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Proceedings Paper

Approximation methods and the computer numerically controlled fabrication of optical surfaces
Author(s): Thomas A. Porsching; Charles A. Hall
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Paper Abstract

In this paper we consider an approximation theoretic approach to the computer numerically controlled manufacturing of optical studies. Given the kinematic parameters defining a grinding/polishing tool, we develop an expression for the associated material removal rate. Knowing this, and assuming descriptions of the tool center path and speed, we can then derive a general formula for the amount of material removed at a point on the workpiece by the machine. The final phase of the analysis centers on the determination of strategies for tool center movement so as to achieve a desired pattern of material removal. We discuss two means of formulating such a strategy. The first involves the use of constrained best discrete Lp approximation problems, which for p equals 1,2 can be solved by linear and quadratic programming methods. The second employs the notion of a mollifier or smoothing function and avoids the need for discretization. The results of some computational experiments based on the above methods are included.

Paper Details

Date Published: 1 January 1992
PDF: 11 pages
Proc. SPIE 1531, Advanced Optical Manufacturing and Testing II, (1 January 1992); doi: 10.1117/12.134863
Show Author Affiliations
Thomas A. Porsching, Univ. of Pittsburgh (United States)
Charles A. Hall, Univ. of Pittsburgh (United States)

Published in SPIE Proceedings Vol. 1531:
Advanced Optical Manufacturing and Testing II
Victor J. Doherty, Editor(s)

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