Date of Publication


Document Type


Degree Name

Master of Science (M.S.) in Physics






Electromagnetic lenses



Physical Description

1 online resource (v, 56 leaves)


A study of the hyperbolic electrostatic electron mirror is presented. The focal properties of the mirror are determined both theoretically and experimentally. In the theoretical study the mirror field is formed between a positive hyperbolic potential surface and the negative asymptotic cone of half angle arctan 1:2 [square root of 2]. The focal properties are obtained from the solutions of the equations for the radial and axial motions of the electron in the mirror field. The analysis includes the effect of an axial aperture (for entrance and exit of electrons) in the positive surface. The paraxial values of focal length arid focal distance and their second order spherical aberrations are calculated by expanding the expressions for the focal properties in terms of the incident radial height. The mirror field in the experimental study is formed between a similar negative electrode and a flat apertured positive electrode. The experimental values of the focal properties are determined by a ray tracing method in which the pattern of shadows cast by a grid in the incident and reflected beams is analyzed. Comparison of the experimentally measured and the theoretically calculated focal properties shows satisfactory agreement. The mirror exhibits over-corrected spherical aberration in certain ranges of its operation which suggests its use to improve the resolution limit of electron optical devices.


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Portland State University. Dept. of Physics

Persistent Identifier