Orthonormal vector polynomials in a unit circle, Part II: Completing the basis set

Chunyu Zhao, James H Burge

Research output: Contribution to journalArticle

50 Citations (Scopus)

Abstract

Zernike polynomials provide a well known, orthogonal set of scalar functions over a circular domain, and are commonly used to represent wavefront phase or surface irregularity. A related set of orthogonal functions is given here which represent vector quantities, such as mapping distortion or wavefront gradient. Previously, we have developed a basis of functions generated from gradients of Zernike polynomials. Here, we complete the basis by adding a complementary set of functions with zero divergence - those which are defined locally as a rotation or curl.

Original languageEnglish (US)
Pages (from-to)6586-6591
Number of pages6
JournalOptics Express
Volume16
Issue number9
DOIs
StatePublished - Apr 28 2008

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polynomials
orthogonal functions
gradients
irregularities
divergence
scalars

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Orthonormal vector polynomials in a unit circle, Part II : Completing the basis set. / Zhao, Chunyu; Burge, James H.

In: Optics Express, Vol. 16, No. 9, 28.04.2008, p. 6586-6591.

Research output: Contribution to journalArticle

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