### 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 language | English (US) |
---|---|

Pages (from-to) | 6586-6591 |

Number of pages | 6 |

Journal | Optics Express |

Volume | 16 |

Issue number | 9 |

DOIs | |

State | Published - Apr 28 2008 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Optics Express*,

*16*(9), 6586-6591. https://doi.org/10.1364/OE.16.006586

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

Research output: Contribution to journal › Article

*Optics Express*, vol. 16, no. 9, pp. 6586-6591. https://doi.org/10.1364/OE.16.006586

}

TY - JOUR

T1 - Orthonormal vector polynomials in a unit circle, Part II

T2 - Completing the basis set

AU - Zhao, Chunyu

AU - Burge, James H

PY - 2008/4/28

Y1 - 2008/4/28

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=43049130025&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=43049130025&partnerID=8YFLogxK

U2 - 10.1364/OE.16.006586

DO - 10.1364/OE.16.006586

M3 - Article

C2 - 18545361

AN - SCOPUS:43049130025

VL - 16

SP - 6586

EP - 6591

JO - Optics Express

JF - Optics Express

SN - 1094-4087

IS - 9

ER -