pour la dérivation des résonances optiques tridimensionnelles, utilisant directement la matrice de diffraction [14]. Si on connaît les résonances d’un système isolé, il est aussi possible d’obtenir une approximation des résonances dans le cas d’un système combiné à l’aide de notre méthode du couplage des résonances [15, 16]. Cette méthode permet de décrire le régime de couplage des champs lointain et proche, y compris le couplage fort avec les résonances Fabry-Perot, pour des systèmes qui se composent d’un empilement de deux structures planes et périodiques. Pour cette raison, on peut étudier efficacement le couplage de ces systèmes. Cette thèse est écrite de manière à donner une idée d’ensemble du formalisme de la matrice de diffraction et de la méthode modale de Fourier. En outre, nous décrivons notre généralisation de ces méthodes et nous montrons la validité de nos approches pour différents exemplesThe optical properties of nanostructures such as photonic crystals and metamaterials have drawn a lot of attention in recent years [1–9]. The numerical derivation of these properties, however, turned out to be quite complicated, especially in the case of metallo-dielectric structures with plasmonic resonances. Hence, advanced numerical methods as well as semi-analytical models are required. In this work, we will show that the scattering matrix formalism can provide both. The scattering matrix approach is a very general concept in physics. In the case of periodic grating structures, the scattering matrix can be derived by the Fourier modal method [10]. For an accurate description of non-trivial planar geometries, we have extended the Fourier modal method by the concept of matched coordinates [11], in which we introduce a new coordinate system that contains the material interfaces as surfaces of constant coordinates. In combination with adaptive spatial resolution [12,13], we can achieve a tremendously improved convergence behavior which allows us to calculate complex metallic shapes efficiently. Using the scattering matrix, it is not only possible to obtain the optical properties for far field incidence, such as transmission, reflection, absorption, and near field distributions, but also to solve the emission from objects inside a structure and to calculate the optical resonances of a system. In this work, we provide an efficient method for the ab initio derivation of three-dimensional optical resonances from the scattering matrix [14]. Knowing the resonances in a single system, it is in addition possible to obtain approximated resonance positions for stacked systems using our method of the resonant mode coupling [15, 16]. The method allows describing both near field and far field regime for stacked two-layer systems, including the strong coupling to Fabry-Perot resonances. Thus, we can study the mutual coupling in such systems efficiently. The work will provide the reader with a basic understanding of the scattering matrix formalism and the Fourier modal method. Furthermore, we will describe in detail our extensions to these methods and show their validity for several examples
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Wei, Zhiyong. "Thermo-fluid modeling and robust control of modern optic fiber drawing processes." Diss., Available online, Georgia Institute of Technology, 2004, 2004. http://etd.gatech.edu/theses/available/etd-04092004-135913/unrestricted/wei%5Fzhiyong%5F200405%5Fphd.pdf.
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Thesis (Ph. D.)--Mechanical Engineering, Georgia Institute of Technology, 2004.Kok-Meng Lee, Committee Chair ; Andrei G. Fedorov, Committee Member ; William E. Singhose, Committee Member ; David G. Taylor, Committee Member ; Zhi Zhou, Committee Member. Includes bibliographical references.
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Anderson, Edward James. "The logic of illusion in modern optics and its apologetical implications for science and religion." Online full text .pdf document, available to Fuller patrons only, 2003. http://www.tren.com.
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Marmie, John A. "Modern numerical electromagnetic techniques applied to aviation problems." Ohio : Ohio University, 1989. http://www.ohiolink.edu/etd/view.cgi?ohiou1182443521.
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Weiss, Thomas [Verfasser], and Harald [Akademischer Betreuer] Giessen. "Advanced numerical and semi-analytical scattering matrix calculations for modern nano-optics / Thomas Weiss. Betreuer: Harald Giessen." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2011. http://d-nb.info/1014147603/34.
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Enckell, Merit. "Structural health monitoring using modern sensor technology : long-term monitoring of the New Årsta Railway Bridge." Licentiate thesis, KTH, Civil and Architectural Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4236.
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Structural Health Monitoring (SHM) is a helpful tool for engineers in order to control and verify the structural behaviour. SHM also guides the engineers and owners of structures in decision making concerning the maintenance, economy and safety of structures. Sweden has not a very sever tradition in monitoring, as countries with strong seismic and/or aerodynamic activities. Anyway, several large scale monitoring projects have taken place in recent years and SHM is slowly making entrance as an essential implement in managing structures by engineers as well as owners.
This licentiate thesis presents a state-of-the art-review of health monitoring activities and over sensory technologies for monitoring infrastructure constructions like bridges, dams, off-shore platforms, historical monuments etc. related to civil engineering. The fibre optic equipment is presented with special consideration.
The permanent monitoring system of the New Årsta Bridge consists of 40 fibre optic sensors, 20 strain transducers, 9 thermocouples, 6 accelerometers and one LVDT. The aims of the static study are: to control the maximal strains and stresses; to detect cracking in the structure; to report strain changes under construction, testing period and in the coming 10 years; and to compare conventional system with fibre optic system.
The system installation started in January 2003 and was completed October 2003. The measurements took place from the very beginning and are suppose to continue for at least 10 years of operation. At the construction phase the measurements were performed manually and later on automatically through broad band connection between the office and central data acquisition systems located inside the bridge.
The monitoring project of the New Årsta Railway Bridge is described from the construction phase to the testing phase of the finished bridge. Results of the recorded statistical data, crack detection and loading test are presented and a comparison between traditional techniques like strain transducers and fibre optic sensors is done.
Various subjects around monitoring and sensor technologies that were found under the project are brought up in order to give the reader a good understanding, as well of the topics, techniques and of the bridge. Example of few applications is given with the aim of a deeper insight into monitoring related issues.
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Larson, Jonas. "Extended Jaynes-Cummings Models In Cavity Qed." Doctoral thesis, Stockholm, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-404.
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Carney, Melody Noelle. "The Impact of the Optical Phenomena of Color Adjustment Potential and Kubelka-Munk Layering of Dental Composite Resins on Modern Esthetic Dentistry." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429403504.
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Brown, Jeffrey Michael. "Exactly Solvable Light-Matter Interaction Models for Studying Filamentation Dynamics." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/612844.
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This dissertation demonstrates the usefulness of exactly solvable quantum models in the investigation of light-matter interaction phenomena associated with the propagation of ultrashort laser pulses through gaseous media. This work fits into the larger research effort towards remedying the weaker portions of the standard set of medium modeling equations commonly used in simulations. The ultimate goal is to provide a self-consistent quantum mechanical description that can integrate Maxwell and Schrödinger systems and provide a means to realistically simulate nonlinear optical experiments on relevant scales. The study of exactly solvable models begins with one of the simplest quantum systems available, one with a 1D Dirac-delta function potential plus interaction with the light field. This model contains, in the simplest form, the most important "ingredients" that control optical filamentation, i.e. discrete and continuum electronic states. The importance of both states is emphasized in the optical intensity regime in which filaments form, where both kinds of electronic states simultaneously play a role and may not even be distinguishable. For this model atom, an analytical solution for the time-dependent light-induced atomic response from an arbitrary excitation waveform is obtained. Although this system is well-known and has been studied for decades, this result is probably the most practically useful and general one obtained thus far. Numerical implementation details of the result are also given as the task is far from trivial. Given an efficient implementation, the model is used in light-matter interaction simulations and from these it is apparent that even this toy model can qualitatively reproduce many of the nonlinear phenomena seen in experiments. Not only does this model capture the basic physics of optical filamentation, but it is also well-suited for high harmonic generation simulations. Next, a theoretical framework for using Stark resonant states (or metastable states) to represent the medium's polarization response is presented. Researchers have recognized long ago the utility of Gamow resonant states as a description of various decay processes. Even though a bound electron experiences a similar decay-like process as it transitions into the continuum upon ionization, it was unclear whether field-induced Stark resonant states carry physically relevant information. It is found that they do, and in particular it is possible to use them to capture a medium's polarization response. To this end, two quantum systems with potentials represented by a 1D Dirac-delta function and a 1D square well are solved, and all the necessary quantities for their use as medium models are presented. From these results it is possible to conjecture some general properties that hold for all resonance systems, including systems that reside in higher than one dimensional space. Finally, as a practical application of this theory, the Metastable Electronic State Approach (MESA) is presented as a quantum-based replacement for the standard medium modeling equations.
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McCall, Matthew Christopher. "Looking at the Surface of the Mind: Descartes on Visual Sensory Perception." The Ohio State University, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=osu1503315104748657.
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Furness, Charles Zachary. "Parameter identification of a flexible beam using a modal domain optical fiber sensor." Thesis, Virginia Tech, 1990. http://hdl.handle.net/10919/42058.
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An optical fiber sensor is used for identification of a cantilevered beam under conditions of various concentrated mass loadings. A model of the sensor as well as the dynamic system is developed and used to test the reliability of the identification. Input/output data from an experiment is gathered and used in the identification. A survey of the existing areas of damage detection and parameter identification is included, along with suggestions for incorporating fiber optic sensors into existing techniques. The goal of this research was to show that the fiber sensor can be used for identification purposes, and that it is sensitive to parameter changes within the system (in this case concentrated mass changes).
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Gargallo, Jaquotot Bernardo Andrés. "Advanced arrayed waveguide gratings: models, design strategies and experimental demonstration." Doctoral thesis, Universitat Politècnica de València, 2016. http://hdl.handle.net/10251/74646.
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[EN] The present PhD thesis deals on the model, design and experimental demonstration of Arrayed Waveguide Grating (AWG) with advanced features. Firstly, building upon existing AWG formulations, design equations are provided, libraries developed and all this is experimentally validated with devices in Indium Phosphide (InP) and Silicon-on-insulator (SOI) technologies. Next, a model and experimental validation is reported for an Interleave-Chirped Arrayed Waveguide Grating (IC-AWG), which is able to process optical signals as WDM demultiplexer, polarization splitter and phase diversity component all in a single device. This device was fabricated and tested in InP technology. The second innovative AWG demonstrated in this thesis, a Reflective type (R-AWG), whose layout allows for tailoring the pass-band shape and to change the spectral resolution. A demonstration of design and fabrication for this device is provided in SOI technology. The last AWG with innovative concepts is one driven by Surface Acoustic Waves (AWG-SAW), where the spectral channels can be tuned by means of acousto-optic effect. The device was fabricated in Aluminium Gallium Arsenide (AlGaAs) technology, and measurements are provided to validate the concept and design flow. In parallel this thesis has resulted in the development of different AWG layouts for a wide number of (generic) technologies and foundries, coded into design libraries, of use in a de-facto standard software employed for the design of photonic integrated circuits. These design libraries have been licensed to the UPV spin-off company VLC Photonics S.L.[ES] La presente tesis se ha centrado en el modelado, diseño y demostración experimental del dispositivo Arrayed Waveguide Grating (AWG) con funcionalidades avanzadas. Primero, usando la formulación existente sobre AWGs se aportan ecuaciones y librerías de diseño, y se validan experimentalmente por medio de dispositivos fabricados en tecnologías de Indium Phosphide (InP) y Silicon-on-insulator (SOI). Después, se reporta un modelo y demostración experimental para un Interleave-Chirped Arrayed Waveguide Grating (IC-AWG), el cual es capaz de procesar señales ópticas como demultiplexor WDM, divisor de polarización y componente de diversidad de fase en un único dispositivo. Este dispositivo fue fabricado y probado en tecnología de InP. El segundo AWG innovador demostrado en esta tesis es de tipo Reflectante (R-AWG), cuyo diseño permite modificar la forma espectral del canal y cambiar su resolución espectral, incluyendo una demostración de diseño y fabricación de este dispositivo en tecnología de SOI. El último AWG que incluye conceptos innovadores es uno sintonizable por Acoustic Waves (AWGSAW), donde los canales espectrales pueden ser sintonizados por medio del efecto acusto-óptico. Dicho dispositivo fue fabricado en tecnología de Aluminium Gallium Arsenide (AlGaAs), y se han incluido medidas experimentales para validar el concepto y el flujo de diseño. En paralelo junto con esta tesis se han desarrollado diferentes diseños para el AWG en un amplio número de tecnologías (genéricas) y plataformas de fabricación, implementadas en unas librerías de diseño para uno de los softwares m¿as utilizados para el diseño de circuitos integrados ópticos, siendo actualmente el estándar de facto. Dichas librerías de diseño han sido licenciadas a la compañía VLC Photonics S.L., spin-off de la UPV.
[CAT] La present tesi ha estat centrada en el modelatge, disseny i demostració experimental del dispositiu Arrayed Waveguide Grating (AWG) amb funcionalitats avançades. Primer, usant la formulació existent sobre AWGs s'aporten equacions i llibreries de disseny, i es validen experimentalment per mitjà de dispositius fabricats en tecnologies de Indium Phosphide (InP) i Silicon-on-insulator (SOI). Després, es reporta un model i demostració experimental per a un Interleave-Chirped Arrayed Waveguide Grating (IC-AWG), el qual és capaç de processar senyals òptiques com demultiplexor WDM, divisor de polarització i component de diversitat de fase en un únic dispositiu. Aquest dispositiu va ser fabricat i provat en tecnologia de InP. El segon AWG innovador demostrat en aquesta tesi és de tipus Reflector (R-AWG), amb un disseny que permet modificar la forma espectral del canal i canviar la seua resolució espectral, incloent una demostració de disseny i fabricació d'aquest dispositiu en tecnologia de SOI. L'últim AWG que inclou conceptes innovadors és un sintonitzable per Acoustic Waves (AWG-SAW), on els canals espectrals poden ser sintonitzats per mitjà de l'efecte acusto-òptic. Aquest dispositiu va ser fabricat en tecnologia de Aluminium Gallium Arsenide (AlGaAs), i s'han inclòs mesures experimentals per validar el concepte i el flux de disseny. En paral.lel juntament amb aquesta tesi s'han desenvolupat diferents dissenys per al AWG en un ampli nombre de tecnologies (genèriques) i plataformes de fabricació, implementades en unes llibreries de disseny per a un dels programaris més utilitzats per al disseny de circuits integrats òptics, sent actualment l'estàndard de facto. Aquestes llibreries de disseny han estat llicenciades a la companyia VLC Photonics S.L., spin-off de la UPV.
Gargallo Jaquotot, BA. (2016). Advanced arrayed waveguide gratings: models, design strategies and experimental demonstration [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/74646
TESIS
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Caccavano, Adam. "Optics and Spectroscopy in Massive Electrodynamic Theory." PDXScholar, 2013. https://pdxscholar.library.pdx.edu/open_access_etds/1485.
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The kinematics and dynamics for plane wave optics are derived for a massive electrodynamic field by utilizing Proca's theory. Atomic spectroscopy is also examined, with the focus on the 21 cm radiation due to the hyperfine structure of hydrogen. The modifications to Snell's Law, the Fresnel formulas, and the 21 cm radiation are shown to reduce to the familiar expressions in the limit of zero photon mass.
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Hart, Quinn James 1965. "Surface and aerosol models for use in radiative transfer codes." Thesis, The University of Arizona, 1990. http://hdl.handle.net/10150/277334.
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Absolute radiometric calibrations of Landsat 5 Thematic Mapper satellite are improved with the inclusion of a method to invert optical depth measurements to obtain an aerosol particle size distribution and a non-lambertian surface reflectance model. Also, a program is developed to improve speed and standardization of the entire calibration procedure. The inverted size distributions can predict radiances varying from the previous jungian distributions by as much as 5 percent, though the reduction in the estimated error is less than one percent. An empirical model for the surface reflection of White Sands using a two-degree polynomial fit as a function of scattering angle was employed. The model reduced estimated errors in radiance predictions by up to one percent. Satellite calibrations dating from October, 1984 are reprocessed using the improved methods and a linear estimation of satellite counts per unit radiance versus time since launch is determined.
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Andrawis, Alfred S. "A new compound modulation technique for multi-channel analog video transmission on fiber." Diss., Virginia Tech, 1991. http://hdl.handle.net/10919/39877.
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Present analog optical fiber multi-channel video transmission systems are very sensitive to laser nonlinearities and are consequently limited in the optical modulation depth (OMD) that may be used. This, in turn limits the power budget achievable, signal-to-noise ratio, and the channel capacity.
In this dissertation a new analog transmission technique for multi-channel TV transmission on fiber USIng frequency modulation/pulse amplitude modulation/time division multiplexing (FM/TDM) is described and compared with present digital and analog systems. Parameters for the proposed system are selected and the relationship between the performance and parameter values is discussed. Analysis and simulations indicate that the proposed system has a very low sensitivity to nonlinearities and is similar to that of digital systems, and much better than current Frequency Modulated/Frequency Division Multiplexed (FM/FDM) systems. This permits the use of higher OMD (as high as in digital systems), which results in achieving a high signal-to-noise ratio and a large power budget. Analysis of the number of channels as a function of adjacent channel intersymbol interference indicates that the proposed system has a better spectral efficiency than present analog systems. Simulations are also used to predict the performance of the proposed system with laser diodes poorer than the ones presently used for multi-channel analog systems. Considerably poorer lasers may be used while achieving acceptable transmission quality. Finally, carrier-to-noise penalty caused by timing errors and jitter effects are analyzed.Ph. D.
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Yau, Chin-ko. "Superresolution imaging models and algorithms /." Click to view the E-thesis via HKUTO, 2008. http://sunzi.lib.hku.hk/HKUTO/record/B3955904X.
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游展高 and Chin-ko Yau. "Superresolution imaging: models and algorithms." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2008. http://hub.hku.hk/bib/B3955904X.
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André, Tomas. "Benchmarking Physical Properties of Water Models." Thesis, Uppsala universitet, Molekyl- och kondenserade materiens fysik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388336.
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Water is a fundamental part of life as we know it, and by that also a fundamental for biology, chemistry, and parts of physics. Understanding how water behaves and interacts is key in many fields of all these three branches of science. Numerical simulation using molecular dynamics can aid in building insight in the behavior and interactions of water. In this thesis molecular dynamics is used to simulate common rigid 3 point water models to see how well they replicate certain physical and chemical properties as functions of temperature. This is done with molecular dynamics program GROMACS which offers a complete set of tools to run simulations and analyze results. Everything has been automated to work with a python script and a file of input parameters. Most of the models follow the same trends and are valid within a limited temperature range.Vatten är en av de fundamentala byggstenarna för liv, därmed är det även fundamentalt för biologi, kemi och delar av fysiken. Att förstå hur vatten beter sig och interagerar är en stor fråga inom dessa tre grenar av vetenskap. Med molekyldynamik går det att utföra numeriska simuleringar som kan användas som hjälpmedel för att bygga en djupare förståelse för riktigt vatten. I den här uppsatsen så har molekyldynamik använts till att simulera vanliga rigida 3 punkts parametiseringar av vatten för att se hur bra de kan replikera vissa egenskaper som funktioner av temperatur. Simuleringen är gjord med hjälp av molekyldynamik programet GROMACS som ger en fullständig uppsättning verktyg för att simulera och analysera molekylsystem. Alla simuleringar och analys är automatiserat med ett pythonprogram och en fil för parametrar. De allra flesta modeller följer liknande trender och är giltiga inom små temperaturintervall.
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Yamashita, Tsuyoshi. "Unraveling photonic bands : characterization of self-collimation in two-dimensional photonic crystals." Diss., Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-06072005-104606/.
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Thesis (Ph. D.)--School of Materials Science and Engineering, Georgia Institute of Technology, 2006.Summers, Christopher, Committee Chair ; Chang, Gee-Kung, Committee Member ; Carter, Brent, Committee Member ; Wang, Zhong Lin, Committee Member ; Meindl, James, Committee Member ; Li, Mo, Committee Member.
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Rovenská, Katarína. "Dielektrické metapovrchy jako moderní optické prvky." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417149.
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Vďaka ich vysokej verzatilite a nízkej priestorovej náročnosti sú metapovrchy sľubným nasledovníkom tradičných optických komponentov. Táto práca sa upriamuje na metapovrchy, ktoré môžu nahradiť polvlnné doštičky a difraktívne deliče zväzku. Práca prezentuje dve stratégie výroby nanoštruktúr z oxidu titaničitého s vysokým pomerom strán -- jedna používa reaktívne iónové leptanie vrstvy TiO2 skrz kovovú masku, kým druhá používa štrukturovaný elektrónový rezist ako formu pre depozíciu atomárnych vrstiev TiO2. V závere práce sú charakterizované a analyzované optické vlastnosti vyrobených štruktúr, predovšetkým ich fázový posun a transmisivita.
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Walker, Joe Alan 1945. "Models and validation measurements of bidirectional reflectance factor for diffuse reflecting materials." Diss., The University of Arizona, 1998. http://hdl.handle.net/10150/282695.
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A physical model developed from scattering theory by Hapke was applied to bidirectional reflectance factor (BRF) measurement data for several diffuse reflecting materials. All of the material samples were some form of polytetrafluoroethelyne (PTFE) powder. The solar illuminated diffuser for the Moderate Resolution Imaging Spectroradiometer (MODIS) was one of the samples. The BRF was characterized in seven wavelength bands, covering a spectral range of 400 nm to 2100 nm. The BRFs were determined, using the Santa Barbara Remote Sensing (SBRS) scattering goniopolarimeter, by measuring all four linear polarization components and using those measurements in the BRF equations of Clarke. The scattering goniopolarimeter was carefully characterized in a series of measurements. It was calibrated by comparing BRF measurements to the BRF calibration values of a reflectance standard. A detailed error analysis was done. The uncertainties for each of the four polarization components was considered individually, and then combined to obtain the total estimated uncertainty in the BRF values. The mean-square errors of the measured BRF sample averages were compared to the estimated uncertainties. Results of BRF evaluations and the measurement uncertainties for the different diffusers are presented. A study of several variations of the Hapke scattering model was made. The models were successfully applied to each of the four polarization components of BRF, in addition to the unpolarized BRF. The quality of the models was evaluated using the "root-mean-square of the fit" merit function, RMSf The simplest Hapke model gave RMSf values from two percent down to less than one percent, but the vegetation canopy form of the Hapke model gave higher RMSf values, from six to ten percent. The Henyey-Greenstein single scattering phase function, even when used in the simplest Hapke model, gave RMSf values between two and eight percent, whereas Legendre polynomial phase functions resulted in RMSf values of less than one percent. Equations with an additional forward scatter term usually made a slight improvement, on the order of one to two tenths of a percent. To obtain a representative model, at least two sets of BRF data at different incidence angles were needed.
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Colvin, Thomas. "Comparing computational models of vision to human behaviour." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/50196/.
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Biological vision and computational models of vision can be split into three independent components (image description, decision process, and image set). The thesis presented here aimed to investigate the influence of each of these core components on computational model’s similarity to human behaviour. Chapter 3 investigated the similarity of different computational image descriptors to their biological counterparts, using an image matching task. The results showed that several of the computational models could explain a significant amount of the variance in human performance on individual images. The deep supervised convolutional neural net explained the most variance, followed by GIST, HMAX and then PHOW. Chapter 4 investigated which computational decision process best explained observers’ behaviour on an image categorization task. The results showed that Decision Bound theory produced behaviour the closest to that of observers. This was followed by Exemplar theory and Prototype theory. Chapter 5 examined whether the naturally differing image set between computational models and observers could partially account for the difference in their behaviour. The results showed that, indeed, the naturally differing image set between computational models and observers was affecting the similarity of their behaviour. This gap did not alter which image descriptor best fit observers’ behaviour and could be reduced by training observers on the image set the computational models were using. Chapter 6 investigated, using computational models of vision, the impact of the neighbouring (masking) images on the target images in a RSVP task. This was done by combining the neighbouring images with the target image for the computational models’ simulation for each trial. The results showed that models behaviour became closer to that of the human observers when the neighbouring mask images were included in the computational simulations, as would be expected given an integration period for neural mechanisms. This thesis has shown that computational models can show quite similar behaviours to human observers, even at the level of how they perform with individual images. While this shows the potential utility in computational models as a tool to study visual processing, It has also shown the need to take into account many aspects of the overall model of the visual process and task; not only the image description, but the task requirements, the decision processes, the images being used as stimuli and even the sequence in which they are presented.
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Reshidko, Dmitry, and Dmitry Reshidko. "Topics in Modern Lens Design." Diss., The University of Arizona, 2016. http://hdl.handle.net/10150/623177.
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Many advances have occurred in the field of optical design during the past decade. Some of the newer topics and concepts associated with the design and use of optical systems are complex and require comprehensive understanding of theory, expertise in state-of-the-art technology, and extensive computer simulations. This dissertation focuses on development of practical methods and tools for successful lens design and evaluation of state-of-the-art imaging and illumination systems. The dissertation addresses several current topics in modern optical engineering and utilizes approaches to provide insights into the inner workings of optical systems. Examples of modern mobile camera lenses are provided to show how specific methods can help to better understand these lens designs and to expand the imaging capabilities of miniature camera systems. Two simple but effective real ray tracing methods for correcting chromatic aberrations in imaging systems are described. The proposed methods separate monochromatic and chromatic aberration correction into two independent problems. This two-step approach provides effective alternatives in correcting chromatic aberrations. A number of unique calculations have been performed and some novel and interesting theoretical results, including the fourth-order theory of irradiance changes in axially symmetric optical systems, are reported. The specific relationships between the irradiance distribution and wavefront aberration coefficients to fourth order are derived for the first time. The practical case of relative illumination at the image plane of an optical system is also discussed in some detail.
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Horne, Jimmy D. Jr. "Modeling optical turbulence with COAMPS during two observation periods at Vandenberg AFB." Thesis, Monterey, California. Naval Postgraduate School, 2004. http://hdl.handle.net/10945/1671.
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Approved for public release, distribution is unlimitedThe objective of this thesis is to investigate the forecastability of optical turbulence using the U.S. Navy's Coupled Ocean Atmosphere Mesoscale Prediction System (COAMPS). First, a detailed synoptic study was performed over the Eastern Pacific region for observation periods in October 2001 and March 2002 to focus on mesoscale features affecting Vandenberg AFB. Second, a modified version of COAMPS version 2.0.16 model output was evaluated to ensure reasonable modeling of the mesoscale. Next, temperature and dewpoint temperature vertical profiles of COAMPS, modified with the Turbulent Kinetic Energy (TKE) Method, were compared with balloon-launched rawinsondes, initially, then with higher resolution thermosondes. Optical turbulence parameters were then calculated from the data and a comparison between synthetic profiles and thermosonde-derived profiles were qualitatively and quantitatively studied. Then the vertical resolution of the model was increased for selected forecasts to determine the potential for forecast improvement.
Lieutenant Commander, United States Navy
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Whalen, Patrick. "Full Field Propagation Models And Methods For Extreme Nonlinear Optics." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/347238.
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This dissertation examines models, methods, and applications of electric field pulse propagation in nonlinear optics. Standard nonlinear optical propagation models such as the NLS equation are derived using a procedure invoking a slowly-varying wave approximation which amounts to discarding second order derivatives in the propagation direction. This work follows a more intuitive procedure emphasizing unidirectionality, the core trait of laser light propagation, by projecting a nonlinear wave system onto a unidirectional subspace. The projection method is discussed as a general theory and then applied to a series of different electric field configurations. Two important full-field propagation models are examined. The unidirectional pulse propagation equations (UPPE's) are generated from Maxwell's equations with the sole approximation being that of unidirectionality. The second model studied is the MKP equation which is a canonical full-field propagation equation particularly amenable to mathematical analysis due to its status as a conserved system. Applications unique to full-field propagation including electric field shock and harmonic walk-off induced collapse arrest are studied through numerical simulations. An emphasis is placed on the mid-infrared to long-infrared wavelength regime where significant differences between envelope models and electric field models manifest as a result of extremely weak dispersion. Presented are the first embedded Runge-Kutta exponential time-differencing (RKETD) methods of fourth order with third order embedding and fifth order with third order embedding for non-Rosenbrock type nonlinear systems. A procedure for constructing RKETD methods that accounts for both order conditions and stability is outlined. In the stability analysis, the fast time scale is represented by a full linear operator in contrast to particular scalar cases considered before. An effective time-stepping strategy based on reducing both ETD function evaluations and rejected steps is described. Comparisons of performance with adaptive-stepping integrating factor (IF) are carried out on a set of canonical partial differential equations including the standard z-propagated UPPE.
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Tsang, Suk-chong, and 曾淑莊. "A numerical study of coupled nonlinear Schrödinger equations arising in hydrodynamics and optics." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B26652651.
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CHENG, YEOU-YEN. "MULTIPLE-WAVELENGTH PHASE SHIFTING INTERFEROMETRY (OPTICAL-TESTING, ASPHERIC SURFACE)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187928.
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The problems of combining ideas of phase shifting interferometry (PSI) and synthetic-wavelength techniques to extend the phase measurement range of conventional single-wavelength PSI are investigated. This combination of PSI and synthetic-wavelengths gives multiple-wavelength phase-shifting interferometry the advantages of: (1) larger phase measurement range and (2) higher accuracy of phase measurement. Advantages, error sources, and limitations of single-wavelength PSI are discussed. Some practical methods to calibrate the piezoelectric transducer (PZT), used to phase shift the reference beam, are presented with experimental results. Two methods of two-wavelength PSI are used to solve the 2π ambiguity problem of single-wavelength PSI. For the first method, two sets of phase data (with 2π ambiguities) for shorter wavelengths are calculated and stored in the computer which calculates the new phase data for the equivalent-wavelength λ(eq). The "error magnification effect," which reduces the measurement precision of the first method, is then investigated. The second, more accurate method, uses the results of the first method as a reference to correct the 2π ambiguities in the single-wavelength phase data. Experimental results are included to confirm theoretical predictions. The enhancement of two-wavelength PSI is investigated, and requires the phase data of a third wavelength. Experiments are performed to verify the capability of multiple-wavelength PSI. For the wavefront being measured, the difference of the optical-path-difference (OPD) between adjacent pixels is as large as 3.3 waves. After temporal averaging of five sets of data, the repeatability of the measurement is better than 2.5 nm (0.0025%) rms (λ = 632.8 nm). This work concludes with recommendations for future work that should make the MWLPSI a more practical technique for the testing of steep aspheric surfaces.
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Hunter, Ashley. "Photon propagation models to determine the optical properties of scattering media." Thesis, University of Nottingham, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.323249.
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Chapman, S. J. "Macroscopic models of superconductivity." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.303594.
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After giving a description of the basic physical phenomena to be modelled, we begin by formulating a sharp-interface free-boundary model for the destruction of superconductivity by an applied magnetic field, under isothermal and anisothermal conditions, which takes the form of a vectorial Stefan model similar to the classical scalar Stefan model of solid/liquid phase transitions and identical in certain two-dimensional situations. This model is found sometimes to have instabilities similar to those of the classical Stefan model. We then describe the Ginzburg-Landau theory of superconductivity, in which the sharp interface is `smoothed out' by the introduction of an order parameter, representing the number density of superconducting electrons. By performing a formal asymptotic analysis of this model as various parameters in it tend to zero we find that the leading order solution does indeed satisfy the vectorial Stefan model. However, at the next order we find the emergence of terms analogous to those of `surface tension' and `kinetic undercooling' in the scalar Stefan model. Moreover, the `surface energy' of a normal/superconducting interface is found to take both positive and negative values, defining Type I and Type II superconductors respectively. We discuss the response of superconductors to external influences by considering the nucleation of superconductivity with decreasing magnetic field and with decreasing temperature respectively, and find there to be a pitchfork bifurcation to a superconducting state which is subcritical for Type I superconductors and supercritical for Type II superconductors. We also examine the effects of boundaries on the nucleation field, and describe in more detail the nature of the superconducting solution in Type II superconductors - the so-called `mixed state'. Finally, we present some open questions concerning both the modelling and analysis of superconductors.
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Hang, Zhihong. "Experimental investigation on the effect of disorder in metallo-photonic band gap system /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202004%20HANG.
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Sidahmed, Abdelmgid Osman Mohammed. "Mesh free methods for differential models in financial mathematics." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_3917_1319185202.
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Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial products exists in the market, such as forwards, futures, swaps and options. Our main focus in this thesis is to use the numerical analysis tools to solve some option pricing problems. Depending upon the inter-relationship of the financial derivatives, the dimension of the associated problem increases drastically and hence conventional methods (for example, the finite difference methods or finite element methods) for solving them do not provide satisfactory results. To resolve this issue, we use a special class of numerical methods, namely, the mesh free methods. These methods are often better suited to cope with changes in the geometry of the domain of interest than classical discretization techniques. In this thesis, we apply these methods to solve problems that price standard and non-standard options. We then extend the proposed approach to solve Heston' volatility model. The methods in each of these cases are analyzed for stability and thorough comparative numerical results are provided.
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Gleeson, Cameron Banking & Finance Australian School of Business UNSW. "Pricing and hedging S&P 500 index options : a comparison of affine jump diffusion models." Awarded by:University of New South Wales. School of Banking and Finance, 2005. http://handle.unsw.edu.au/1959.4/22379.
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This thesis examines the empirical performance of four Affine Jump Diffusion models in pricing and hedging S&P 500 Index options: the Black Scholes (BS) model, Heston???s Stochastic Volatility (SV) model, a Stochastic Volatility Price Jump (SVJ) model and a Stochastic Volatility Price-Volatility Jump (SVJJ) model. The SVJJ model structure allows for simultaneous jumps in price and volatility processes, with correlated jump size distributions. To the best of our knowledge this is the first empirical study to test the hedging performance of the SVJJ model. As part of our research we derive the SVJJ model minimum variance hedge ratio. We find the SVJ model displays the best price prediction. The SV model lacks the structural complexity to eliminate Black Scholes pricing biases, whereas our results indicate the SVJJ model suffers from overfitting. Despite significant evidence from in and out-of-sample pricing that the SV and SVJ models were better specified than the BS model, this did not result in an improvement in dynamic hedging performance. Overall the BS delta hedge and SV minimum variance hedge produced the lowest errors, although their performance across moneyness-maturity categories differed greatly. The SVJ model???s results were surprisingly poor given its superior performance in out-of-sample pricing. We attribute the inadequate performance of the jump models to the lower hedging ratios these models provided, which may be a result of the negative expected jump sizes.
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Welch, Gisele Sawaya. "Application of coherence theory to enhanced backscatter and superresovling optical imaging systems." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/13705.
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Carlin, Paul. "Modelling vergence, accommodation and their interaction." Thesis, Glasgow Caledonian University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241881.
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The vergence and accommodation systems, which are examples of physiological control systems, enable us to acquire and maintain clear single images of objects at a variety of distances in our visual world. Vergence and accommodation systems are interact with one each other and have both visual and non-visual components thus adding to their complexity. This thesis reviews the evolution of control theory models of vergence and accommodation from the 1960's to the present day and has outlined several properties of the systems which require further study. The thesis introduces the concept of Fuzzy Logic Control (FLC) to models of oculomotor control. FLC offers a new approach to modelling natural control systems and produces more realistic models than those obtained using conventional control theory techniques. Several characteristics of the vergence and accommodation systems were investigated with the aim of incorporating experimental data into control theory models using conventional techniques and FLC. The accommodation response to anisometropic stimuli was measured objectively. No evidence of a non-consensual response was found, from which it can be concluded that accommodation is consensual. A control theory model of binocular accommodation was simulated to illustrate the control strategies adopted by the accommodation during anisometropic stimulation. A Virtual Reality (VR) stimulus was used to investigate the possibility of adaptation of the crosslink components of vergence and accommodation by placing different demands on the vergence and accommodation systems. Crosslink behaviour was altered as a result of the VR stimulus which suggests that the links between vergence and accommodation (accommodative vergence and vergence accommodation) are amenable to adaptation. Control theory models were used to illustrate the effects of the VR stimulus on vergence and accommodation. The effect of proximity was investigated by measuring accommodation responses in the presence and absence of proximal cues. The effect of proximal cues under closed loop conditions was found to be minimal which suggests that proximal cues are only effective when visual cues are reduced. The results were extended to include the vergence system and a FLC model of proximal vergence and accommodation was implemented. Simulation of the model produced similar findings to a previous study which supports the use of FLC in models of oculomotor control. Voluntary vergence and accommodation were measured objectively under open loop conditions in a group of naive subjects. All subjects were able to produce voluntary responses corresponding to near and far. The ability of subjects to distinguish intermediate distances was more varied. The results show that voluntary responses can be produced without training and it is suggested that voluntary vergence and accommodation may be an important mode of response. The results were included in a control model of voluntary vergence and accommodation using FLC. The work presented provides support for the use of Fuzzy Logic in models of oculomotor control which can be used to improve models and complement existing models using conventional techniques.
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Anisimova, Lyubov. "Nonlinear susceptibility study in superconductors based on Bean and Kim-Anderson models." Diss., Online access via UMI:, 2009.
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Churmakov, Dmitry. "Multipurpose Monte Carlo model for modern optical diagnostics and its biomedical applications." Thesis, Cranfield University, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.422977.
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Chen, Sijin. "Asian Spread Option Pricing Models and Computation." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2369.
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In the commodity and energy markets, there are two kinds of risk that traders and analysts are concerned a lot about: multiple underlying risk and average price risk. Spread options, swaps and swaptions are widely used to hedge multiple underlying risks and Asian (average price) options can deal with average price risk. But when those two risks are combined together, then we need to consider Asian spread options and Asian-European spread options for hedging purposes. For an Asian or Asian-European spread call option, its payoff depends on the difference of two underlyings' average price or of one average price and one final (at expiration) price. Asian and Asian-European spread option pricing is challenging work. Even under the basic assumption that each underlying price follows a log-normal distribution, the average price does not have a distribution with a simple form. In this dissertation, for the first time, a systematic analysis of Asian spread option and Asian-European spread option pricing is proposed, several original approaches for the Black-Scholes-Merton model and a special stochastic volatility model are developed and some numerical computation tests are conducted as well.
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Paulin, Carl, and Maja Lindström. "Option pricing models: A comparison between models with constant and stochastic volatilities as well as discontinuity jumps." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-172226.
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The purpose of this thesis is to compare option pricing models. We have investigated the constant volatility models Black-Scholes-Merton (BSM) and Merton’s Jump Diffusion (MJD) as well as the stochastic volatility models Heston and Bates. The data used were option prices from Microsoft, Advanced Micro Devices Inc, Walt Disney Company, and the S&P 500 index. The data was then divided into training and testing sets, where the training data was used for parameter calibration for each model, and the testing data was used for testing the model prices against prices observed on the market. Calibration of the parameters for each model were carried out using the nonlinear least-squares method. By using the calibrated parameters the price was calculated using the method of Carr and Madan. Generally it was found that the stochastic volatility models, Heston and Bates, replicated the market option prices better than both the constant volatility models, MJD and BSM for most data sets. The mean average relative percentage error for Heston and Bates was found to be 2.26% and 2.17%, respectively. Merton and BSM had a mean average relative percentage error of 6.90% and 5.45%, respectively. We therefore suggest that a stochastic volatility model is to be preferred over a constant volatility model for pricing options.Syftet med denna tes är att jämföra prissättningsmodeller för optioner. Vi har undersökt de konstanta volatilitetsmodellerna Black-Scholes-Merton (BSM) och Merton’s Jump Diffusion (MJD) samt de stokastiska volatilitetsmodellerna Heston och Bates. Datat vi använt är optionspriser från Microsoft, Advanced Micro Devices Inc, Walt Disney Company och S&P 500 indexet. Datat delades upp i en träningsmängd och en test- mängd. Träningsdatat användes för parameterkalibrering med hänsyn till varje modell. Testdatat användes för att jämföra modellpriser med priser som observerats på mark- naden. Parameterkalibreringen för varje modell utfördes genom att använda den icke- linjära minsta-kvadratmetoden. Med hjälp av de kalibrerade parametrarna kunde priset räknas ut genom att använda Carr och Madan-metoden. Vi kunde se att de stokastiska volatilitetsmodellerna, Heston och Bates, replikerade marknadens optionspriser bättre än båda de konstanta volatilitetsmodellerna, MJD och BSM för de flesta dataseten. Medelvärdet av det relativa medelvärdesfelet i procent för Heston och Bates beräknades till 2.26% respektive 2.17%. För Merton och BSM beräknades medelvärdet av det relativa medelvärdesfelet i procent till 6.90% respektive 5.45%. Vi anser därför att en stokastisk volatilitetsmodell är att föredra framför en konstant volatilitetsmodell för att prissätta optioner.
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Oh, Chang Jin, Andrew E. Lowman, Matt Dubin, Greg Smith, Eric Frater, Chunyu Zhao, and James H. Burge. "Modern technologies of fabrication and testing of large convex secondary mirrors." SPIE-INT SOC OPTICAL ENGINEERING, 2016. http://hdl.handle.net/10150/622427.
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Modern large telescopes such as TAO, LSST, TMT and EELT require 0.9m-4m monolithic convex secondary mirrors. The fabrication and testing of these large convex secondary mirrors of astronomical telescopes is getting challenging as the aperture of the mirror is getting bigger. The biggest challenge to fabricate these large convex aspheric mirrors is to measure the surface figure to a few nanometers, while maintaining the testing and fabrication cycle to be efficient to minimize the downtime. For the last a couple of decades there was huge advancement in the metrology and fabrication of large aspheric secondary mirrors. College of Optical Sciences in the University Arizona developed a full fabrication and metrology process with extremely high accuracy and efficiency for manufacturing the large convex secondary mirrors. In this paper modern metrology systems including Swing-Arm Optical Coordinate Measuring System (SOCMM) which is comparable to Interferometry and a Sub-aperture stitching interferometry scalable to a several meters have been presented. Also a Computer Controlled Fabrication Process which produces extremely fine surface figure and finish has been demonstrated. These most recent development has been applied to the fabrication and testing of 0.9m aspheric convex secondary mirror for the Tokyo Atacama Observatory's 6.5m telescope and the result has been presented.
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Strahler, Jeremy A. "Integration of an active optical system for Flexlab." Ohio : Ohio University, 2000. http://www.ohiolink.edu/etd/view.cgi?ohiou1173204753.
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Dalmagro, Lucas Bassani. "Avaliação de derivativos de taxas de juros : uma aplicação do Modelo CIR sobre opções de IDI." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/127250.
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Este trabalho tem por objetivo principal aplicar o modelo de precificação de opções de taxas de juros proposto por Barbachan e Ornelas (2003), com base nos modelos de taxa de juro e avaliação de opções de Cox, Ingerssol e Ross (1985), para avaliação de opções de compra sobre o Índice de Taxa Média de Depósitos Interfinanceiros de Um Dia (IDI), negociadas na BM&FBovespa. Para estimação dos parâmetros deste modelo, foi empregado o método de Máxima Verossimilhança. Neste contexto, também fez-se uso da fórmula de precificação de opções proposta por Black (1976), adaptada para o mercado de derivativos brasileiros, conforme implementação verificada no trabalho de Gluckstern et al. (2002). Tal aplicação torna-se interessante, pois este modelo é amplamente utilizado pelo mercado brasileiro para avaliação de opções sobre o IDI. De forma a verificar a aderência dos preços teóricos gerados pelos modelos, em comparação aos preços de mercado, métricas de erro foram empregadas. De forma geral, nossos resultados mostraram que ambos os modelos apresentam erros sistemáticos de precificação, onde o modelo CIR subavalia os prêmios das opções e o modelo de Black superprecifica. No entanto, bons resultados foram encontrados ao avaliarmos opções in-the-money e out-of-money com o modelo de Black.This work aims to apply the interest rate option pricing model proposed by Barbachan and Ornelas (2003), based on the interest rate model and option pricing model developed by Cox, Ingersoll and Ross (1985), to evaluate call options on the 1 day Brazilian Interfinancial Deposits Index - IDI, traded at BM&FBovespa. The Maximum Likelihood method was applied to estimate the model parameters. In this context, the option pricing formula proposed by Black (1976), adapted for the Brazilian derivative Market, was also used, according implementation verified in Gluckstern et al. (2002). This application becomes interesting because this model is widely used by the Brazilian Market to evaluate options on IDI. In order to verify the adherence of theoretical prices generated by the models, in comparison to the Market prices, error metrics were applied. In general, our results pointed out that both models presented systematic pricing errors, in which the CIR model underestimates the option prices and Black’s model overestimates. However, good results were found on the evaluation of options in-the-money and out-of-money with the Black’s Model.
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Cozma, Andrei. "Numerical methods for foreign exchange option pricing under hybrid stochastic and local volatility models." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:44a27fbc-1b7a-4f1a-bd2d-abeb38bf1ff7.
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In this thesis, we study the FX option pricing problem and put forward a 4-factor hybrid stochastic-local volatility model. The model, which describes the dynamics of an exchange rate, its volatility and the domestic and foreign short rates, allows for a perfect calibration to European options and has a good hedging performance. Due to the high-dimensionality of the problem, we propose a Monte Carlo simulation scheme that combines the full truncation Euler scheme for the stochastic volatility component and the stochastic short rates with the log-Euler scheme for the exchange rate. We analyze exponential integrability properties of Euler discretizations for the square-root process driving the stochastic volatility and the short rates, properties which play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a large class of stochastic differential equations in finance, including the ones studied in this thesis. Hence, we prove the strong convergence of the exchange rate approximations and the convergence of Monte Carlo estimators for a number of vanilla and exotic options. Then, we calibrate the model to market data and discuss its fitness for pricing FX options. Next, due to the relatively slow convergence of the Monte Carlo method in the number of simulations, we examine a variance reduction technique obtained by mixing Monte Carlo and finite difference methods via conditioning. We consider a purely stochastic version of the model and price vanilla and exotic options by simulating the paths of the volatility and the short rates, and then evaluating the "inner" Black-Scholes-type expectation by means of a partial differential equation. We prove the convergence of numerical approximations and carry out a theoretical variance reduction analysis. Finally, we illustrate the efficiency of the method through a detailed quantitative assessment.
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Song, Na, and 宋娜. "Mathematical models and numerical algorithms for option pricing and optimal trading." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50662168.
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Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance.
An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis.
The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem.
Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively.published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
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Bükk, Suzanne Sigurd Gunilla. "Exploring alternative price models for an application on IBM mainframe : [Master Thesis in Information Systems in Logistics] /." Göteborg : IT-universitetet, Chalmers tekniska högskola och Göteborgs universitet, 2007. http://www.ituniv.se/w/index.php?option=com_itu_thesis&Itemid=319.
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Wang, Zibo. "Quantum Optical Models of Photosynthetic Reaction Centers: A Quantum Heat Engine Perspective." Miami University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=miami1626968994170585.
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Terenzi, Giulia. "Option prices in stochastic volatility models." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC1132/document.
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L’objet de cette thèse est l’étude de problèmes d’évaluation d’options dans les modèles à volatilité stochastique. La première partie est centrée sur les options américaines dans le modèle de Heston. Nous donnons d’abord une caractérisation analytique de la fonction de valeur d’une option américaine comme l’unique solution du problème d’obstacle parabolique dégénéré associé. Notre approche est basée sur des inéquations variationelles dans des espaces de Sobolev avec poids étendant les résultats récents de Daskalopoulos et Feehan (2011, 2016) et Feehan et Pop (2015). On étudie aussi les propriétés de la fonction de valeur d’une option américaine. En particulier, nous prouvons que, sous des hypothèses convenables sur le payoff, la fonction de valeur est décroissante par rapport à la volatilité. Ensuite nous nous concentrons sur le put américaine et nous étendons quelques résultats qui sont bien connus dans le monde Black-Scholes. En particulier nous prouvons la convexité stricte de la fonction de valeur dans la région de continuation, quelques propriétés de la frontière libre, la formule de Prime d’Exercice Anticipée et une forme faible de la propriété du smooth fit. Les techniques utilisées sont de type probabiliste. Dans la deuxième partie nous abordons le problème du calcul numérique du prix des options européennes et américaines dans des modèles à volatilité stochastiques et avec sauts. Nous étudions d’abord le modèle de Bates-Hull-White, c’est-à-dire le modèle de Bates avec un taux d’intérêt stochastique. On considère un algorithme hybride rétrograde qui utilise une approximation par chaîne de Markov (notamment un arbre “avec sauts multiples”) dans la direction de la volatilité et du taux d’intérêt et une approche (déterministe) par différence finie pour traiter le processus de prix d’actif. De plus, nous fournissons une procédure de simulation pour des évaluations Monte Carlo. Les résultats numériques montrent la fiabilité et l’efficacité de ces méthodes. Finalement, nous analysons le taux de convergence de l’algorithme hybride appliqué à des modèles généraux de diffusion avec sauts. Nous étudions d’abord la convergence faible au premier ordre de chaînes de Markov vers la diffusion sous des hypothèses assez générales. Ensuite nous prouvons la convergence de l’algorithme: nous étudions la stabilité et la consistance de la méthode hybride par une technique qui exploite les caractéristiques probabilistes de l’approximation par chaîne de MarkovWe study option pricing problems in stochastic volatility models. In the first part of this thesis we focus on American options in the Heston model. We first give an analytical characterization of the value function of an American option as the unique solution of the associated (degenerate) parabolic obstacle problem. Our approach is based on variational inequalities in suitable weighted Sobolev spaces and extends recent results of Daskalopoulos and Feehan (2011, 2016) and Feehan and Pop (2015). We also investigate the properties of the American value function. In particular, we prove that, under suitable assumptions on the payoff, the value function is nondecreasing with respect to the volatility variable. Then, we focus on an American put option and we extend some results which are well known in the Black and Scholes world. In particular, we prove the strict convexity of the value function in the continuation region, some properties of the free boundary function, the Early Exercise Price formula and a weak form of the smooth fit principle. This is done mostly by using probabilistic techniques.In the second part we deal with the numerical computation of European and American option prices in jump-diffusion stochastic volatility models. We first focus on the Bates-Hull-White model, i.e. the Bates model with a stochastic interest rate. We consider a backward hybrid algorithm which uses a Markov chain approximation (in particular, a “multiple jumps” tree) in the direction of the volatility and the interest rate and a (deterministic) finite-difference approach in order to handle the underlying asset price process. Moreover, we provide a simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed methods.Finally, we analyze the rate of convergence of the hybrid algorithm applied to general jump-diffusion models. We study first order weak convergence of Markov chains to diffusions under quite general assumptions. Then, we prove the convergence of the algorithm, by studying the stability and the consistency of the hybrid scheme, in a sense that allows us to exploit the probabilistic features of the Markov chain approximation
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Payne, M. K. "Hedging and trading models for currency options portfolios." Thesis, Imperial College London, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.296907.
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Mimouni, Karim. "Three essays on volatility specification in option valuation." Thesis, McGill University, 2007. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103274.
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Most recent empirical option valuation studies build on the affine square root (SQR) stochastic volatility model. The SQR model is a convenient choice, because it yields closed-form solutions for option prices. However, relatively little is known about the empirical shortcomings of this model. In the first essay, we investigate alternatives to the SQR model, by comparing its empirical performance with that of five different but equally parsimonious stochastic volatility models. We provide empirical evidence from three different sources. We first use realized volatilities to assess the properties of the SQR model and to guide us in the search for alternative specifications. We then estimate the models using maximum likelihood on a long sample of S& P500 returns. Finally, we employ nonlinear least squares on a time series of cross sections of option data. In the estimations on returns and options data, we use the particle filtering technique to retrieve the spot volatility path. The three sources of data we employ all point to the same conclusion: the SQR model is misspecified. Overall, the best of alternative volatility specifications is a model we refer to as the VAR model, which is of the GARCH diffusion type.In the second essay, we estimate the Constant Elasticity of Variance (CEV) model in order to study the level of nonlinearity in the volatility dynamic. We also estimate a CEV process combined with a jump process (CEVJ) and analyze the effects of the jump component on the nonlinearity coefficient. Estimation is performed using the particle filtering technique on a long series of S&P500 returns and on options data. We find that both returns data and returns-and-options data favor nonlinear specifications for the volatility dynamic, suggesting that the extensive use of linear models is not supported empirically. We also find that the inclusion of jumps does not affect the level of nonlinearity and does not improve the CEV model fit.
The third essay provides an empirical comparison of two classes of option valuation models: continuous-time models and discrete-time models. The literature provides some theoretical limit results for these types of dynamics, and researchers have used these limit results to argue that the performance of certain discrete-time and continuous-time models ought to be very similar. This interpretation is somewhat contentious, because a given discrete-time model can have several continuous-time limits, and a given continuous-time model can be the limit for more than one discrete-time model. Therefore, it is imperative to investigate whether there exist similarities between these specifications from an empirical perspective. Using data on S&P500 returns and call options, we find that the discrete-time models investigated in this paper have the same performance in fitting the data as selected continuous-time models both in and out-of-sample.
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Le, Truc. "Stochastic volatility models." Monash University, School of Mathematical Sciences, 2005. http://arrow.monash.edu.au/hdl/1959.1/5181.
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