OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 33, Iss. 34 — Dec. 1, 1994
  • pp: 8125–8127

Zernike Annular Polynomials and Optical Aberrations of Systems with Annular Pupils

By Virendra N. Mahajan  »View Author Affiliations

Applied Optics, Vol. 33, Issue 34, pp. 8125-8127 (1994)

View Full Text Article

Enhanced HTML    Acrobat PDF (629 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Zernike annular polynomials that represent orthogonal and balanced aberrations suitable for systems with annular pupils are described. Their numbering scheme is the same as for Zernike circle polynomials. Expressions for standard deviation of primary and balanced primary aberrations are given.

© 1994 Optical Society of America

By Virendra N. Mahajan, "Zernike Annular Polynomials and Optical Aberrations of Systems with Annular Pupils," Appl. Opt. 33, 8125-8127 (1994)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. V. N. Mahajan, “Zernike circle polynomials and optical aberrations of systems with circular pupils.” Eng. Lab. Notes in Opt. & Phot. News 5, (1994).
  2. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 71, 75–85, 1408 (1981),J. Opt. Soc. Am.A1, 685 (1984). [CrossRef]
  3. V. N. Mahajan, “Uniform versus Gaussian beams: A comparison of the effects of diffraction, obscuration, and aberrations,” J. Opt. Soc. Am. A3, 470–485 (1986). [CrossRef]
  4. W. H. Steel, “Etude des effets combines des aberrations et d'une obturation centrale de la pupille sur le contraste des images optiques,” Rev. Opt. (Paris) 32, 143–178 (1953).
  5. B. Tatian, “Aberration balancing in rotationally symmetric lenses,” J. Opt. Soc. Am. 64, 1083–1091 (1974). [CrossRef]
  6. S. Szapiel, “Aberration balancing techniques for radially symmetric amplitude distributions: a generalization of the Maréchal approach,” J. Opt. Soc. Am. 2, 947–956 (1985).
  7. V. N. Mahajan, Aberration Theory Made Simple, SPIE Press, 1991, Section 9.2.3. Note that the expressions for standard deviation of spherical aberration and astigmatism given in Table 9-2 of the first and second printing of this reference have some errors. Correct expressions appear in the third printing. [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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited