Considerations for tolerancing aspheric optical components.

Optical designs often specify both surface form and centering (tilt and lateral displacement) tolerances on aspheric surfaces. In contrast to spherical surfaces, form and centering errors are coupled for aspheric surfaces. Current standards do not specify how to interpret such tolerances, and in particular they do not define the position of an aspheric surface that has form errors. The straightforward definition that uses the best-fit surface position that minimizes rms error has subtle problems. The best-fit surface position for aspheric surfaces is influenced by power error and can be highly sensitive to surface form errors when the derivative of aspheric departure is small. We analyze the conditions under which form and centering tolerances may be considered compatible when the best-fit surface-position definition is used. We propose alternative definitions of surface position that do not suffer from the same problems and consider their consequences for optical design and metrology.