OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 18 — Jun. 20, 2012
  • pp: 4210–4214

Mathematical construction and perturbation analysis of Zernike discrete orthogonal points

Zhenguang Shi, Yongxin Sui, Zhenyu Liu, Ji Peng, and Huaijiang Yang  »View Author Affiliations


Applied Optics, Vol. 51, Issue 18, pp. 4210-4214 (2012)
http://dx.doi.org/10.1364/AO.51.004210


View Full Text Article

Enhanced HTML    Acrobat PDF (328 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Zernike functions are orthogonal within the unit circle, but they are not over the discrete points such as CCD arrays or finite element grids. This will result in reconstruction errors for loss of orthogonality. By using roots of Legendre polynomials, a set of points within the unit circle can be constructed so that Zernike functions over the set are discretely orthogonal. Besides that, the location tolerances of the points are studied by perturbation analysis, and the requirements of the positioning precision are not very strict. Computer simulations show that this approach provides a very accurate wavefront reconstruction with the proposed sampling set.

© 2012 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(220.4840) Optical design and fabrication : Testing
(080.1005) Geometric optics : Aberration expansions

History
Original Manuscript: March 20, 2012
Revised Manuscript: April 28, 2012
Manuscript Accepted: April 29, 2012
Published: June 18, 2012

Citation
Zhenguang Shi, Yongxin Sui, Zhenyu Liu, Ji Peng, and Huaijiang Yang, "Mathematical construction and perturbation analysis of Zernike discrete orthogonal points," Appl. Opt. 51, 4210-4214 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-18-4210

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