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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: James C. Wyant
  • Vol. 46, Iss. 21 — Jul. 20, 2007
  • pp: 4642–4649

Use of linear programming to calculate dwell times for the design of petal tools

Agustin Santiago-Alvarado, Jorge González-García, Cuauhtémoc Castañeda-Roldan, Alberto Cordero-Dávila, Erika Vera-Díaz, and Carlos Ignacio Robledo-Sánchez  »View Author Affiliations


Applied Optics, Vol. 46, Issue 21, pp. 4642-4649 (2007)
http://dx.doi.org/10.1364/AO.46.004642


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Abstract

Two constraints in the design of a petal tool are, the angles that define it must all be positive, and wear must never be greater than the desired wear. The first constraint is equivalent to that of the positive dwell times of a small solid tool. In view of this foregoing, we present a design of petal tools that are used to generate conic surfaces from their nearest spheres and that correct the profile of a surface that is polished. We study optimal angular sizes of a petal tool, which are found after we use linear programming to calculate the optimal dwell times of a set of complete annular tools placed in different zones of the glass surface. We report numerical results of designed petal tools.

© 2007 Optical Society of America

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.4610) Optical design and fabrication : Optical fabrication
(220.5450) Optical design and fabrication : Polishing

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: January 8, 2007
Revised Manuscript: March 22, 2007
Manuscript Accepted: March 25, 2007
Published: July 6, 2007

Citation
Agustin Santiago-Alvarado, Jorge González-García, Cuauhtémoc Castañeda-Roldan, Alberto Cordero-Dávila, Erika Vera-Díaz, and Carlos Ignacio Robledo-Sánchez, "Use of linear programming to calculate dwell times for the design of petal tools," Appl. Opt. 46, 4642-4649 (2007)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-46-21-4642


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References

  1. R. A. Jones, "Optimization of computer controlled polishing," Appl. Opt. 16, 218-224 (1977). [CrossRef] [PubMed]
  2. M. N. Golovanova, S. S. Kachkin, Ye. I. Krylova, L. S. Tsesnek, and L. I. Shevel'kova, "A method of manufacturing aspherical surfaces which deviate only slightly from the sphere," Sov. J. Opt. Technol. 35, 254-256 (1968).
  3. Yu. K. Lysyannyy and L. S. Tsesnek, "Computation of the contour of a mask tool surface for shaping a concave paraboloid of revolution," Sov. J. Opt. Technol. 40, 446-448 (1973).
  4. Yu. K. Lysyannyy, L. S. Tsesnek, L. N. Gurevich, and L. N. Khokhlenkov, "The shaping of optical surfaces by the successively corrected mask method," Sov. J. Opt. Technol. 44, 226-227 (1977).
  5. A. Cordero-Dávila, V. Cabrera-Peláez, J. Cuautle-Cortés, J. González-García, C. Robledo-Sánchez, and N. Bautista-Elivar, "Experimental results and wear predictions of petal tools that freely rotate," Appl. Opt. 44, 1434-1441 (2005). [CrossRef] [PubMed]
  6. F. W. Preston, "The theory and design of plate glass polishing machines," J. Soc. Glass Technol. 11, 214-256 (1927).
  7. N. J. Brown, "Computationally directed axisymmetric aspheric figuring," J. Soc. Photo-Opt. Instrum. Eng. 17, 602-620 (1978).
  8. O. D. Macias Bautista and A. Cordero-Dávila, "Pulido de superficies convexas con herramientas de pétalo," in Program of the 47th Congreso Nacional de Física de la Sociedad Mexicana de Física, Bull. Soc. Mex. Fis. Suppl. 18, 96-97 (2004).
  9. J. González-García, A. Cordero-Dávila, I. Leal-Cabrera, C. I. Robledo-Sánchez, and A. Santiago-Alvarado, "Calculating petal tools using genetic algorithms," Appl. Opt. 45, 6126-6136 (2006). [PubMed]
  10. R. E. Wagner and R. R. Shannon, "Fabrication of aspherics using a mathematical model for material removal," Appl. Opt. 13, 1683-1689 (1974). [CrossRef] [PubMed]
  11. D. J. Bajuk, "Computer controlled generation of rotationally symmetric aspheric surfaces," Opt. Eng. 15, 401-406 (1976).
  12. R. Aspden, R. McDonough, and F. R. Nitchie, Jr., "Computer assisted optical surfacing," Appl. Opt. 11, 2739-2747 (1972). [CrossRef] [PubMed]
  13. R. A. Jones, "Optimization of computer controlled polishing," Appl. Opt. 16, 218-224 (1977). [CrossRef] [PubMed]
  14. J. R. Johnson and E. Waluschka, "Optical fabrication--process modeling--analysis tool box," in Advanced Optical Manufacturing and Testing, Gregory M. Sanger, Paul B. Reid, and Lionel R. Baker, eds., Proc. SPIE 1333, 106-117 (1990). [CrossRef]
  15. A. P. Bogdanov, "Optimizing the technological process of automated grinding and polishing of high-precision large optical elements with a small tool," Opt.-Mekh. Prom-st. 52, 32-36 (1985).
  16. A. P. Bogdanov and L. S. Tsesnek, "Contact problems in the shaping of optical surfaces," Opt.-Mekh. Prom-st. 46, 8-10 (1979).
  17. A. P. Bogdanov and L. S. Tsesnek, "Solving contact problems in the shaping of optical surfaces," Opt.-Mekh. Prom-st. 46, 18-20 (1979).
  18. A. Santiago-Alvarado, S. Vázquez-Montiel, R. Nivón-Santiago, and C. Castañeda-Roldán, "Uso de programación lineal para conocer los parámetros geométricos de superficies cónicas convexas," Rev. Mex. Fis. 50, 358-365 (2004).
  19. H. A. Taha, Operations Research: An Introduction (Prentice Hall, 2006).
  20. M. Bazaraa, J. Jarvis, and H. Sherali, Linear Programming and Network Flows (Wiley, 1989).
  21. J. González-García, A. Cordero-Dávila, I. Leal-Cabrera, C. I. Robledo-Sánchez, G. Castro-González, A. Santiago-Alvarado, and L. J. Manzano-Sumano, "Design of petal tools based on the dwell-times of annular tools to generate convex surfaces," in Program of the 49th Congreso Nacional de Física de la Sociedad Mexicana de Física, Bull. Soc. Mex. Fis. Suppl. 20, 126 (2006).

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