In situ surface topography measurement method of granite base in scanning wafer stage with laser interferometer

Topography of a granite surface has an effect on the vertical positioning of a wafer stage in a lithographic tool, when the wafer stage moves on the granite. The inaccurate measurement of the topography results in a bad leveling and focusing performance. In this paper, an in situ method to measure the topography of a granite surface with high accuracy is present. In this method, a high-order polynomial is set up to express the topography of the granite surface. Two double-frequency laser interferometers are used to measure the tilts of the wafer stage in the X- and Y-directions. From the sampling tilts information, the coefficients of the high-order polynomial can be obtained by a special algorithm. Experiment results shows that the measurement reproducibility of the method is better than 10 nm. (c) 2006 Elsevier GmbH. All rights reserved.

Distributed Optimal Control of Cyber-Physical Systems: Controller Synthesis, Architecture Design and System Identification

The centralized paradigm of a single controller and a single plant upon which modern control theory is built is no longer applicable to modern cyber-physical systems of interest, such as the power-grid, software defined networks or automated highways systems, as these are all large-scale and spatially distributed. Both the scale and the distributed nature of these systems has motivated the decentralization of control schemes into local sub-controllers that measure, exchange and act on locally available subsets of the globally available system information. This decentralization of control logic leads to different decision makers acting on asymmetric information sets, introduces the need for coordination between them, and perhaps not surprisingly makes the resulting optimal control problem much harder to solve. In fact, shortly after such questions were posed, it was realized that seemingly simple decentralized optimal control problems are computationally intractable to solve, with the Wistenhausen counterexample being a famous instance of this phenomenon. Spurred on by this perhaps discouraging result, a concerted 40 year effort to identify tractable classes of distributed optimal control problems culminated in the notion of quadratic invariance, which loosely states that if sub-controllers can exchange information with each other at least as quickly as the effect of their control actions propagates through the plant, then the resulting distributed optimal control problem admits a convex formulation.

The identification of quadratic invariance as an appropriate means of "convexifying" distributed optimal control problems led to a renewed enthusiasm in the controller synthesis community, resulting in a rich set of results over the past decade. The contributions of this thesis can be seen as being a part of this broader family of results, with a particular focus on closing the gap between theory and practice by relaxing or removing assumptions made in the traditional distributed optimal control framework. Our contributions are to the foundational theory of distributed optimal control, and fall under three broad categories, namely controller synthesis, architecture design and system identification.

We begin by providing two novel controller synthesis algorithms. The first is a solution to the distributed H-infinity optimal control problem subject to delay constraints, and provides the only known exact characterization of delay-constrained distributed controllers satisfying an H-infinity norm bound. The second is an explicit dynamic programming solution to a two player LQR state-feedback problem with varying delays. Accommodating varying delays represents an important first step in combining distributed optimal control theory with the area of Networked Control Systems that considers lossy channels in the feedback loop. Our next set of results are concerned with controller architecture design. When designing controllers for large-scale systems, the architectural aspects of the controller such as the placement of actuators, sensors, and the communication links between them can no longer be taken as given -- indeed the task of designing this architecture is now as important as the design of the control laws themselves. To address this task, we formulate the Regularization for Design (RFD) framework, which is a unifying computationally tractable approach, based on the model matching framework and atomic norm regularization, for the simultaneous co-design of a structured optimal controller and the architecture needed to implement it. Our final result is a contribution to distributed system identification. Traditional system identification techniques such as subspace identification are not computationally scalable, and destroy rather than leverage any a priori information about the system's interconnection structure. We argue that in the context of system identification, an essential building block of any scalable algorithm is the ability to estimate local dynamics within a large interconnected system. To that end we propose a promising heuristic for identifying the dynamics of a subsystem that is still connected to a large system. We exploit the fact that the transfer function of the local dynamics is low-order, but full-rank, while the transfer function of the global dynamics is high-order, but low-rank, to formulate this separation task as a nuclear norm minimization problem. Finally, we conclude with a brief discussion of future research directions, with a particular emphasis on how to incorporate the results of this thesis, and those of optimal control theory in general, into a broader theory of dynamics, control and optimization in layered architectures.

Corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media

The coupled differential recurrence equations for the corrections to the paraxial approximation solutions in transversely nonuniform refractive-index media are established in terms of the perturbation method. All the corrections (including the longitudinal field corrections) to the paraxial approximation solutions are presented in the weak-guidance approximation. As a concrete application, the first-order longitudinal field correction and the second-order transverse field correction to the paraxial approximation of a Gaussian beam propagating in a transversely quadratic refractive index medium are analytically investigated. (C) 1999 Optical Society of America [S0740-3232(99)00310-5].

Company financial performance: Does board size matter? Case of the EUROSTOXX50 index

[EN] This study analyzes the relationship between board size and economic-financial performance in a sample of European firms that constitute the EUROSTOXX50 Index. Based on previous literature, resource dependency and agency theories, and considering regulation developed by the OECD and European Union on the normative of corporate governance for each country in the sample, the authors propose the hypotheses of both positive linear and quadratic relationships between the researched parameters. Using ROA as a benchmark of financial performance and the number of members of the board as measurement of the board size, two OLS estimations are performed. To confirm the robustness of the results the empirical study is tested with two other similar financial ratios, ROE and Tobin s Q. Due to the absence of significant results, an additional factor, firm size, is employed in order to check if it affects firm performance. Delving further into the nature of this relationship, it is revealed that there exists a strong and negative relation between firm size and financial performance. Consequently, it can be asseverated that the generic recommendation one size fits all cannot be applied in this case; which conforms to the Recommendations of the European Union that dissuade using generic models for all countries.

Estimativa de erros no cálculo de gradientes em malhas de Voronoi

O presente trabalho propõe analisar metodologias para o cálculo do gradiente em malhas não-estruturadas do tipo Voronoi que são utilizadas no método de Volumes Finitos. Quatro metodologias para o cálculo do gradiente são testadas e comparadas com soluções analíticas. As técnicas utilizadas são: Método do Balanço de Forças, Método do Mínimo Resíduo Quadrático, Método da Média dos Gradientes Projetos e Método da Média dos Gradientes Projetados Corrigidos. Uma análise por série de Taylor também foi feita, e as equações analíticas comparadas com resultados numéricos. Os testes são realizados em malhas cartesianas e malhas triangulares, que em um trabalho anterior apresentaram alguns resultados inconsistentes. A influência do ponto gerador e do ângulo de rotação é analisada. É verificado que a posição do ponto gerador e a metodologia utilizada em cada malha influencia no cálculo do gradiente. Dependendo da malha e da metodologia utilizada, as equações analíticas indicaram que existem erros associados, que prejudicam o cálculo do gradiente.

Propagation properties of off-axis Hermite-cosh-Gaussian beam combinations through a first-order optical system

Based on the Collins integral formula, the analytic expressions of propagation of the coherent and the incoherent off-axis Hermite-cosh-Gaussian (HChG) beam combinations with rectangular symmetry passing through a paraxial first-order optical system are derived, and corresponding numerical examples are given and analysed. The resulting beam quality is discussed in terms of power in the bucket (PIB). The study suggests that the resulting beam cannot keep the initial intensity shape during the propagation and the beam quality for coherent mode is not always better than that for incoherent mode. Reviewing the numerical simulations of Gaussian, Hermite-Gaussian (HG) and cosh Gaussian (ChG) beam combinations indicates that the Hermite polynomial exerts a chief influence on the irradiance profile of composite beam and far field power concentration.

Modelagem e otimização de experimentos para o tratamento térmico de recozimento: um estudo com o algoritmo simulated annealing

Esta dissertação apresenta um estudo da modelagem de experimentos aplicados a um processo industrial de tratamento térmico. A motivação deste trabalho surgiu diante das dificuldades associadas aos processos de recozimento industrial de aços do tipo baixa liga, na tentativa de encontrar temperaturas nas quais as durezas superficiais dos aços atingissem valores suficientemente baixos, adequados para etapas posteriores de fabricação, em especial a usinagem. Inicialmente forem realizados diversos experimentos com diferentes aços, onde a dureza superficial é obtida em função da temperatura de recozimento e dos teores de carbono e silício das amostras utilizadas. Em seguida propôs-se um modelo quadrático para modelar a dureza superficial como função dessas três variáveis. A estimação de parâmetros do modelo proposto foi realizada com o emprego do algoritmo Simulated Annealing, uma meta-heurística para otimização global que procura imitar o processo de recozimento de um material sólido. Finalmente, usando-se o modelo proposto, foi resolvido o chamado problema inverso, o qual consiste na estimação da temperatura de recozimento em função dos teores de carbono e silício e da dureza desejada.

Intense frequency upconversion fluorescence of Er3+/Yb3+ co-doped lithium-strontium-lead-bismuth glasses

Infrared-to-visible upconversion fluorescence of Er(3+)/Yb(3+) co-doped lithium-strontium-lead-bismuth (LSPB) glasses for developing potential upconversion lasers has been studied under 975-nm excitation. Based on the results of energy transfer efficiency and upconversion spectra, the optimal Yb(3+)-Er(3+) concentration ratio is found to be 5:1. Intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions 2H_(11/2)-->4I_(15/2), 4S_(3/2)-->4I_(15/2), and 4F_(9/2)-->4I_(15/2), respectively, were observed. The quadratic dependence of the 525-, 546-, and 657-nm emissions on excitation power indicates that a two-photon absorption process occurs under 975-nm excitation. The high-populated 4I_(11/2) level is supposed to serve as the intermediate state responsible for the upconversion processes. The intense upconversion luminescence of Er(3+)/Yb(3+) co-doped LSPB glasses may be a potentially useful material for developing upconversion optical devices.

Energy transfer and infrared-to-visible upconversion luminescence of Er3+/Yb3+-codoped halide modified tellurite glasses

We report on the energy transfer and frequency upconversion spectroscopic properties of Er3+-doped and Er3+/Yb3+-codoped TeO2-ZnO-Na2O-PbCl2 halide modified tellurite glasses upon excitation with 808 and 978 nm laser diode. Three intense emissions centered at around 529, 546 and 657 nm, alongwith a very weak blue emission at 4 10 nm have clearly been observed for the Er3+/Yb3+-codoped halide modified tellurite glasses upon excitation at 978 nm and the involved mechanisms are explained. The quadratic dependence of fluorescence on excitation laser power confirms the fact that the two-photon contribute to the infrared to green-red upconversion emissions. And the blue upconversion at 410 nm involved a sequential three-photon absorption process. (c) 2005 Elsevier Ltd. All rights reserved.

Frequency up-conversion properties of Er3(+)-doped TeO2-ZnO-PbCl2 oxyhalide tellurite glasses

This paper reports on the successful preparation and a detailed study on the up-conversion properties of Er3+ -doped TeO2-ZnO-PbCl2 oxylialide tellurite glasses. Three intense emissions centered at around 527, 549 and 666 nm have been clearly observed under 977 nm excitation and the involved mechanisms have been explained. The green emissions centered at 527 and 549 nin are due to the H-2(11/2 ->) I-4(15/2) and S-4(3/2) -> I-4(15/2) transitions, and the red up-conversion emission centered at 666 nm is associated with the F-4(9/2) -> I-4(15/2) transitions of Er3+ ions, respectively. The quadratic dependence of fluorescence on excitation laser power confirm that two-photons contribute to up-conversion of the green-red emissions. (c) 2005 Elsevier B.V. All rights reserved.

Efficient frequency upconversion emission in Er3+-doped novel strontium lead bismuth glass

Er3+ -doped strontium lead bismuth glass for developing upconversion lasers has been fabricated and characterized. The Judd-Ofelt intensity parameters Omega(1) (t = 2,4,6), calculated based on the experimental absorption spectrum and Judd-Ofelt theory, were found to be Omega(2) = 2.95 x 10(-20), Omega(4) = 0-91 X 10(-20), and Omega(6) = 0.36 x 10(-20) cm(2). Under 975 nm excitation, intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions H-2(11/2) --> I-4(15/2), S-4(3/2) I-4(15/2), and F-4(9/2) --> I-4(15/2) respectively were observed. The upconversion mechanisms are discussed based oil the energy matching and quadratic dependence on excitation power, and the dominant mechanisms are excited state absorption and energy transfer upconversion for the green and red emissions. The long-lived I-4(11/2) level is supposed to serve as the intermediate state responsible for the upconversion processes. (C) 2004 Published by Elsevier B.V.

Infrared-to-visible upconversion flurescence of Er3+/Yb3+-codoped bismuthate glasses

Er3+/Yb3+-codoped bismuthate glasses for developing potential upconversion lasers have been fabricated and characterized. The optimal Yb3+ doping content was investigated in the glasses with different Yb3+-Er3+ concentration ratios and the optimal Yb3+-Er3+ concentration ratio is 5:1. Under 975 nm excitation, intense green and red emissions centered at 525, 546 and 657 nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2) and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The quadratic dependence of the 525, 546 and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs under 975 nm excitation. (c) 2004 Elsevier Ltd. All rights reserved.

Infrared-to-visible upconversion fluorescence of Er3+-doped novel lithium-barium-lead-bismuth glass

Er3+-doped lithium-barium-lead-bismuth glass for developing upconversion lasers has been fabricated and characterized. The Judd-Ofelt intensity parameters Omega(t) (t = 2, 4, 6), calculated based on the experimental absorption spectrum and Judd-Ofelt theory, were found to be Omega(2) = 3.05 x 10(-20) cm(2), Omega(4) = 0.95 x 10(-20) cm(2), and Omega(6) = 0.39 x 10(-20) cm(2). Under 975 nm excitation, intense green and red emissions centered at 525, 546, and 657 nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The upconversion mechanisms are discussed based on the energy matching and quadratic dependence on excitation power, and the dominant mechanisms are excited state absorption and energy transfer upconversion for the green and red emissions. The long-lived I-4(11/2) level is supposed to serve as the intermediate state responsible for the intense upconversion processes. The intense upconversion luminescence of Er3+-doped lithium-barium-lead-bismuth glass may be a potentially useful material for developing upconversion optical devices. (c) 2004 Elsevier B.V. All rights reserved.

Upconversion fluorescence property of Er3+/Yb3+-codoped novel bismuth-germanium glass

Infrared-to-visible upconversion fluorescence property of Er3+/Yb3+ codoped novel bismuth-germanium glass under 975 nm LD excitation has been studied. Intense green and red emissions centered at 525, 546 and 657 nm, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed at room temperature. The quadratic dependence of the 525, 546 and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs. The structure of the bismuth-germanium glass has been investigated by peak-deconvolution of FT-Raman spectrum, and the structural information was obtained from the peak wavenumbers. This novel bismuth-germanium glass with low maximum phonon energy (similar to 750 cm(-1)) can be used as potential host material for upconversion lasers. (c) 2005 Elsevier Ltd. All rights reserved.

Intense frequency upconversion fluorescence of Er3+/Yb3+-codoped novel potassium-barium-strontium-lead-bismuth glasses

Er3+/Yb3+-codoped potassium-barium-strontium-lead-bismuth glasses for developing potential upconversion lasers have been fabricated and characterized. Based on the results of energy transfer efficiency, the optimal Yb3+/Er3+ concentration ratio is found to be 5:1. Intense green and red emissions centered at 525, 546, and 657 run, corresponding to the transitions H-2(11/2) -> I-4(15/2), S-4(3/2) -> I-4(15/2), and F-4(9/2) -> I-4(15/2), respectively, were observed. The quadratic dependence of the 525, 546, and 657 nm emissions on excitation power indicates that a two-photon absorption process occurs under 975 nm excitation. The long-lived I-4(11/2) level is supposed to serve as the intermediate state responsible for the upconversion processes. (c) 2004 Elsevier B.V. All rights reserved.