A theoretical and experimental study of spherical and chromatic aberrations in an electrostatic hyperbolic lens.

摘要

A theoretical and experimental investigation into the properties of an electrostatic hyperbolic electron lens is presented. The hyperbolic lens consists of a converging hyperbolic field terminated by apertures for entrance and exit of electrons. The analytical investigation makes use of exact solutions for the hyperbolic potential field, as well as the effect of the end apertures to study the focusing of electrons passing through the lens. The paraxial properties of the image as well as the spherical and chromatic aberrations are calculated and used to determine the focal properties of the lens.; The experimental investigation employs a unipotential lens whose inner surfaces possess a hyperbolic geometry. The paraxial properties of the image as well as the spherical and chromatic aberrations are measured using the shadowgraph method. This method employs wire meshes of known mesh pitch with 2000 bars/in for rear-mesh shadowgraphs or 600 bars/in for front-mesh shadowgraphs. The shadows cast by the mesh bars can be analyzed and used to determine both the image and lens properties by employing geometric methods, such as similar triangles, as well as basic geometric optics.; The theoretical investigation also employs a software package for the simulation of charged particle trajectories. A hyperbolic lens is modeled possessing dimensions closely matching those of the actual lens. Data is collected and the focal properties of the lens are found using similar techniques as used in the experimental work.; It is found that the experimental results of the hyperbolic lens support both the analytical study and the software simulation. It is also found that the experimental results of the hyperbolic lens closely match those of the conventionally designed lens, indicating that the hyperbolic model possesses properties that are general characteristics of all conventional unipotential lenses. The results also demonstrate that the hyperbolic lens is not free of spherical aberration, as has been previously posited in the relevant literature, but instead suffers from spherical aberration, as do conventional electrostatic lenses. Furthermore, it is demonstrated that the lens properties Sf, Sg, Cf and Cg can be used to calculate the image properties Cs ' and Cc'.