Construction, specification, and mathematical description of aspheric surfaces.

Rotationally symmetrical aspheric surfaces of spectacle lenses are constructed as either "zonal aspherics" or "continuous aspherics." Zonal aspherics consist of annular zones surrounding a central zone with each zone being nominally spherical with progressively lower surface power the farther the zone is from the surface vertex. Aspheric surfaces are often specified by the radial drop in surface power from the center to the edge of the lens (e.g., Welsh Four-drop), but for assessment purposes the surface shape must be specified more precisely. The formulas for the description of continuous aspherics can be manipulated into different forms. Mathematical descriptions are given or developed which will enable theoretical assessment of the performances of all lenses with rotationally symmetrical aspheric surfaces.