OSA's Digital Library

Optics Letters

Optics Letters


  • Editor: Anthony J. Campillo
  • Vol. 31, Iss. 4 — Feb. 15, 2006
  • pp: 501–503

Zernike aberration coefficients transformed to and from Fourier series coefficients for wavefront representation

Guang-ming Dai  »View Author Affiliations

Optics Letters, Vol. 31, Issue 4, pp. 501-503 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (144 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The set of Fourier series is discussed following some discussion of Zernike polynomials. Fourier transforms of Zernike polynomials are derived that allow for relating Fourier series expansion coefficients to Zernike polynomial expansion coefficients. With iterative Fourier reconstruction, Zernike representations of wavefront aberrations can easily be obtained from wavefront derivative measurements.

© 2006 Optical Society of America

OCIS Codes
(000.3870) General : Mathematics
(010.1080) Atmospheric and oceanic optics : Active or adaptive optics
(010.1290) Atmospheric and oceanic optics : Atmospheric optics
(220.1010) Optical design and fabrication : Aberrations (global)
(330.4460) Vision, color, and visual optics : Ophthalmic optics and devices

ToC Category:
Optical Design and Fabrication

Original Manuscript: September 6, 2005
Revised Manuscript: October 15, 2005
Manuscript Accepted: October 17, 2005

Virtual Issues
Vol. 1, Iss. 3 Virtual Journal for Biomedical Optics

Guang-ming Dai, "Zernike aberration coefficients transformed to and from Fourier series coefficients for wavefront representation," Opt. Lett. 31, 501-503 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. K. Tyson, Opt. Lett. 7, 262 (1982). [CrossRef] [PubMed]
  2. G. Conforti, Opt. Lett. 8, 390 (1983). [CrossRef]
  3. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, 1965), Sec. 9.2.
  4. F. Roddier and C. Roddier, Appl. Opt. 30, 1325 (1991). [CrossRef] [PubMed]
  5. L. A. Poyneer, M. Troy, B. Macintosh, and D. T. Gavel, Opt. Lett. 28, 798 (2003). [CrossRef] [PubMed]
  6. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Formulas, Graphs, and Mathematical Tables (Dover, 1972), formulas 9.1.44, 9.1.45, and 11.4.6.
  7. R. J. Noll, J. Opt. Soc. Am. 66, 207 (1976). [CrossRef]
  8. Equation in Ref. has an extra multiplication factor of 1/pi.
  9. G.-m. Dai, J. Opt. Soc. Am. A 13, 1218 (1996). [CrossRef]
  10. V. N. Mahajan, in Proc. SPIE 5173, 1 (2003). [CrossRef]

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