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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 33, Iss. 34 — Dec. 1, 1994
  • pp: 8121–8124

Zernike Circle Polynomials and Optical Aberrations of Systems with Circular Pupils

Virendra N. Mahajan  »View Author Affiliations


Applied Optics, Vol. 33, Issue 34, pp. 8121-8124 (1994)
http://dx.doi.org/10.1364/AO.33.008121


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Abstract

Zernike circle polynomials, their numbering scheme, and relationship to balanced optical aberrations of systems with circular pupils are discussed.

© 1994 Optical Society of America

Citation
Virendra N. Mahajan, "Zernike Circle Polynomials and Optical Aberrations of Systems with Circular Pupils," Appl. Opt. 33, 8121-8124 (1994)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-33-34-8121


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References

  1. F. Zernike, “Diffraction theory of knife-edge test and its improved form, the phase contrast method,” Mon. Not. R. Astron. Soc. 94, 377–384 (1934);“Beugungs-theorie des Schneidenverfahrens und Seiner Verbes-serten Form, der Phasenkontrastmethode,” Physica 1, 689–704 (1934).
  2. B. R. A. Nijboer, “The diffraction theory of aberrations,” Ph.D. thesis (University of Groningen, The Netherlands, 1942).Also, Physica 23, 605–620 (1947.
  3. M. Born, E. Wolf, Principles of Optics, 5th ed. Pergamon, New York, N.Y. (1975), Chapter 9.
  4. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  5. Bill Swantner, “Comparison of Zernike polynomial sets in commercial software,” Opt & Phot. News 9 (1992), pp. 42–43.
  6. R. K. Tyson, “Using Zernike polynomials,” Opt. & Phot. News 12, 3 (1992).
  7. J. R. Rogers, “Zernike polynomials,” Opt. & Phot. News 8, 2–3 (1993).
  8. 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]
  9. 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]
  10. C.-J. Kim, R. R. Shannon, “Catalog of Zernike polynomials,” in Applied Optics and Optical Engineering, Vol. X, pp. 193–221, R. R. Shannon, J. Wyant eds. Academic Press, New York, N.Y. (1987).
  11. S. Zhang, R. R. Shannon, “Catalog of spot diagrams,” in Applied Optics and Optical Engineering, Vol. XI, pp. 201–238, R. R. Shannon, J. Wyant eds. Academic Press, New York, N.Y. (1992).
  12. J. Wyant, K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, Vol. XI, pp. 1–53, R. R. Shannon, J. Wyant Eds. Academic Press, New York, N.Y. (1992).

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