Abstract
The process of grinding and polishing optical surfaces using a Computer Numerically Controlled machine produces a machine material removal profile. The profiles achievable by the machine depend on the nature of the tool used in the process, and the tool center motions. In this paper machine material removal profiles are developed as mollifications of given workpiece profiles for a variety of tool configurations. The form of the mollilication, in effect, defines the tool center motion. Convergence of the machine's material removal profile to the given workpiece profile as the support of the tool goes to zero is established under mild assumptions. Numerical examples are included.
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