Geometrical optics is used for design of gradient-index (GRIN) laser beam shapers with the conditions of conservation of energy and constant optical path length for all rays passing through the system. The exact ray intercepts for a Gaussian to top-hat beam transform at the output plane are the ray trace target values used during the optimization process. After constructing a beam shaping merit function, the commercial software ZEMAX has been used to minimize the merit function for a well known two-element plano-aspheric beam shaper to establish the effectiveness of this new beam shaping merit function. Then, this method is used to design of several GRIN laser beam shapers while using ZEMAX's catalog GRADIUM elements from LightPath glass types. The optical component shape and spacing parameters are also used for optimization variables. Both spherical surfaces and conic surfaces of the different elements of the GRIN laser beam shaper are studied. The ZEMAX software was used for performance analysis of the GRIN beam shapers and is discussed.
Geometrical methods have been used to design two-mirror laser beam shaping systems with rectangular symmetry and no central obscuration. These systems are able to transform an input laser beam with an elliptical cross section and a two-axis Gaussian irradiance profile into a rectangularly symmetric output beam with uniform irradiance. The optical design software ZEMAX has been used for modeling and performance analysis of these systems.
A differential equation method is applied to the design of a three-mirror telescope. The resulting system is mostly free of spherical aberration, coma and astigmatism. From caustic theory and a generalization of the Coddington Equations, the Abbe sine condition and the constant optical path length condition, three coupled differential equations, one for each reflecting surface, are generated. A system which satisfies these conditions will have a high resolution over a wide field of view. Analysis of this application is presented as a comparison to a similar three-mirror telescope system produced by conventional optimization techniques.
The generalized Coddington equations from caustic theory, the Abbe sine condition, and the constant optical path length condition have been used to design two-mirror microscope systems. These two-microscope systems are free of two of the three aberrations -- spherical aberration, coma, or astigmatism, depending on which two of the three design conditions are used. The optical performance of the resulting two-microscope systems has been compared to that of the Schwarzschild microscope and the Head microscope. The goal of this study is to identify design methods for reflective systems which will yield diffraction limited performance for large numerical apertures and fields of view. Also, these design methods are being extended to a three-mirror telescope.
The encircled energy of grazing incidence Wolter telescopes has been studied by application of Saha's transverse ray aberration theory. A formula has been derived for the encircled energy of the Wolter telescopes. It has been used to the calculate the encircled energy of several Wolter I and II grazing incidence telescopes. The results derived from the formula have been compared with those obtained by exact ray tracing. The effects of third, fifth, and seventh-order aberration theory have been studied.
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