## Recurrence relations for the Cartesian derivatives of the Zernike polynomials |

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

http://dx.doi.org/10.1364/JOSAA.31.000708

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### Abstract

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

**History**

Original Manuscript: October 28, 2013

Revised Manuscript: December 18, 2013

Manuscript Accepted: January 3, 2014

Published: March 13, 2014

**Citation**

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

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-4-708

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