The spherical and chromatic aberrations of a converging electron mirror are of opposite sign from those of electron lenses. This important property makes it possible in principle to compensate the aberrations of electron lenses by means of an electron mirror and to design electron microscopes based on a corrected optics system incorporating an electron mirror. In this paper the properties of the hyperbolic electron mirror are calculated, and the conditions for simultaneous correction of spherical and chromatic aberrations are worked out for several types of electron microscopes. The hyperbolic mirror field is a rotationally symmetric potential field between two electrodes. The electrodes are shaped as equipotential surfaces of the hyperbolic field, except for an aperture on the axis of the positive electrode for entrance and exit of electrons. The effect of the aperture is to create a thin diverging aperture lens at the termination of the hyperbolic field. The properties of the mirror are calculated analytically. The problem of separating the electron beam incident on the mirror from the beam returning from the mirror without impairing the image quality is solved by means of magnetic deflecting fields located at image planes. The mirror corrections can be applied to either magnetic or electrostatic lenses. The parameters for correction of aberrations are calculated for systems using electrostatic lenses. With appropriate polarity of the accelerating voltage and the lens and mirror voltages the calculations apply to ion imaging systems as well.

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.

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