Thesis (M.S.)--Ohio State University, 1984. / Includes bibliographical references (leaves 118-119). Available online via OhioLINK's ETD Center

Pacific Rim International Conference on Advanced Materials and Processing <DA14524950> (5th : 2004 : Beijing, China)

Thesis (Ph. D.)--University of Washington, 1996. / Vita. Includes bibliographical references (p. [357]-360).

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.

No description available.

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.

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.

The subject of this thesis is lens design using a system of functional differential equations arising from Fermat's Principle in geometrical optics. The emphasis is primarily on existence, uniqueness, and analyticity, properties of solutions to these equations, but some asymptotic methods are developed for special cases. Three specific lens problems are considered in detail: the first is an axial lens having two pairs of foci on the optical axis, the second is an axial lens which focuses light at two different frequencies to two distinct points, the third is a lens symmetric about an axis having foci not on said axis.

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.