Theoretical and numerical modeling of optical systems are increasingly being utilized in a wide range of areas in physics and engineering for characterizing and improving existing systems or developing new methods. This dissertation focuses on determining and improving the performance of imaging and non-imaging optical systems through modeling and developing model-aware enhancement methods. We evaluate the performance, demonstrate enhancements in terms of resolution and light collection efficiency, and improve the capabilities of the systems through changes to the system design and through post-processing techniques. We consider application areas in integrated circuit (IC) imaging for fault analysis and malicious circuitry detection, and free-form lens design for creating prescribed illumination patterns. The first part of this dissertation focuses on sub-surface imaging of ICs for fault analysis using a solid immersion lens (SIL) microscope. We first derive the Green's function of the microscope and use it to determine its resolution limits for bulk silicon and silicon-on-insulator (SOI) chips. We then propose an optimization framework for designing super-resolving apodization masks that utilizes the developed model and demonstrate the trade-offs in designing such masks. Finally, we derive the full electromagnetic model of the SIL microscope that models the image of an arbitrary sub-surface structure. With the rapidly shrinking dimensions of ICs, we are increasingly limited in resolving the features and identifying potential modifications despite the resolution improvements provided by the state-of-the-art microscopy techniques and enhancement methods described here. In the second part of this dissertation, we shift our focus away from improving the resolution and consider an optical framework that does not require high resolution imaging for detecting malicious circuitry. We develop a classification-based high-throughput gate identification method that utilizes the physical model of the optical system. We then propose a lower-throughput system to increase the detection accuracy, based on higher resolution imaging to supplement the former method. Finally, we consider the problem of free-form lens design for forming prescribed illumination patterns as a non-imaging application. Common methods that design free-form lenses for forming patterns consider the input light source to be a point source, however using extended light sources with such lenses lead to significant blurring in the resulting pattern. We propose a deconvolution-based framework that utilizes the lens geometry to model the blurring effects and eliminates this degradation, resulting in sharper patterns.

Neste trabalho buscou-se consolidar a união entre três áreas do conhecimento: a parametrização de curvas e superfícies do tipo B-spline racionais não-uniformes (NURBS), a otimização matemática e a análise estrutural por elementos finitos. A união destas três áreas é realizada neste trabalho através da otimização de formas de cascas, devido ao fato de que as características mecânicas dos materiais devem refletir-se na forma da estrutura e sua distribuição de espessura expressando um máximo desempenho. Estas variáveis, forma e distribuição de espessura, possuem um rol dominante nos projetos de engenharia, já que mínimas quantidades de materiais, uma frequência específica, um estado puro de tensões de membrana são típicos objetivos de projeto. Neste contexto, obter a forma e a distribuição de espessura adequadas são conceitos intrínsecos à otimização estrutural. Portanto, implementaram-se técnicas para modificar a geometria de cascas, sem perder a parametrização, sem a necessidade de gerar uma nova malha de elementos finitos ao se modificar a forma e ainda ter controle sobre a distorção da malha para evitar erros numéricos inaceitáveis. A modificação de forma é fomentada pelo código de otimização, programação quadrática sequencial (SQP), motivado pelas análises da casca por elementos finitos. A modificação de forma é realizada pela técnica de deformação livre de forma (free-form deformation) com a parametrização NURBS. Nos resultados da otimização de formas de cascas obtiveram-se cascas com alto desempenho estrutural e esteticamente agradáveis. / Consolidation of the link among three fields, curves and surfaces described by non-uniform rational B-spline (NURBS), mathematical optimization and finite element structural analysis, applied to shape optimization of shells, is the main objective of this work. Shape optimization of shells are performed taking into account the fact that the material mechanical caracteristics influence the structural shape and the thickness variation in order to obtain the best performace. These two variables, shape and thickness variation, have an essential role considering that the minimum material quantities, a specific frequency and a pure membrane stress state are typical design objectives. Suitable shapes and thickness variation are intrinsic concepts of structural optimization. Therefore, some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation and controlling mesh distortion in order to avoid relevant numerical errors. The shape modification is conducted by the optimization code and it is based in the data obtained by finite element analysis. In this work the optimization procedure is performed using a Sequential Quadratic Programming (SQP) algorithm, while the shape modification is carried out by the freeform deformation technique, based on NURBS parameterization. As a consequence of the shape optimization, shells with high structural performance and esthetically beautiful were obtained.

Neste trabalho buscou-se consolidar a união entre três áreas do conhecimento: a parametrização de curvas e superfícies do tipo B-spline racionais não-uniformes (NURBS), a otimização matemática e a análise estrutural por elementos finitos. A união destas três áreas é realizada neste trabalho através da otimização de formas de cascas, devido ao fato de que as características mecânicas dos materiais devem refletir-se na forma da estrutura e sua distribuição de espessura expressando um máximo desempenho. Estas variáveis, forma e distribuição de espessura, possuem um rol dominante nos projetos de engenharia, já que mínimas quantidades de materiais, uma frequência específica, um estado puro de tensões de membrana são típicos objetivos de projeto. Neste contexto, obter a forma e a distribuição de espessura adequadas são conceitos intrínsecos à otimização estrutural. Portanto, implementaram-se técnicas para modificar a geometria de cascas, sem perder a parametrização, sem a necessidade de gerar uma nova malha de elementos finitos ao se modificar a forma e ainda ter controle sobre a distorção da malha para evitar erros numéricos inaceitáveis. A modificação de forma é fomentada pelo código de otimização, programação quadrática sequencial (SQP), motivado pelas análises da casca por elementos finitos. A modificação de forma é realizada pela técnica de deformação livre de forma (free-form deformation) com a parametrização NURBS. Nos resultados da otimização de formas de cascas obtiveram-se cascas com alto desempenho estrutural e esteticamente agradáveis. / Consolidation of the link among three fields, curves and surfaces described by non-uniform rational B-spline (NURBS), mathematical optimization and finite element structural analysis, applied to shape optimization of shells, is the main objective of this work. Shape optimization of shells are performed taking into account the fact that the material mechanical caracteristics influence the structural shape and the thickness variation in order to obtain the best performace. These two variables, shape and thickness variation, have an essential role considering that the minimum material quantities, a specific frequency and a pure membrane stress state are typical design objectives. Suitable shapes and thickness variation are intrinsic concepts of structural optimization. Therefore, some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation and controlling mesh distortion in order to avoid relevant numerical errors. The shape modification is conducted by the optimization code and it is based in the data obtained by finite element analysis. In this work the optimization procedure is performed using a Sequential Quadratic Programming (SQP) algorithm, while the shape modification is carried out by the freeform deformation technique, based on NURBS parameterization. As a consequence of the shape optimization, shells with high structural performance and esthetically beautiful were obtained.

Neste trabalho buscou-se consolidar a união entre três áreas do conhecimento: a parametrização de curvas e superfícies do tipo B-spline racionais não-uniformes (NURBS), a otimização matemática e a análise estrutural por elementos finitos. A união destas três áreas é realizada neste trabalho através da otimização de formas de cascas, devido ao fato de que as características mecânicas dos materiais devem refletir-se na forma da estrutura e sua distribuição de espessura expressando um máximo desempenho. Estas variáveis, forma e distribuição de espessura, possuem um rol dominante nos projetos de engenharia, já que mínimas quantidades de materiais, uma frequência específica, um estado puro de tensões de membrana são típicos objetivos de projeto. Neste contexto, obter a forma e a distribuição de espessura adequadas são conceitos intrínsecos à otimização estrutural. Portanto, implementaram-se técnicas para modificar a geometria de cascas, sem perder a parametrização, sem a necessidade de gerar uma nova malha de elementos finitos ao se modificar a forma e ainda ter controle sobre a distorção da malha para evitar erros numéricos inaceitáveis. A modificação de forma é fomentada pelo código de otimização, programação quadrática sequencial (SQP), motivado pelas análises da casca por elementos finitos. A modificação de forma é realizada pela técnica de deformação livre de forma (free-form deformation) com a parametrização NURBS. Nos resultados da otimização de formas de cascas obtiveram-se cascas com alto desempenho estrutural e esteticamente agradáveis. / Consolidation of the link among three fields, curves and surfaces described by non-uniform rational B-spline (NURBS), mathematical optimization and finite element structural analysis, applied to shape optimization of shells, is the main objective of this work. Shape optimization of shells are performed taking into account the fact that the material mechanical caracteristics influence the structural shape and the thickness variation in order to obtain the best performace. These two variables, shape and thickness variation, have an essential role considering that the minimum material quantities, a specific frequency and a pure membrane stress state are typical design objectives. Suitable shapes and thickness variation are intrinsic concepts of structural optimization. Therefore, some techniques were implemented to modify the shell geometry conserving the same parameterization without a new finite element mesh generation and controlling mesh distortion in order to avoid relevant numerical errors. The shape modification is conducted by the optimization code and it is based in the data obtained by finite element analysis. In this work the optimization procedure is performed using a Sequential Quadratic Programming (SQP) algorithm, while the shape modification is carried out by the freeform deformation technique, based on NURBS parameterization. As a consequence of the shape optimization, shells with high structural performance and esthetically beautiful were obtained.

A typical approach to optimize wind turbine blades separates the airfoil shape design from the blade planform design. This approach is sequential, where the airfoils along the blade span are pre-selected or optimized and then held constant during the blade planform optimization. In contrast, integrated blade design optimizes the airfoils and the blade planform concurrently and thereby has the potential to reduce cost of energy (COE) more than sequential design. Nevertheless, sequential design is commonly performed because of the ease of precomputation, or the ability to compute the airfoil analyses prior to the blade optimization. This research investigates two integrated blade design approaches, the precomputational and free-form methods, that are compared to sequential blade design. The first approach is called the precomputational method because it maintains the ability to precompute, similar to sequential design, and allows for partially flexible airfoil shapes. This method compares three airfoil analysis methods: a panel method (XFOIL), a Reynolds-averaged Navier-Stokes computational fluid dynamics method (RANS CFD), and using wind tunnel data. For each airfoil analysis method, there are two airfoil parameterization methods: the airfoil thickness-to-chord ratio and blended airfoil family factor. The second approach is called the free-form method because it allows for fully flexible airfoil shapes, but no longer has the ease of precomputation as the airfoil analyses are performed during the blade optimization. This method compares XFOIL and RANS CFD using the class-shape-transformation (CST) method to parameterize the airfoil shapes. This study determines if the precomputational method can capture the majority of the benefit from integrated design or if there is a significant additional benefit from the free-form method. Optimizing the NREL 5-MW reference turbine shows that integrated design reduce COE significantly more than sequential design. The precomputational method improved COE more than sequential design by 1.6%, 2.8%, and 0.7% using the airfoil thickness-to-chord ratio, and by 2.2%, 3.3%, and 1.4% using the blended airfoil family factor when using XFOIL, RANS CFD, and wind tunnel data, respectively. The free-form method improved COE more than sequential design by 2.7% and 4.0% using the CST method with XFOIL and RANS CFD, respectively. The additional flexibility in airfoil shape reduced COE primarily through an increase in annual energy production. The precomputational method captures the majority of the benefit of integrated design (about 80%) for minimal additional computational cost and complexity, but the free-form method provides modest additional benefits if the extra effort is made in computational cost and development time.

In today's competitive manufacturing industries, companies strive to reduce manufacturing development costs and lead times in hopes of reducing costs and capturing more market share from early release of their new or redesigned products. Tooling lead time constraints are some of the more significant challenges facing product development of advanced free-form components. This is especially true for complex designs in which large dies, molds or other large forming tools are required. The lead time for tooling, in general, consists of three main components; material acquisition, tool design and engineering, and tool manufacturing. Lead times for material acquisition and tool manufacture are normally a function of vendor/outsourcing constraints, manufacturing techniques and complexity of tooling being produced. The tool design and engineering component is a function of available manpower, engineering expertise, type of design problem (initial design or redesign of tooling), and complexity of the design problem. To reduce the tool design/engineering lead time, many engineering groups have implemented Computer-Aided Design, Engineering, and Manufacturing (CAD/CAE/CAM or CAx) tools as their standard practice for the design and analysis of their products. Although the predictive capabilities are efficient, using CAx tools to expedite advanced die design is time consuming due to the free-form nature and complexity of the desired part geometry. Design iterations can consume large quantities of time and money, thus driving profit margins down or even being infeasible from a cost and schedule standpoint. Any savings based on a reduction in time are desired so long as quality is not sacrificed. This thesis presents an automated tool design methodology that integrates state-of-the-art numerical surface fitting methods with commercially available CAD/CAE/CAM technologies and optimization software. The intent is to virtually create tooling wherein work-piece geometries have been optimized producing products that capture accurate design intent. Results show a significant reduction in design/engineering tool development time. This is due to the integration and automation of associative tooling surfaces automatically derived from the known final design intent geometry. Because this approach extends commercially available CAx tools, this thesis can be used as a blueprint for any automotive or aerospace tooling need to eliminate significant time and costs from the manufacture of complex free-form components.

Compact and lightweight optical designs achieving acceptable image quality, field of view, eye clearance, eyebox size, operating across the visible spectrum, are the key to the success of next generation head-worn displays. The first part of this thesis reports on the design, fabrication, and analysis of off-axis magnifier designs. The first design is catadioptric and consists of two elements. The lens utilizes a diffractive optical element and the mirror has a free-form surface described with an x-y polynomial. A comparison of color correction between doublets and single layer diffractive optical elements in an eyepiece as a function of eye clearance is provided to justify the use of a diffractive optical element. The dual-element design has an 8 mm diameter eyebox, 15 mm eye clearance, 20 degree diagonal full field, and is designed to operate across the visible spectrum between 450-650 nm. 20% MTF at the Nyquist frequency with less than 3% distortion has been achieved in the dual-element head-worn display. An ideal solution for a head-worn display would be a single free-form surface mirror design. A single surface mirror does not have dispersion; therefore, color correction is not required. A single surface mirror can be made see-through by machining the appropriate surface shape on the opposite side to form a zero power shell. The second design consists of a single off-axis free-form mirror described with an x-y polynomial, which achieves a 3 mm diameter exit pupil, 15 mm eye relief, and a 24 degree diagonal full field of view. The second design achieves 10% MTF at the Nyquist frequency set by the pixel spacing of the VGA microdisplay with less than 3% distortion. Both designs have been fabricated using diamond turning techniques. Finally, this thesis addresses the question of what is the optimal surface shape for a single mirror constrained in an off-axis magnifier configuration with multiple fields? Typical optical surfaces implemented in raytrace codes today are functions mapping two dimensional vectors to real numbers. The majority of optical designs to-date have relied on conic sections and polynomials as the functions of choice. The choice of conic sections is justified since conic sections are stigmatic surfaces under certain imaging geometries. The choice of polynomials from the point of view of surface description can be challenged. A polynomial surface description may link a designer s understanding of the wavefront aberrations and the surface description. The limitations of using multivariate polynomials are described by a theorem due to Mairhuber and Curtis from approximation theory. This thesis proposes and applies radial basis functions to represent free-form optical surfaces as an alternative to multivariate polynomials. We compare the polynomial descriptions to radial basis functions using the MTF criteria. The benefits of using radial basis functions for surface description are summarized in the context of specific head-worn displays. The benefits include, for example, the performance increase measured by the MTF, or the ability to increase the field of view or pupil size. Even though Zernike polynomials are a complete and orthogonal set of basis over the unit circle and they can be orthogonalized for rectangular or hexagonal pupils using Gram-Schmidt, taking practical considerations into account, such as optimization time and the maximum number of variables available in current raytrace codes, for the specific case of the single off-axis magnifier with a 3 mm pupil, 15 mm eye relief, 24 degree diagonal full field of view, we found the Gaussian radial basis functions to yield a 20% gain in the average MTF at 17 field points compared to a Zernike (using 66 terms) and an x-y polynomial up to and including 10th order. The linear combination of radial basis function representation is not limited to circular apertures. Visualization tools such as field map plots provided by nodal aberration theory have been applied during the analysis of the off-axis systems discussed in this thesis. Full-field displays are used to establish node locations within the field of view for the dual-element head-worn display. The judicious separation of the nodes along the x-direction in the field of view results in well-behaved MTF plots. This is in contrast to an expectation of achieving better performance through restoring symmetry via collapsing the nodes to yield field-quadratic astigmatism.

No description available.

This thesis proposes a hypothetical building that intends to provide a relatively "private space" while in a public park to facilitate a conversation with therapists, small group-talk sessions, and classrooms to practice yoga. People are encouraged to walk and talk, and exercises are methods of psychotherapy. The architecture plan of this thesis encourages people with depression to evolve with others, and all programs have at least two people as a group. The distance between the two is the main key for all the designing of space. In other words, this thesis is also about a study of human psychology about "comfort zones." / Overall, the project is going to be a two-story building on the empty space of an urban park while its existence does not break the original park's intention which is providing space for the community to relax and enjoy life. It is a project with its form and function that embodies care for humanity physically and psychologically.

Yes / This paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitrary set of boundary conditions. Both the boundary conditions which are defined as curves in 3-space and the spine of the corresponding PDE are utilized as interactive design tools for creating and manipulating geometry intuitively. In order to facilitate interactive design in real time, a compact analytic solution for the chosen arbitrary order PDE is formulated. This solution scheme even in the case of general boundary conditions satisfies exactly the boundary conditions where the resulting surface has an closed form representation allowing real time shape manipulation. In order to enable users to appreciate the powerful shape design and manipulation capability of the method, we present a set of practical examples.