Best-fit Sphere Research Articles

Diamond Turning at a Large Optical Manufacturer

The development of precision machines for generating aspheric optical surfaces at. Bell & Howell Company, which were the ancestors of many of today's diamond turning machines, is outlined together with present machine capability. A practical procedure for compensating for repeatable machine position errors based upon measurement of a best-fit sphere is described. Applications of diamond turning to reflective and transmissive (germanium and silicon) infrared optical elements are illustrated.

Elastic Deformation of Lightweight Mirrors

Results of analytical and experimental studies on the elastic deformation of lightweight mirrors under various support conditions are presented and compared. The analytical results were obtained using the finite-element method, which employs elements having stretching, bending, and twisting capability. Both structural deformation and deviation from the best-fit sphere are shown to be dependent upon cell-wall thickness and generally independent of cell shape. This suggests that the choice of cell pattern would be governed by ease of fabrication rather than by structural action, provided that the cell size is made sufficiently small to prevent local waffling.

Best-Fit Sphere Approximation to a General Aspheric Surface

In manufacturing an aspheric lens or mirror, it is often convenient to generate a spherical surface as a starting point. The radius of the sphere should be such that the volume of glass which must be removed to achieve the final aspheric is a minimum. Equations for this best-fit sphere are developed and arranged in a form well suited for computer programming.