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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 31, Iss. 4 — Apr. 1, 2014
  • pp: 708–715

Recurrence relations for the Cartesian derivatives of the Zernike polynomials

Philip C. L. Stephenson  »View Author Affiliations

JOSA A, Vol. 31, Issue 4, pp. 708-715 (2014)

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A recurrence relation for the first-order Cartesian derivatives of the Zernike polynomials is derived. This relation is used with the Clenshaw method to determine an efficient method for calculating the derivatives of any linear series of Zernike polynomials.

OCIS Codes
(000.3860) General : Mathematical methods in physics
(220.0220) Optical design and fabrication : Optical design and fabrication
(220.1250) Optical design and fabrication : Aspherics
(260.1960) Physical optics : Diffraction theory
(080.1005) Geometric optics : Aberration expansions

ToC Category:
Optical Design and Fabrication

Original Manuscript: October 28, 2013
Revised Manuscript: December 18, 2013
Manuscript Accepted: January 3, 2014
Published: March 13, 2014

Philip C. L. Stephenson, "Recurrence relations for the Cartesian derivatives of the Zernike polynomials," J. Opt. Soc. Am. A 31, 708-715 (2014)

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Fig. 1. Fig. 2.

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