OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 27 — Dec. 19, 2011
  • pp: 26962–26974

Edge clustered fitting grids for φ-polynomial characterization of freeform optical surfaces

Ilhan Kaya, Kevin P. Thompson, and Jannick P. Rolland  »View Author Affiliations


Optics Express, Vol. 19, Issue 27, pp. 26962-26974 (2011)
http://dx.doi.org/10.1364/OE.19.026962


View Full Text Article

Enhanced HTML    Acrobat PDF (2955 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

With the recent emergence of slow-servo diamond turning, optical designs with surfaces that are not intrinsically rotationally symmetric can be manufactured. In this paper, we demonstrate some important limitations to Zernike polynomial representation of optical surfaces in describing the evolving freeform surface descriptions that are effective for optical design and encountered during optical fabrication. Specifically, we show that the ray grids commonly used in sampling a freeform surface to form a database from which to perform a φ-polynomial fit is limiting the efficacy of computation. We show an edge-clustered fitting grid that effectively suppresses the edge ringing that arises as the polynomial adapts to the fully nonsymmetric features of the surface.

© 2011 OSA

OCIS Codes
(000.3860) General : Mathematical methods in physics
(080.2740) Geometric optics : Geometric optical design
(220.0220) Optical design and fabrication : Optical design and fabrication

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: October 17, 2011
Manuscript Accepted: November 28, 2011
Published: December 16, 2011

Citation
Ilhan Kaya, Kevin P. Thompson, and Jannick P. Rolland, "Edge clustered fitting grids for φ-polynomial characterization of freeform optical surfaces," Opt. Express 19, 26962-26974 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-27-26962


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. E. Abbe, Lens system. U.S. Patent No. 697,959, (April, 1902).
  2. G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express15(8), 5218–5226 (2007). [CrossRef] [PubMed]
  3. B. Ma, L. Li, K. P. Thompson, and J. P. Rolland, “Applying slope constrained Q-type aspheres to develop higher performance lenses,” Opt. Express19(22), 21174–21179 (2011). [CrossRef] [PubMed]
  4. Y. Tohme and R. Murray, “Principles and Applications of the Slow Slide Servo,” Moore Nanotechnology Systems White Paper (2005).
  5. F. Zernike, “Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode,” Physica1(7-12), 689–704 (1934). [CrossRef]
  6. J. P. Rolland, C. Dunn, and K. P. Thompson, “An Analytic Expression for the Field Dependence of FRINGE Zernike Polynomial Coefficients in Rotationally Symmetric Optical Systems,” Proc. SPIE7790, (2010).
  7. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express19(22), 21919–21928 (2011). [CrossRef] [PubMed]
  8. O. Cakmakci, B. Moore, H. Foroosh, and J. P. Rolland, “Optimal local shape description for rotationally non-symmetric optical surface design and analysis,” Opt. Express16(3), 1583–1589 (2008). [CrossRef] [PubMed]
  9. G. W. Forbes, “Robust and fast computation for the polynomials of optics,” Opt. Express18(13), 13851–13862 (2010). [CrossRef] [PubMed]
  10. M. Born and E. Wolf, Principles of Optics, (Cambridge, 1999).
  11. A. B. Bhatia, E. Wolf, and M. Born, “On the circle polynomials of Zernike and related orthogonal sets,” Proc. Camb. Philos. Soc.50(1), 40–48 (1954). [CrossRef]
  12. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions, chap. 22, (Dover, 1972).
  13. G. E. Fasshauer, Meshfree Approximation Methods with MATLAB (World Scientific Publishing, Singapore, 2007).
  14. B. Fornberg, E. Larsson, and N. Flyer, “Stable computations with Gaussian radial basis functions,” SIAM J. Sci. Comput.33(2), 869–892 (2011). [CrossRef]
  15. R. Platte, Accuracy and Stability of Global Radial Basis Function Methods for the Numerical Solution of Partial Differential Equations, Ph.D. Thesis, (University of Delaware, 2005).

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