### 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 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

## Fingerprint Dive into the research topics of 'Orthonormal vector polynomials in a unit circle, Part II: Completing the basis set'. Together they form a unique fingerprint.

## Cite this

Zhao, C., & Burge, J. H. (2008). Orthonormal vector polynomials in a unit circle, Part II: Completing the basis set.

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