Shao-Hua Chao

Geometric optics-based design of laser beam shapers

When diffraction effects are not important, geometrical optics (ray tracing, conservation of energy within a bundle of rays, and the constant optical path length condition) can be used to design laser beam shapers by solving beam shaping equations or by optimizing a beam shaping merit function for the configurations, including aspheric elements or spherical-surface gradient-index lenses, which are required to change the input irradiance and phase profile into a more useful form. Geometrical optics-based methods are presented for shaping both rotationally and rectangular symmetric laser beam profiles. Solutions of the beam shaping equations are presented for a two-plano-aspheric lens system for shaping a circular symmetric Gaussian beam into a top-hat output beam profile and a two-mirror system with no central obscuration for shaping an elliptical Gaussian input beam into a Fermi-Dirac output beam profile.

Design of GRIN laser beam shaping system

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 ZEMAXs 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.

Design and analysis of an elliptical Gaussian laser beam shaping system

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.

Theoretical analysis of stable and unstable aspherical laser cavities

The low- order resonant modes of the stable and unstable aspherical resonators are studied by the Fox- Li method. An integral equation is given with which the effect of varying the aspherical cavity surface parameters on the field distribution, the energy loss and the intensity profile have been studied.

Spectral slicing X-ray telescope

Layered synthetic microstructure (LSM) x-ray optics may be used to couple a conventional glancing incidence x-ray mirror to a high sensitivity x-ray detector. The LSM mirror is a thin-film multilayer optic that effectively reflects only narrow spectral slices of the incident radiation by Bragg diffraction. By the use of figured LSM optics, it is possible to magnify the x-ray image produced by the primary mirrors so as to maintain their high inherent spatial resolution when used with currently available solid-state detectors. The results of theoretical design and analysis studies of several Spectral Slicing X-Ray Telescope (SSXRT) systems utilizing LSM mirrors figured as hyperboloids, spheres, ellip-soids, and constant optical path aspheric elements are presented. The rms spot size and point response function calculations are given for telescopes in which the LSM optics are designed to yield magnifications of 2 X, 6 X, and 8 X. The results of tilt and decentration studies are discussed. It has been demonstrated that the off-axis optical performance of the SSXRT is superior to that produced by the conventional glancing incidence primary mirror alone. The Stanford/Marshall Space Flight Center Rocket X-Ray Telescope, which will utilize normal incidence LSM optics to couple a Wolter-Schwarzschild primary mirror to high resolution detectors for solar x-ray/EUV studies, is briefly discussed.

Design of three-mirror telescopes via a differential equation method

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.

Optical Design of Laser Beam Shaping Optics

A geometrical optics-based merit function was used to optimize the design of refractive beam shapers for converting a Gaussian beam into a more uniform profile, while minimizing the curvature of aspheric optics.

Design of an anastigmat two-mirror microscope

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.

Application of aberration theory to calculate encircled energy of Wolter I-II telescopes

The encircled energy of grazing incidence Wolter telescopes has been studied by application of Sahas 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.

Application of the flux flow equation to the Wolter I x-ray telescope and thin-film multilayered optics

The flux flow equation of Burkhard and Shealy is a simplified equation which can be used to evaluate the energy flux density at the image plane for a general optical system. Since the flux flow equation is based on the differential geometry of the wave front passing through the system, the energy flux density at the image plane can be computed by tracing a single ray through the system and using the flux flow equation. This technique has been used to calculate the meridional section of the point spread function of Wolter I x-ray telescopes and thin-film multilayered optics. Results, which have been obtained by the flux flow ray tracing method for the point spread function of several Wolter I x-ray telescopes and hybrid x-ray telescopes using convexed thin-film multilayered optics located near the primary focus, are compared with the rms blur circle results and the point spread function results obtained by conventional ray tracing techniques.