Abstract

Astronomical telescopes of the future need large paraboloidal mirrors as fast as f/1. Machines for numerically-controlled generation of such aspheric surfaces are now available. However, polishing fast aspherics at close to diffraction limited performance remains a difficult problem. We have analyzed the capabilities and limitations of different polishing tools. These include small rigid laps, flexible and soft faced laps and actively stressed laps. We apply to each a criterion for successful fine grinding and figuring, namely that a lap should be able to accomodate to the surface to within a certain accuracy, about 0.3μm for figuring. This leads directly to stringent size limitations for rigid laps that are rotated or radially stroked. Laps that conform to changes in curvature by bending under the polishing pressure must be adequately flexible. Formulae for lap thickness to meet the above criterion are derived. The effect of small errors of lap fit are in general largely averaged out, except at the mirror edges where overhang droop always tends to produce the same error. Lap thickness to keep the systematic error low, say below λ/10, are derived as a function of the amount of overhang. Finally actively stressed laps are analyzed to determine the combined bending effects of moment actuators and polishing pressure. A lap with 24 computer-controlled edge moment actuators is now being built. It will offer very substantial advantages for steep aspherics, provided that the applied bending moments are controlled accurately enough, about 0.1% for an f/1 mirror soon to be polished. For secondary mirrors and Schmidt plates, a tool which bends under edge moments produced by levers and springs is proposed.

© 1986 Optical Society of America