Unipotential electrostatic lenses: Paraxial properties and aberrations of focal length and focal point

An experimental study of electrostatic electron lenses as a function of geometrical and electrical parameters is described. The lenses are of the symmetrical three-electrode unipotential type. The parameters are the thickness of the center electrode and the interelectrode spacing, both relative to the center electrode aperture diameter, and the ratio of lens voltage to cathode voltage. The lens properties are characterized in terms of the focal length and focal distance, and the spherical and chromatic aberrations of these quantities. In general, the principal surfaces of a lens are not plane, and the aberrations of focal length and focal distance are not the same. Expressions are derived relating the focal length and focal distance aberrations to the spherical and chromatic imaging aberration coefficients Cs and Cc, and the magnification aberrations. The advantages of formulating the lens properties in terms of focal length and focal distance and their aberrations, and the usefulness of the data presented here, are illustrated with several examples.