An electron–optical system capable of producing a highly collimated, large-diameter beam was designed, built and tested. The system consisted of a strong, decelerating condenser lens followed by an accelerating, collimating, “Kan” lens. The lenses were designed with the help of a large digital computer, using a combination of relaxation and analytical techniques. The Kan lens, which was the critical component, had a parabolic potential on a cylindrical boundary and terminated in an endplate containing an array of small exit holes. System performance was investigated by ray-tracing techniques; over-all angular accuracy was 0.005 mrad. Several systems were built, with an insulated-ring construction method, and tested by both a Moiré pattern technique and an extended column method, the latter accurate to 0.05 mrad. It was found that by recessing the endplate, thereby creating a weak divergent lens the spherical aberration of the system could be nearly cancelled, resulting in a final miscollimation of 0.06 mrad over a 2- in. diam. When the collimated beam was focused by a lens, an off-axis radial ellipticity was discovered, the origin of which was found to be chromatic aberration resulting from the Boersch effect.

Wang, C. C. T., Harte, K. J., Curland, N., Likuski, R. K., & Dougherty, E. C. (1973). Computer-Aided Design and Experimental Investigation of an Electron–Optical Collimating Lens. Journal of Vacuum Science and Technology, 10(6), 1110–1113.