The effects of rounding of the edge on the focal properties of spherical-depression geodesic lenses are calculated. The focal length for paraxial rays is increased very slightly for slight rounding. For greater rounding, a decrease in focal length results from the increased optical path. Edge-rounding has very little effect on lens aberrations.
Van E. Wood, "Effects of edge-rounding on geodesic lenses," Appl. Opt. 15, 2817-2820 (1976)