OSA's Digital Library

Optics Letters

Optics Letters

| RAPID, SHORT PUBLICATIONS ON THE LATEST IN OPTICAL DISCOVERIES

  • Editor: Alan E. Willner
  • Vol. 38, Iss. 14 — Jul. 15, 2013
  • pp: 2487–2489

Recursive formula to compute Zernike radial polynomials

Barmak Honarvar Shakibaei and Raveendran Paramesran  »View Author Affiliations


Optics Letters, Vol. 38, Issue 14, pp. 2487-2489 (2013)
http://dx.doi.org/10.1364/OL.38.002487


View Full Text Article

Enhanced HTML    Acrobat PDF (192 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In optics, Zernike polynomials are widely used in testing, wavefront sensing, and aberration theory. This unique set of radial polynomials is orthogonal over the unit circle and finite on its boundary. This Letter presents a recursive formula to compute Zernike radial polynomials using a relationship between radial polynomials and Chebyshev polynomials of the second kind. Unlike the previous algorithms, the derived recurrence relation depends neither on the degree nor on the azimuthal order of the radial polynomials. This leads to a reduction in the computational complexity.

© 2013 Optical Society of America

OCIS Codes
(100.2960) Image processing : Image analysis
(080.1005) Geometric optics : Aberration expansions

ToC Category:
Geometric Optics

History
Original Manuscript: May 7, 2013
Revised Manuscript: June 15, 2013
Manuscript Accepted: June 16, 2013
Published: July 9, 2013

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

Citation
Barmak Honarvar Shakibaei and Raveendran Paramesran, "Recursive formula to compute Zernike radial polynomials," Opt. Lett. 38, 2487-2489 (2013)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-38-14-2487

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited