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.
Theodore W. J. Unti, "Best-Fit Sphere Approximation to a General, Aspheric Surface," Appl. Opt. 5, 319-319 (1966)