Abstract
Most present methods of determining optimal fitting spherical surface for rotationally symmetrical aspheric optics are either unsuitable for off-axis optics or unable to guarantee “the condition of positive removal” (distances from points on desired concave aspheric surface to the center of fitting sphere are all longer than radius of sphere while distances from points on desired convex aspheric surface to the center of fitting sphere are all shorter than radius of sphere). To surmount the two problems, this paper proposes three methods of determining starting spherical surface in finishing/polishing aspheric optics: method of using the function of “lsqlin” provided in Matlab, the modified method of least squares and the method of exhaustive search of tangent spheres. An example is presented to validate the three methods and to demonstrate all of them gain some advantages over conventional one by comparing attributes (normal deviation distribution, maximum normal deviation, volume of material to be removed, rms of normal deviation distribution, etc.) of their optimal fitting spheres against those of sphere obtained by utilizing conventional method.
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