OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 22 — Oct. 24, 2011
  • pp: 21174–21179

Applying slope constrained Q-type aspheres to develop higher performance lenses

Bin Ma, Lin Li, Kevin P. Thompson, and Jannick P. Rolland  »View Author Affiliations

Optics Express, Vol. 19, Issue 22, pp. 21174-21179 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1108 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



It has recently been shown that the coefficients that specify the aspheric departure from a spherical surface in high NA lithographic lenses routinely require more significant digits than are available in even double precision computers when they are described as part of a power series in aperture-squared. The Q-type aspheric description has been introduced to solve this problem. An important by-product of this new surface description is that it allows the slope of a surface to be directly constrained during optimization. Results show that Q-type aspheric surfaces that are optimized with slope constraints are not only more testable, an original motivation, but, they can also lead to solutions that are less sensitive to assembly induced misalignments for lithographic quality lenses. Specifically, for a representative NA 0.75 lens, the sensitivity to tilt and decenter is reduced by more than 3X, resulting in significantly higher lens performance in-use.

© 2011 OSA

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1250) Optical design and fabrication : Aspherics
(220.3740) Optical design and fabrication : Lithography
(220.4830) Optical design and fabrication : Systems design

ToC Category:
Optical Design and Fabrication

Original Manuscript: July 11, 2011
Revised Manuscript: August 18, 2011
Manuscript Accepted: September 21, 2011
Published: October 10, 2011

Bin Ma, Lin Li, Kevin P. Thompson, and Jannick P. Rolland, "Applying slope constrained Q-type aspheres to develop higher performance lenses," Opt. Express 19, 21174-21179 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Abbe, “Lens system,” U.S. Patent 697,959 (Apr. 1902).
  2. G. W. Forbes, “Robust, efficient computational methods for axially symmetric optical aspheres,” Opt. Express 18(19), 19700–19712 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-19-19700 . [CrossRef] [PubMed]
  3. G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express 15(8), 5218–5226 (2007), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-8-5218 . [CrossRef] [PubMed]
  4. J. Kross, F. W. Oertmann, and R. Schuhmann, “On aspherics in optical systems,” Proc. SPIE 655, 300–309 (1986).
  5. 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]
  6. G. W. Forbes, “Manufacturability estimates for optical aspheres,” Opt. Express 19(10), 9923–9941 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-10-9923 . [CrossRef] [PubMed]
  7. D. Stephenson, “Improving asphere manufacturability using Forbes polynomials,” in Proceedings of the SPIE OptiFab, TD07–38 (2011).
  8. Y. Omura, “Projection exposure methods and apparatus, and projection optical systems,” U.S. Patent 6,606,144 Bl (Aug. 2003).
  9. T. G. Kuper and J. R. Rogers, “Automatic determination of optimal aspheric placement,” in International Optical Design Conference, Technical Digest (CD) (Optical Society of America, 2010), paper IThB3. http://www.opticsinfobase.org/abstract.cfm?URI=IODC-2010-IThB3 .
  10. J. R. Rogers, “Using global synthesis to find tolerance-insensitive design forms,” in International Optical Design Conference, Technical Digest (CD) (Optical Society of America, 2006), paper TuA4. http://www.opticsinfobase.org/abstract.cfm?URI=IODC-2006-TuA4 .
  11. P. Murphy, J. Fleig, G. Forbes, D. Miladinovic, G. DeVries, and S. O'Donohue, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930J, 62930J-10 (2006). [CrossRef]
  12. J. E. Greivenkamp, A. E. Lowman, and R. J. Palum, “Sub-Nyquist interferometry: implementation and measurement capability,” Opt. Eng. 35(10), 2962–2969 (1996). [CrossRef]
  13. Optical Research Associates, “Release Notes CODE V 10.3 ALPHA” (2010).

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.


Fig. 1 Fig. 2

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited