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Applied Optics

Applied Optics


  • Vol. 43, Iss. 20 — Jul. 9, 2004
  • pp: 3963–3966

Zernike expansion of separable functions of Cartesian coordinates

Colin J. R. Sheppard, Sam Campbell, and Michael D. Hirschhorn  »View Author Affiliations

Applied Optics, Vol. 43, Issue 20, pp. 3963-3966 (2004)

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A Zernike expansion over a circle is given for an arbitrary function of a single linear spatial coordinate. The example of a half-plane mask (Hilbert filter) is considered. The expansion can also be applied to cylindrical aberrations over a circular pupil. A product of two such series can thus be used to expand an arbitrary separable function of two Cartesian coordinates.

© 2004 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(080.1010) Geometric optics : Aberrations (global)
(260.1960) Physical optics : Diffraction theory

Original Manuscript: October 4, 2003
Revised Manuscript: April 22, 2004
Published: July 10, 2004

Colin J. R. Sheppard, Sam Campbell, and Michael D. Hirschhorn, "Zernike expansion of separable functions of Cartesian coordinates," Appl. Opt. 43, 3963-3966 (2004)

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