OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 4, Iss. 4 — Apr. 1, 1987
  • pp: 643–650

Polynomial expansion of severely aberrated wave fronts

Joseph Braat  »View Author Affiliations


JOSA A, Vol. 4, Issue 4, pp. 643-650 (1987)
http://dx.doi.org/10.1364/JOSAA.4.000643


View Full Text Article

Enhanced HTML    Acrobat PDF (707 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The optimization of an optical system is generally carried out by minimizing the wave-front aberrations, the x and y transverse aberrations, or a combination of both. In the last-named, most general case, the optimization implies the treatment of a large number of functions of quite a different nature. We propose to use, together with the Zernike polynomials that orthogonalize the wave-front aberrations, a new set of wave-front polynomials that orthogonalize the transverse aberrations. These polynomials turn out to be a simple linear combination of Zernike polynomials. The combination of these two sets of wave-front polynomials with proper weighting yields the possibility of optimizing the frequency response of both slightly and severely aberrated systems in a formally identical way. The advantage of the method is that one does not have to leave the domain of the wave-front aberration to characterize an optical system, even when severe aberrations are present. The polynomials that minimize the transverse aberrations yield optimum response at very low frequencies; other linear combinations of Zernike polynomials are shown to maximize the frequency response at relatively high spatial frequencies.

© 1987 Optical Society of America

History
Original Manuscript: September 30, 1986
Manuscript Accepted: October 30, 1986
Published: April 1, 1987

Citation
Joseph Braat, "Polynomial expansion of severely aberrated wave fronts," J. Opt. Soc. Am. A 4, 643-650 (1987)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-4-4-643


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. M. Born, E. Wolf, Principles of Optics, 4th ed. (Pergamon, New York, 1970), p. 465.
  2. H. H. Hopkins, “The use of diffraction-based criteria of image quality in automatic optical design,” Opt. Acta 13, 343–369 (1966). [CrossRef]
  3. A. M. Goodbody, Tables of Optical Frequency Response, Summer School on Applied Optics (Imperial College, London, 1959).
  4. R. W. Gostick, “OTF-based optimization criteria for automatic optical design,” Opt. Quantum Electron. 8, 31–37 (1974). [CrossRef]
  5. B. R. A. Nijboer, “The diffraction theory of aberrations,” Ph.D. dissertation (University of Groningen, Groningen, The Netherlands, 1942).
  6. W. T. Welford, Aberrations of Optical Systems (Adam Hilger, Bristol, UK, 1986), p. 258.
  7. J. Kross, “Beschreibung, Analyse und Bewertung der Bildfehler optischer Systeme durch interpolierende Darstellungen mit Hilfe von Zernike-Kreispolynomen,” Optik 29, 65–80 (1969).

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited