A machine has been constructed for fabricating concave aspheric surfaces of diameter up to 200 mm and reference radius from 20 mm to 150 mm. The principle is to use a plastic-bonded silicon carbide wheel with a convex cutting surface, which is continually dressed by a diamond form dresser. The cam used for directing the grinding wheel is cut on a numerically controlled jig borer with a tool of the same diameter as the cam follower. In operation, the location of the diamond dresser is used to provide feedback corrections for the grinding wheel.
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Hiroshi Hashimoto (1973) studied this question.