A new optical design technique for catadioptric imaging optics is described, that permits near-zero values for the classical Seidel aberrations at relative apertures faster than f/1, with field angles over 3 deg arc, ~ 106 resolved pixels, a 600-nm bandwidth in the visible and near infrared and zero vignetting. Performance is limited only by high-order aberrations. The principle is that of combining the concentricities of a spherical concentric catoptric and a spherical concentric catadioptric, by optical superposition of the centers of curvature. The only full-aperture component is a spherical mirror; all other surfaces are spherical, except for an optional small weak zonal corrector. The new design approach is suited to aperture diameters of ~ 100 mm to > 1m when used with appropriate electronic detectors. Variants are possible for any segment of the electromagnetic spectrum for which there are suitable refractive and reflective media. In general, a large improvement in data acquisition rate is possible compared to that of existing designs.