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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 20 — Sep. 24, 2012
  • pp: 22683–22691

Comparative assessment of freeform polynomials as optical surface descriptions

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

Optics Express, Vol. 20, Issue 20, pp. 22683-22691 (2012)

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Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enables the fabrication of freeform optics, or more specifically, optical surfaces for imaging applications that are not rotationally symmetric. Various forms of polynomials for describing freeform optical surfaces exist in optical design and to support fabrication. A popular method is to add orthogonal polynomials onto a conic section. In this paper, recently introduced gradient-orthogonal polynomials are investigated in a comparative manner with the widely known Zernike polynomials. In order to achieve numerical robustness when higher-order polynomials are required to describe freeform surfaces, recurrence relations are a key enabler. Results in this paper establish the equivalence of both polynomial sets in accurately describing freeform surfaces under stringent conditions. Quantifying the accuracy of these two freeform surface descriptions is a critical step in the future application of these tools in both advanced optical system design and optical fabrication.

© 2012 OSA

OCIS Codes
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.4610) Optical design and fabrication : Optical fabrication
(220.4830) Optical design and fabrication : Systems design

ToC Category:
Optical Design and Fabrication

Original Manuscript: June 20, 2012
Manuscript Accepted: August 28, 2012
Published: September 19, 2012

Ilhan Kaya, Kevin P. Thompson, and Jannick P. Rolland, "Comparative assessment of freeform polynomials as optical surface descriptions," Opt. Express 20, 22683-22691 (2012)

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  1. O. Cakmakci, S. Vo, K. P. Thompson, and J. P. Rolland, “Application of radial basis functions to shape description in a dual-element off-axis eyewear display: Field-of-view limit,” Inf. Display - J. Soc. I 16, 1089–1098 (2008).
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