Toward the Accurate Coverage of Aspheric Surfaces Using Two-Dimensional Scanning Paths for Minimizing Regular Errors


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This paper describes a two-dimensional tool-path planning model for minimizing the regularly distributed errors or mid-frequency errors during computer controlled optical surfacing (CCOS) by optimally connecting different tool-path segments. The model was established based on a neuro-fuzzy algorithm, a path neighborhood function which is defined as a victorious output element calculated in a self-organization way, then, the optimum material removal function with a modified weight was derived. The material removal function was studied theoretically and the results of simulation present a Gaussian distribution feature. Discrete removal points and optimized tool-path grid were simulated. Finally, an experiment involving a parabolic mirror was performed for residual error removal and the two-dimensional tool-path planning algorithm was found to be valid.



Key Engineering Materials (Volumes 364-366)

Edited by:

Guo Fan JIN, Wing Bun LEE, Chi Fai CHEUNG and Suet TO




H. B. Cheng et al., "Toward the Accurate Coverage of Aspheric Surfaces Using Two-Dimensional Scanning Paths for Minimizing Regular Errors", Key Engineering Materials, Vols. 364-366, pp. 64-68, 2008

Online since:

December 2007




[1] R.B. Johnson: Optical Engineering Vol. 27(1) (1988), p.1046.

[2] R. A. Jones and W.J. Rupp: Optical Engineering Vol. 30(1) (1991), p. (1962).

[3] G. Doughty and J. Smith: Applied Optics Vol. 26(2)(1987), p.2421.

[4] M. Negishi M: International Journal of the Japan Society for Precision Engineering Vol. 29(1) (1995), p.1.

[5] R. A. Jones: Optical Engineering Vol. 25(6) (1986), p.785.

[6] S.D. Jacobs, D. Golini, Y. Hsu, B. E. Puchebner, D. Strafford, W. I. Kordonsky, I. V. Prokhorov, E. Fess, D. Pietrowski and V. W. Kordonski: Proceedings of SPIE Vol. 2576(1995), p.372.


[7] R. E. Wagner and R. R. Shannon: Applied Optics Vol. 13(7) (1974), p.1683.

[8] A. S. Savel'ev and A. P. Bogdanov: Soviet Journal of Optical Technology Vol. 52(5) (1985), p.294.

[9] F. W. Preston: J. Soc. Glass Technology Vol. 11(1927), p.124.

[10] Jyh-Shing Roger Jang, Chuen-Tai Sun and Eiji Mizutani: Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence (NJ: Prenhall Hall, 1997).

[11] H. B. Cheng, Z. J. Feng and K. Cheng: International Journal of Machine Tools & Manufacture Vol. 45(9) (2005), p.1085.