OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editors: Andrew Dunn and Anthony Durkin
  • Vol. 8, Iss. 3 — Apr. 4, 2013

Sagittal and meridional radii of curvature for a surface with symmetry of revolution by using a null-screen testing method

Amilcar Estrada-Molina, Manuel Campos-García, and Rufino Díaz-Uribe  »View Author Affiliations


Applied Optics, Vol. 52, Issue 4, pp. 625-634 (2013)
http://dx.doi.org/10.1364/AO.52.000625


View Full Text Article

Enhanced HTML    Acrobat PDF (847 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

An algorithm to compute the sagittal and meridional radii of curvature for a surface of revolution is presented. The sagittal radius is obtained from the surface normal, and the meridional radius is calculated from a function fitted to the derivative of the sagittal curvature by using the surface-normals raw data. A calibration spherical surface is tested by using the null-screen testing method. Experimental results of the spherical surface show that the sagittal and meridional radii of curvature differ by 2.600% and 2.604%, respectively, with respect to the actual radius of the calibration spherical surface.

© 2013 Optical Society of America

OCIS Codes
(080.0080) Geometric optics : Geometric optics
(080.2720) Geometric optics : Mathematical methods (general)
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(330.7325) Vision, color, and visual optics : Visual optics, metrology
(330.7327) Vision, color, and visual optics : Visual optics, ophthalmic instrumentation

History
Original Manuscript: October 23, 2012
Revised Manuscript: December 14, 2012
Manuscript Accepted: December 17, 2012
Published: January 30, 2013

Virtual Issues
Vol. 8, Iss. 3 Virtual Journal for Biomedical Optics

Citation
Amilcar Estrada-Molina, Manuel Campos-García, and Rufino Díaz-Uribe, "Sagittal and meridional radii of curvature for a surface with symmetry of revolution by using a null-screen testing method," Appl. Opt. 52, 625-634 (2013)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=ao-52-4-625


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. R. Díaz-Uribe and M. Campos-García, “Null-screen testing of fast convex aspheric surface,” Appl. Opt. 39, 2670–2677 (2000). [CrossRef]
  2. M. Campos-García, R. Díaz-Uribe, and F. Granados-Agustín, “Testing fast aspheric convex surfaces with a linear array of sources,” Appl. Opt. 43, 6255–6264 (2004). [CrossRef]
  3. L. Carmona-Paredes and R. Díaz-Uribe, “Geometric analysis of the null screen used for testing convex optical surfaces,” Rev. Mex. Fís. 53, 421–430 (2007).
  4. M. Campos-García, R. Bolado-Gómez, and R. Díaz-Uribe, “Testing aspheric concave surfaces with a cylindrical null screen,” Appl. Opt. 47, 849–859 (2008). [CrossRef]
  5. I. Funes-Maderey, “Flat field videokeratometry,” B. Sc. dissertation (College of Sciences of The Autonomous National University of Mexico, 1998).
  6. R. Colín, “New developments on flat field videokeratometry,” B. Sc. dissertation (College of Sciences of The Autonomous National University of Mexico, 2007).
  7. A. Estrada-Molina, “Design and construction of a portable videokeratometer for neonates,” M. Sc. dissertation (Graduate School of The Autonomous National University of Mexico, 2010).
  8. M. Campos-García, A. Estrada-Molina, and R. Díaz-Uribe, “New null screen design for corneal topography,” Proc. SPIE 8011, 801124 (2011). [CrossRef]
  9. O. N. Stavroudis, The Mathematics of Geometrical and Physical Optics (Wiley-VCH, 2006).
  10. D. J. Struik, Lectures on Classical Differential Geometry(Addison-Wesley, 1961).
  11. M. P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice Hall, 1976).
  12. A. Estrada-Molina and R. Díaz-Uribe, “Tangential and sagittal curvature from the normals computed by the null screen method in corneal topography,” Proc. SPIE 8011, 80119J (2011). [CrossRef]
  13. Y. Mejía-Barbosa and D. Malacara-Hernández, “A review of methods for measuring corneal topography,” Optom. Vis. Sci. 78, 240–253 (2001). [CrossRef]
  14. O. Cardona-Nuñez, J. Pedraza-Contreras, A. Cornejo-Rodríguez, and A. Cordero-Dávila, “Significado de las superficies causticas en óptica,” Rev. Mex. Fís. 29, 245–258 (1983).
  15. S. A. Klein and R. B. Mandell, “Axial and instantaneous power conversion in corneal topography,” Invest. Ophthalmol. Visual Sci. 36, 2155–2159 (1995).
  16. R. Díaz-Uribe, “Medium-precision null-screen testing of off axis parabolic mirrors for segmented primary telescope optics: the large millimeter telescope,” Appl. Opt. 39, 2790–2804 (2000). [CrossRef]
  17. C. Menchaca and D. Malacara, “Directional curvature in a conic mirror,” Appl. Opt. 23, 3258–3260 (1984). [CrossRef]
  18. K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14, 11551–11565(2006). [CrossRef]
  19. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1992).
  20. J. R. Taylor, An Introduction to Error Analysis (University Science, 1997).
  21. Y. Mejía-Barbosa and D. Malacara-Hernández, “Object surface for applying a modified Hartmann test to measure corneal topography,” Appl. Opt. 40, 5778–5786 (2001). [CrossRef]
  22. B. A. Barsky, S. A. Klein, and D. D. Garcia, “Gaussian power with cylinder vector field representation for corneal topography maps,” Optom. Vis. Sci. 74, 917–925 (1997). [CrossRef]
  23. S. A. Klein, “A corneal topography algorithm that produces continuous curvature,” Optom. Vis. Sci. 69, 829–834 (1992). [CrossRef]
  24. T. O. Salmon and D. G. Horner, “Comparison of elevation, curvature, and power descriptors for corneal topographic mapping,” Optom. Vis. Sci. 72, 800–808 (1995). [CrossRef]
  25. Y. Mejía and J. C. Galeano, “Corneal topographer based on the Hartmann test,” Optom. Vis. Sci. 86, 370–381 (2009). [CrossRef]
  26. C. Roberts, “The accuracy of ‘power’ maps to display curvature data in corneal topography data,” Invest. Ophthalmol. Visual Sci. 35, 3525–3532 (1994).
  27. J. Schwiegerling and J. E. Greivenkamp, “Using corneal height maps and polynomial decomposition to determine corneal aberrations,” Optom. Vis. Sci. 74, 906–916 (1997). [CrossRef]
  28. S. A. Klein, “Axial curvature and the skew ray error in corneal topography,” Optom. Vis. Sci. 74, 931–944(1997). [CrossRef]
  29. D. Malacara, “Mathematical representation of an optical surface and its characteristics,” in Optical Shop Testing, D. Malacara, ed., 3rd ed. (Wiley, 2007), pp. 832–851.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited