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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 50, Iss. 24 — Aug. 20, 2011
  • pp: 4817–4823

Local and global surface errors evaluation using Ronchi test, without both approximation and integration

Alberto Cordero-Dávila, Jorge González-García, Carlos Ignacio Robledo-Sánchez, and Irce Leal-Cabrera  »View Author Affiliations


Applied Optics, Vol. 50, Issue 24, pp. 4817-4823 (2011)
http://dx.doi.org/10.1364/AO.50.004817


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Abstract

We have reproduced quantitatively the technique commonly used in optical shop to evaluate surface error from comparison between experimental and simulated Ronchigrams. We used this procedure to evaluate, from Ronchigrams of any number of fringes, the curvature radius and/or conic constant of conic surfaces. The error function is calculated without using integration (numerical or polynomial) so the corresponding problems were avoided. Furthermore, when the error function is described with cubic splines, then the local errors are very well reproduced, which is not the case with the polynomial description. We have described the error functions with conical surfaces or with cubic splines, and for the best reproduction of experimental Ronchigram we used genetic algorithms.

© 2011 Optical Society of America

OCIS Codes
(220.4610) Optical design and fabrication : Optical fabrication
(240.5450) Optics at surfaces : Polishing
(240.6700) Optics at surfaces : Surfaces

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: February 2, 2011
Revised Manuscript: May 24, 2011
Manuscript Accepted: July 8, 2011
Published: August 16, 2011

Citation
Alberto Cordero-Dávila, Jorge González-García, Carlos Ignacio Robledo-Sánchez, and Irce Leal-Cabrera, "Local and global surface errors evaluation using Ronchi test, without both approximation and integration," Appl. Opt. 50, 4817-4823 (2011)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-50-24-4817


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References

  1. A. Cornejo-Rodríguez, “Ronchi test,” in Optical Shop Testing, 3rd ed., D.Malacara (ed.) (Wiley and Sons, 2007), pp. 317–360.
  2. A. Cornejo and A. Cordero “Wavefront slope measurements in optical testing” in Optical Engineering, D.Malacara and B.J.Thompson (eds.) (Marcel Dekker, 2001), pp. 311–338.
  3. D. Malacara-Hernández, “Testing of optical surfaces,” Ph.D. dissertation (The University of Rochester, 1965).
  4. A. Cordero-Dávila, J. M. Núñez-Alfonso, E. Luna-Aguilar, and C. I. Robledo-Sánchez, “Only one fitting for the bironchigrams,” Appl. Opt. 40, 5600–5609 (2001). [CrossRef]
  5. J. L. Rayces, “Exact relation between wave aberration and ray aberration,” Opt. Acta 11, 85–88 (1964). [CrossRef]
  6. J. Arasa, S. Royo, and N. Tomàs, “Simple method for improving the sampling in profile measurements by use of the Ronchi test,” Appl. Opt. 39, 4529–4534 (2000). [CrossRef]
  7. S. Royo, J. Arasa, and C. Pizarro, “Profelometry of toroidal surfaces with an improved Ronchi test,” Appl. Opt. 39, 5721–5731 (2000). [CrossRef]
  8. A. Cordero-Dávila and J. González-García, “Surface evaluation with Ronchi test by using Malacara formula, genetic algorithms and cubic splines,” Proc. SPIE 7652, 76521F(2010). [CrossRef]
  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). [CrossRef] [PubMed]
  10. S. Groening, B. Sick, K. Donner, J. Pfund, N. Lindlein, and J. Schwider, “Wave-front reconstruction with a Shack–Hartmann sensor with an iterative spline fitting method,” Appl. Opt. 39, 561–567 (2000). [CrossRef]
  11. T. P. Vogl, A. K. Rigler, and B. R. Canty, “Asymmetric lens design using bicubic splines: application to the color TV lighthouse,” Appl. Opt. 10, 2513–2516 (1971). [CrossRef] [PubMed]
  12. J. E. Stacy, “Asymmetric spline surfaces: characteristics and applications,” Appl. Opt. 23, 2710–2713 (1984). [CrossRef] [PubMed]
  13. A. K. Rigler and T. P. Vogl, “Spline functions: an alternative representation of aspheric surfaces,” Appl. Opt. 10, 1648–1651(1971). [CrossRef] [PubMed]
  14. F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16, 7323–7329 (2008). [CrossRef] [PubMed]
  15. A. U. Rivera-Ortega and A. y Cordero-Dávila, “Evaluación de superficies ópticas utilizando la prueba de Ronchi y la fórmula de aberración transversal de Malacara,” in Program of the LII Congreso Nacional de Física de la Sociedad Mexicana de Física, Bull. Soc. Mex. Fis. Suppl. 21, 59 (2009).
  16. C. de Boor, A Practical Guide to Splines (Springer-Verlag, 2001).
  17. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in Fortran 77: The Art of Scientific Computing, 2nd ed. (Cambridge University, 2007).
  18. J. Rosaura Kantún-Montiel, A. Cordero-Dávila, and J. González-García, “Quantitative surface evaluation by matching experimental and simulated Ronchigram images,” to be presented and published in the 22nd General Congress of the International Commission for Optics (ICO-22).

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