OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1686–1688

Accurate computation of mean power and astigmatism by means of Zernike polynominals

Rainer G. Dorsch, Walter A. Haimerl, and Gregor K. Esser  »View Author Affiliations

JOSA A, Vol. 15, Issue 6, pp. 1686-1688 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (170 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



In the past few years considerable effort has been made to extract basic surface aberrations, such as mean surface power and surface astigmatism, from corneal surface-height data, e.g., as measured by videokeratoscopes. Two applications are corneal surgery and contact lens adjustment. Another primary application is the derivation of the mean power and astigmatism of a wave front, e.g., in interferometers and other wave-front sensors. Both surface and wave-front quantities can be computed by means of Zernike polynominals. One advantage of this computation is that Zernike polynominal expansion provides all the coefficients at once for calculating Seidel aberrations. We present accurate analytical formulas for computing the mean power and astigmatism of both surface and wave front from Zernike coefficients. Therefore, in general, those quantities are not a function of quadratic-order terms alone, as stated in BornM.WolfE., Principles of Optics (Pergamon, New York, 1975), Sec. 9.2, but include linear-order terms as well.

© 1998 Optical Society of America

OCIS Codes
(080.1010) Geometric optics : Aberrations (global)
(080.2720) Geometric optics : Mathematical methods (general)

Original Manuscript: January 29, 1998
Manuscript Accepted: February 10, 1998
Published: June 1, 1998

Rainer G. Dorsch, Walter A. Haimerl, and Gregor K. Esser, "Accurate computation of mean power and astigmatism by means of Zernike polynominals," J. Opt. Soc. Am. A 15, 1686-1688 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1975), Sec. 9.2.
  2. J. Y. Wang, D. E. Silva, “Wave-front interpretation with Zernike polynominals,” Appl. Opt. 19, 1510–1518 (1980). [CrossRef] [PubMed]
  3. For example, Schaum’s Outline, Differential Geometry (McGraw-Hill, New York, 1980).
  4. J. Schwiegerlin, J. E. Greivenkamp, J. M. Miller, “Zernike polynominal representations of videokeratoscope height data,” in Vision Science and Its Applications, Vol. 1 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 41–44.
  5. J. A. Gomez-Pedrero, G. Rueda-Colinas, E. Bernabeu, “Automatic interferometric method for the study of the oblique central refraction in ophthalmic lenses,” Optik (Stuttgart) 104, 171–174 (1997).
  6. G. Löffler, E. Lingelbach, B. Lingelbach, “Cornea: Abbildungseigenschaften und Topometrie, part I,” Deutsch. Optik. Z. 4, 92–96 (1997); “part II,” 104–107 (1997).

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