Approximation methods and the computer numerically controlled fabrication of optical surfaces

Thomas A. Porsching; Charles A. Hall

doi:10.1117/12.134863

1 January 1992 Approximation methods and the computer numerically controlled fabrication of optical surfaces

Thomas A. Porsching, Charles A. Hall

Proceedings Volume 1531, Advanced Optical Manufacturing and Testing II; (1992) https://doi.org/10.1117/12.134863
Event: San Diego, '91, 1991, San Diego, CA, United States

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.

Citation Download Citation

Thomas A. Porsching and Charles A. Hall "Approximation methods and the computer numerically controlled fabrication of optical surfaces", Proc. SPIE 1531, Advanced Optical Manufacturing and Testing II, (1 January 1992); https://doi.org/10.1117/12.134863

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