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Applied Optics

Applied Optics


  • Vol. 33, Iss. 10 — Apr. 1, 1994
  • pp: 1832–1837

Gram–Schmidt orthonormalization of Zernike polynomials for general aperture shapes

W. Swantner and Weng W. Chow  »View Author Affiliations

Applied Optics, Vol. 33, Issue 10, pp. 1832-1837 (1994)

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We present analytical derivations of aberration functions for annular sector apertures. We show that the Zernike functions for circular apertures can be generalized for any aperture shape. Interferogram reduction when Zernike functions were used as a basis set was performed on annular sectors. We have created a computer program to generate orthogonal aberration functions. Completely general aperture shapes and user-selected basis sets may be treated with a digital Gram–Schmidt orthonormalization approach.

© 1994 Optical Society of America

Original Manuscript: August 7, 1992
Published: April 1, 1994

W. Swantner and Weng W. Chow, "Gram–Schmidt orthonormalization of Zernike polynomials for general aperture shapes," Appl. Opt. 33, 1832-1837 (1994)

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  14. vaxima/macsyma are copyrighted by the Mathlab Group, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Mass.

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