## Robust and fast computation for the polynomials of optics

Optics Express, Vol. 18, Issue 13, pp. 13851-13862 (2010)

http://dx.doi.org/10.1364/OE.18.013851

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### Abstract

Mathematical methods that are poorly known in the field of optics are adapted and shown to have striking significance. Orthogonal polynomials are common tools in physics and optics, but problems are encountered when they are used to higher orders. Applications to arbitrarily high orders are shown to be enabled by remarkably simple and robust algorithms that are derived from well known recurrence relations. Such methods are demonstrated for a couple of familiar optical applications where, just as in other areas, there is a clear trend to higher orders.

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**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

**ToC Category:**

Optical Design and Fabrication

**History**

Original Manuscript: May 12, 2010

Revised Manuscript: June 2, 2010

Manuscript Accepted: June 3, 2010

Published: June 11, 2010

**Citation**

G. W. Forbes, "Robust and fast computation for the polynomials of optics," Opt. Express **18**, 13851-13862 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-13-13851

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