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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 35, Iss. 22 — Aug. 1, 1996
  • pp: 4463–4470

Computationally directed axisymmetric aspheric figuring (after N. J. Brown)

T. A. Porsching and C. A. Hall  »View Author Affiliations


Applied Optics, Vol. 35, Issue 22, pp. 4463-4470 (1996)
http://dx.doi.org/10.1364/AO.35.004463


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Abstract

We examine some computational problems related to the finishing of axisymmetric optical surfaces discussed in a paper by N. J. Brown [Opt. Eng. 17, 602–620 (1978)]. In the spirit of Brown’s paper we develop solution algorithms that are suitable for implementation on today’s personal computers. The use of the algorithms is illustrated by some sample calculations.

© 1996 Optical Society of America

History
Original Manuscript: August 25, 1995
Revised Manuscript: January 22, 1996
Published: August 1, 1996

Citation
T. A. Porsching and C. A. Hall, "Computationally directed axisymmetric aspheric figuring (after N. J. Brown)," Appl. Opt. 35, 4463-4470 (1996)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-35-22-4463


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References

  1. N. J. Brown, “Computationally directed axisymmetric aspheric figuring,” Opt. Eng. 17, 602–620 (1978).
  2. F. W. Preston, “The theory and design of plate glass polishing machines,” J. Soc. Glass Technol. 11, 214–256 (1927).
  3. R. E. Wagner, R. R. Shannon, “Fabrication of aspherics using a mathematical model for material removal,” Appl. Opt. 12, 1683–1689 (1974). [CrossRef]
  4. K. B. Paxton, G. H. Connors, R. J. Cooley, “Uniform polishing of convex aspheres with an elastic lap,” Appl. Opt. 14, 2274–2279 (1975). [CrossRef] [PubMed]
  5. D. J. Bajuk, “Computer controlled generation of rotationally symmetric aspheric surfaces,” Opt. Eng. 15, 401–406 (1976).
  6. D. W. Small, S. J. Hoskins, “An automated aspheric polishing machine,” in Optical Manufacturing, Testing and Aspheric Optics, G. M. Sanger, ed., Proc. SPIE645, 66–74 (1986). Reprinted in Selected Papers On Computer-Controlled Optical Surfacing, R. Jones, ed. (SPIE Optical Engineering Press, Bellingham, Wash., 1991).
  7. R. Aspden, R. McDonough, F. Nitchie, “Computer assisted optical surfacing,” Appl. Opt. 11, 2739–2747 (1972). [CrossRef] [PubMed]
  8. A. P. Bogdanov, “Optimizing the technological process of automated grinding and polishing of high-precision large optical elements with a small tool,” Sov. J. Opt. Technol. 52, 409–413 (1985). Reprinted in R. Jones, ed., Selected Papers On Computer-Controlled Optical Surfacing (SPIE Optical Engineering Press, Bellingham, Wash., 1991).
  9. R. A. Jones, “Optimization of computer controlled polishing,” Appl. Opt. 16, 218–2247 (1977). [CrossRef] [PubMed]
  10. T. A. Porsching, C. A. Hall, T. L. Bennett, J. M. Ernsthausen, “A mathematical model of material removal with application to CNC finishing,” Math. Comput. Model. 18, 25–40 (1993). [CrossRef]
  11. C. A. Hall, T. A. Porsching, “Approximation methods in the computer numerically controlled fabrication of optical surfaces. Part i: finite dimensional material removal profile spaces,” IMA J. Numer. Anal. 12, 67–84 (1992). [CrossRef]
  12. C. A. Hall, T. A. Porsching, “Approximation methods in the computer numerically controlled fabrication of optical surfaces. Part ii: mollifications,” IMA J. Numer. Anal. 12, 259–269 (1992). [CrossRef]
  13. T. A. Porsching, C. A. Hall, “Approximation methods and the computer numerically controlled fabrication of optical surfaces,” in Advanced Optical Manufacturing and Testing II, V. J. Doherty, ed., Proc. SPIE1531, 205–215 (1992).
  14. K. E. Atkinson, An Introduction to Numerical Analysis (Wiley, New York, 1978), Chap. 6, p. 320.
  15. A. E. Taylor, Introduction to Functional Analysis (Wiley, New York, 1967), Chap. 3, p. 105.

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