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Applied Optics

Applied Optics


  • Vol. 19, Iss. 9 — May. 1, 1980
  • pp: 1510–1518

Wave-front interpretation with Zernike polynomials

J. Y. Wang and D. E. Silva  »View Author Affiliations

Applied Optics, Vol. 19, Issue 9, pp. 1510-1518 (1980)

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Several low-order Zernike modes are photographed for visualization. These polynomials are extended to include both circular and annular pupils through a Gram-Schmidt orthogonalization procedure. Contrary to the traditional understanding, the classical least-squares method of determining the Zernike coefficients from a sampled wave front with measurement noise has been found numerically stable. Furthermore, numerical analysis indicates that the so-called Gram-Schmidt method and the least-squares method give practically identical results. An alternate method using the orthogonal property of the polynomials to determine their coefficients is also discussed.

© 1980 Optical Society of America

Original Manuscript: September 13, 1979
Published: May 1, 1980

J. Y. Wang and D. E. Silva, "Wave-front interpretation with Zernike polynomials," Appl. Opt. 19, 1510-1518 (1980)

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