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.