QC 351 A7 no. 69 / The history of modern wide -field, high-speed catadioptric lenses is reviewed. One system comprising only spherical curves and representative of the current art for low-light-level systems is evaluated and used as a baseline design in a weight-reduction study. Five aspheric designs are computed and evaluated. It is found that the use of aspherics will permit weight reduction only in certain instances, i.e., if one element of an all-spherical design can be eliminated or if a fundamentally different configuration that is possible only with aspherics is substituted for the all-spherical configuration. Of these possibilities, the elimination of an element is the best replacement for the baseline design. The case of a highly constrained, purely refractive triplet is studied in some detail. Four designs are computed -from the all-spherical case to the most complex polynomial aspheric. It is found that, if only conic aspherics are employed, significant improvement can be obtained and the problems involved are sensibly the same as those in all-spherical designs. When complex aspherics are applied, the problem becomes surprisingly difficult, and there is some indication that a computer can deal with it better than can a human lens designer.