OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 6 — Feb. 20, 2013
  • pp: 1136–1147

Orthonormal aberration polynomials for optical systems with circular and annular sector pupils

José Antonio Díaz and Virendra N. Mahajan  »View Author Affiliations


Applied Optics, Vol. 52, Issue 6, pp. 1136-1147 (2013)
http://dx.doi.org/10.1364/AO.52.001136


View Full Text Article

Enhanced HTML    Acrobat PDF (1498 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Using the Zernike circle polynomials as the basis functions, we obtain the orthonormal polynomials for optical systems with circular and annular sector pupils by the Gram–Schmidt orthogonalization process. These polynomials represent balanced aberrations yielding minimum variance of the classical aberrations of rotationally symmetric systems. Use of the polynomials obtained is illustrated with numerical examples.

© 2013 Optical Society of America

OCIS Codes
(010.7350) Atmospheric and oceanic optics : Wave-front sensing
(110.0110) Imaging systems : Imaging systems
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1010) Optical design and fabrication : Aberrations (global)

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: November 28, 2012
Manuscript Accepted: December 26, 2012
Published: February 11, 2013

Citation
José Antonio Díaz and Virendra N. Mahajan, "Orthonormal aberration polynomials for optical systems with circular and annular sector pupils," Appl. Opt. 52, 1136-1147 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-6-1136


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. W. Swantner and W. W. Chow, “Gram–Schmidt orthogonalization of Zernike polynomials for general aperture shapes,” Appl. Opt. 33, 1832–1837 (1994). [CrossRef]
  2. D. A. Thomas and J. C. Wyant, “Determination of the dihedral angle errors of a corner cube from its Twyman–Green interferogram,” J. Opt. Soc. Am. 67, 467–472 (1977). [CrossRef]
  3. R. A. Lessard and S. C. Som, “Imaging properties of sector-shaped apertures,” Appl. Opt. 11, 811–817 (1972). [CrossRef]
  4. G. Urcid and A. Padilla, “Far-field diffraction patterns of circular sectors and related apertures,” Appl. Opt. 44, 7677–7696 (2005). [CrossRef]
  5. S. Huang, F. Xi, C. Liu, and Z. Jiang, “Phase retrieval on annular and annular sector pupils by using the eigenfunctions method to solve the transport intensity equation,” J. Opt. Soc. Am. A 29, 513–520 (2012). [CrossRef]
  6. S. D. Goodrow and T. W. Murphy, “Effects of thermal gradients in total internal reflection corner cubes,” Appl. Opt. 51, 8793–8799 (2012). [CrossRef]
  7. T. W. Murphy and S. D. Goodrow, “Polarization and far-field diffraction patterns of total internal reflection corner cubes,” Appl. Opt. 52, 117–126 (2013). [CrossRef]
  8. R. J. Noll, “Zernike polynomials and atmospheric turbulence,” J. Opt. Soc. Am. 66, 207–211 (1976). [CrossRef]
  9. V. N. Mahajan, Optical Imaging and Aberrations, Part II: Wave Diffraction Optics, 2nd ed. (SPIE, 2011).
  10. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers (McGraw-Hill, 1968).
  11. V. N. Mahajan, “Zernike annular polynomials for imaging systems with annular pupils,” J. Opt. Soc. Am. 71, 75–85 (1981). [CrossRef]
  12. V. N. Mahajan, “Zernike annular polynomials and optical aberrations of systems with annular pupils,” Appl. Opt. 33, 8125–8127 (1994). [CrossRef]
  13. G.-M. Dai and V. N. Mahajan, “Nonrecursive orthonormal polynomials with matrix formulation,” Opt. Lett. 32, 74–76 (2007). [CrossRef]
  14. Wolfram Research, Inc., Mathematica, Version 8.0, Champaign, Illinois (2010).

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