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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 52, Iss. 24 — Aug. 20, 2013
  • pp: 5962–5964

Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration: comment

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


Applied Optics, Vol. 52, Issue 24, pp. 5962-5964 (2013)
http://dx.doi.org/10.1364/AO.52.005962


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Abstract

Recently, Hasan and Shaker published a set of orthonormal polynomials for an annular elliptical pupil obtained by the Gram–Schmidt orthogonalization of the Zernike circle polynomials [Appl. Opt. 51, 8490 (2012)]. However, the expressions for many of the polynomials are incorrect, apparently due to wrong usage of the Gram–Schmidt orthogonalization process. We provide the correct equations for the orthogonalization process and the expressions for the orthonormal polynomials obtained by applying them.

© 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:
Image Processing

History
Original Manuscript: March 11, 2013
Manuscript Accepted: May 16, 2013
Published: August 15, 2013

Citation
José Antonio Díaz and Virendra N. Mahajan, "Study of Zernike polynomials of an elliptical aperture obscured with an elliptical obscuration: comment," Appl. Opt. 52, 5962-5964 (2013)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-52-24-5962

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