The initial sphere in the fabrication of conic surfaces with small focal ratio

The fabrication of a conic surface begins vith the grinding of a best-fit s phere, The desired conic surface can then be obtained by further grinding w ith a subaperture tool. Finally, the surface is polished. Normally the best -fit sphere is chosen so as to minimize the second grinding step, However, this method tends to produce mid-spatial frequency errors near the edge of the surface and can cause errors in the paraxial radius of curvature. This paper presents an alternative method of calculating the initial sphere so a s to avoid these errors. It requires more grinding time but far less time f or polishing.