OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 3 — Jan. 30, 2012
  • pp: 2483–2499

Characterizing the shape of freeform optics

G. W. Forbes  »View Author Affiliations

Optics Express, Vol. 20, Issue 3, pp. 2483-2499 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (3456 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A recently introduced method for characterizing the shape of rotationally symmetric aspheres is generalized here for application to a wide class of freeform optics. New sets of orthogonal polynomials are introduced along with robust and efficient algorithms for computing the surface shape as well as its derivatives of any order. By construction, the associated characterization offers a rough interpretation of shape at a glance and it facilitates a range of estimates of manufacturability.

© 2012 OSA

OCIS Codes
(220.1250) Optical design and fabrication : Aspherics
(220.4610) Optical design and fabrication : Optical fabrication
(220.4830) Optical design and fabrication : Systems design
(220.4840) Optical design and fabrication : Testing

ToC Category:
Optical Design and Fabrication

Original Manuscript: November 21, 2011
Revised Manuscript: January 4, 2012
Manuscript Accepted: January 6, 2012
Published: January 19, 2012

G. W. Forbes, "Characterizing the shape of freeform optics," Opt. Express 20, 2483-2499 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. J. Birchall, “Lenses and their combination and arrangement in various instruments and apparatus,” U.S. patent 2,001,952 (21 May 1935).
  2. H. J. Birchall, “Lens of variable focal power having surfaces of involute form,” U.S. patent 2,475,275 (7 March 1949).
  3. C. W. Kanolt, “Multifocal ophthalmic lenses,” U.S. patent 2,878,721 (24 March 1959).
  4. W. T. Plummer, J. G. Baker, and J. Van Tassell, “Photographic optical systems with nonrotational aspheric surfaces,” Appl. Opt.38(16), 3572–3592 (1999). [CrossRef] [PubMed]
  5. L. Wang, P. Benítez, J. C. Miñano, J. Infante, and G. Biot, “Advances in the SMS design method for imaging optics,” Proc. SPIE8167, 81670M (2011). [CrossRef]
  6. F. Muñoz, P. Benítez, and J. C. Miñano, “High-order aspherics: the SMS nonimaging design method applied to imaging optics,” Proc. SPIE7061, 70610G, 70610G-9 (2008). [CrossRef]
  7. K. H. Fuerschbach, K. P. Thompson, and J. P. Rolland, “A new generation of optical systems with φ-polynomial surfaces,” Proc. SPIE7652, 76520C, 76520C-7 (2010). [CrossRef]
  8. J. R. Rogers, “A comparison of anamorphic, keystone, and Zernike surface types for aberration correction,” Proc. SPIE7652, 76520B, 76520B-8 (2010). [CrossRef]
  9. A. Yabe, “Method to allocate freeform surfaces in axially asymmetric optical systems,” Proc. SPIE8167, 816703, 816703-10 (2011). [CrossRef]
  10. R. Steinkopf, L. Dick, T. Kopf, A. Gebhardt, S. Risse, and R. Eberhardt, “Data handling and representation of freeform surfaces,” Proc. SPIE8169, 81690X, 81690X-9 (2011). [CrossRef]
  11. P. Jester, C. Menke, and K. Urban, “B-spline representation of optical surfaces and its accuracy in a ray trace algorithm,” Appl. Opt.50(6), 822–828 (2011). [CrossRef] [PubMed]
  12. G. W. Forbes, “Manufacturability estimates for optical aspheres,” Opt. Express19(10), 9923–9941 (2011). [CrossRef] [PubMed]
  13. G. W. Forbes, “Shape specification for axially symmetric optical surfaces,” Opt. Express15(8), 5218–5226 (2007). [CrossRef] [PubMed]
  14. G. W. Forbes, “Robust, efficient computational methods for axially symmetric optical aspheres,” Opt. Express18(19), 19700–19712 (2010). [CrossRef] [PubMed]
  15. C. Zhao and J. H. Burge, “Orthonormal vector polynomials in a unit circle, Part I: Basis set derived from gradients of Zernike polynomials,” Opt. Express15(26), 18014–18024 (2007). [CrossRef] [PubMed]
  16. G. W. Forbes, “Robust and fast computation for the polynomials of optics,” Opt. Express18(13), 13851–13862 (2010). [CrossRef] [PubMed]

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