A covariant form of Hamilton's Principle of Stationary Action is formulated and used to solve the general eiconal equation describing the wave function of light in a medium carrying ultrasound. Tensor notation is reviewed and the tensor form of Maxwell's equations is developed. Boundary equation that the field quantities must satisfy in order for the variation of Hamilton's action integral to be stationary are determined and used to form the generalized eiconal equation of geometrical optics. The rays are introduced and through a canonical transformation the eiconal for the diffracted medium is solved and plotted.

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published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

<p>In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction.</p><p>In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view.</p><p><b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering</p>

This thesis describes an analytical approach to the optical design of four-mirror anastigmatic optical systems. In all cases investigated here the object is at infinity. In the introduction the field of reflecting, or "catoptric", optical system design is discussed and given some historical context. The concept of the "simplest possible reflecting anastigmat" is raised in connection with Plate Diagram analysis. It is shown that four-plate systems are in general the simplest possible anastigmats, and that four-plate systems comprised of four spherical mirrors are the last family of "simplest possible reflecting anastigmats" for which the complete solution set remains unknown. In chapter 2 third-order aberration coefficients in wavefront measure are derived in a form that is particularly suitable for Plate Diagram analysis. These coefficients are subsequently used to describe the Plate Diagram, and to detail the application of the Plate Diagram to the survey of all possible solutions for four-spherical-mirror anastigmats. The Plate Diagram technique is also generalized to investigate its use as an optical design tool. In the example given a generalized Plate Diagram approach is used to determine solutions for four-mirror anastigmats with a prescribed first-order layout and a minimum number of conicoids. In chapter 3 results are presented for the survey of four-spherical-mirror anastigmats in which all elements are required to be smaller than the primary mirror. Two novel families of four-spherical-mirror anastigmats are presented and these are shown to be the only examples of four-spherical-mirror systems that exist under the given constraints. Chapter 4 gives an example of the application of Plate Diagram analysis to the design of an anastigmatic system with a useful first-order layout and a minimum number of conicoid mirrors. It is shown that systems with useful first-order layouts and only one conicoid mirror can be obtained using this method. In chapter 5 results are presented of the survey of all remaining four-spherical-mirror anastigmatic systems: that is systems in which elements are allowed to exceed the diameter of the entrance pupil, which includes systems with concave and convex primary mirrors. A wide variety of solutions are presented and classified according to both the underlying geometry of the solutions and the first-order layouts. Of these systems only one has been reported in previously published literature. The results presented in this thesis complete the set of "four-plate" reflecting anastigmats, and it can now be said that all possible solutions for four-spherical-mirror anastigmatic systems have been determined.

Geometrical and dimensional metrology is used to verify that manufactured and assembled products satisfy the defined geometrical requirements and thereby the functional requirements. The dimensional measurement planning operation is carried out to define how the measurements are going to be collected and it has to consider the reliability, uncertainty and economics of the measurement procedure. The thesis work has been performed to map the current knowledge regarding measurement strategies and principles and to develop recommendations regarding a framework which defines how the measurement planning work should be carried out. The purpose of the work was thereby to perform a state-of-the-art study to map the available theoretical and empirical measurement strategies and principles. The purpose was also to test the impact of the strategies in a measurement experiment in order to validate the methodology. To fulfil the purpose of the work, a literature review and a case study was initially performed. The literature review investigated the available academically knowledge and the requirements defined in international standards regarding the measurement planning work. The case study mapped the methodologies and principles which were used in industry through contextual research and qualitative interviewing. The majority of the case study was carried out at Saab Aeronautics but to obtain a wider understanding of the topic a survey were also conducted where additional manufacturing companies were participating. The outcome of the case study and the literature review were thereafter merged and further analysed though the measurement analysis. The case study and the literature review shown that there existed several different methodologies and guidelines regarding how the work should be and was performed. Some of the factors which were further investigated were the impact of the number of measurement points, distance between the measurement points, uncertainty of the strategy and the considerations connected to the selection of the geometrical features. The measurement analysis provided insights regarding the impact on average, minimum-, maximum deviation and the variance due to the amount and distribution of the inspection points. The findings were presented as a resulting outcome of the recommended measurement strategy framework methodology. The methodology of analysing the impact of the measurement strategy was therefore implemented into the recommendations regarding the measurement planning framework. The purpose of the framework is to offer a reliable, standardized and traceable measurement planning process where knowledge sharing and continuous improvements are possible to implement. In addition to the analysis of the measurement planning strategy the most important findings to consider in the adjacent process steps were investigated and presented. These findings are presented to enable a broad understanding of the requirements throughout the measurement process at Saab Aeronautics. The knowledge obtained in the literature review, case study and the measurement experiment was included in the measurement strategy framework which was the delivery of the thesis work.

QC 351 A7 no. 37 / This paper derives four one-parameter families of two-surface optical systems having the property that, relative to a well-defined pair of conjugate points, one finite and the other infinite, third-order spherical aberration is zero. The two surfaces can be either refracting or reflecting. Aperture planes are defined for which third-order astigmatism is zero. An expression for coma is also derived. Assuming that the systems will be constructible, a means of defining domains for the free parameter is indicated. Possible applications of these results to optical design are included.

QC 351 A7 no. 57 / A normalization of the Delano y,ÿ diagram is proposed in which the y heights are normalized by the entrance pupil height, the heights by the image height. The normalization constants are expressed in terms of the system parameters, and it is seen that the reduced distances become normalized by the focal length of the system, the marginal ray reduced angles by the numerical aperture of the system, the chief ray angles by the field aperture, and the powers by the total power of the system. It is also shown that any number of refractions and transfers will not affect this normalization, but a stop or conjugate shift will destroy it and renormalization then becomes necessary.

Until the 1960s there was more interest in Josef Albers as an artist. Albers' successful teaching career began in 1923 at the Bauhaus where he was eventually placed in charge of the whole elementary course. Albers' American educational career centered around Black Mountain College in North Carolina and Yale University where he was chairman of the Department of Design.This paper, in effect, will deal with Albers as an artist, teacher, and theorist. Albers as an artist will be explored by a study of Homage to the Square, the series from which much of Albers' present fame is derived. Albers' color theory is contained in his writing, Interaction of Color, a book dedicated to his students which records his method of teaching color. It is the purpose of this paper to show Albers' theory and his paintings, Homage to the Square, exemplify many principles of perception: the realization that color experience is a subjective, inward experience, the Gestalt notions on "good" forms, and the awareness that our knowledge is of the perception of things -- not of things themselves. In order to pursue such a course of study, it will be necessary to investigate other color theories, theories of perception, Albers' work and evaluations of his works.

Três métodos geométricos de traçado de raios são desenvolvidos e aplicados num programa de avaliação de sistema ópticos para microcomputadores padrão IBM-PC. O primeiro método corresponde ao traçado paraxial construído a partir do Invariante de Abbe; o segundo método corresponde ao traçado meridional proposto por Rudolf Kingslake; e o terceiro método corresponde ao traçado espacial proposto por Hainz Haferkorn e Volker Tautz. Dentro do programa estão incluídas algumas das representações das aberrações ópticas que caracterizam um sistema óptico centrado. / Three methods of ray tracing are development for use on IBM PC/XT personal computer. The first method is a paraxial ray tracing derived from the invariant Abbe; the second is a meridional ray tracing proposed by Rudolf Kingslake; and the third is a skew ray tracing proposed by Heinz Haferkorn and Volker Tautz . Based on these three methods some optical aberrations are employed to exemplify an optical centered system.