Orthonormal vector polynomials in a unit circle, application: Fitting mapping distortions in a null test

Chunyu Zhao, James H Burge

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Citations (Scopus)

Abstract

We developed a complete and orthonormal set of vector polynomials defined over a unit circle. One application of these vector polynomials is for fitting the mapping distortions in an interferometric null test. This paper discusses the source of the mapping distortions and the approach of fitting the mapping relations, and justifies why the set of vector polynomials is the appropriate choice for this purpose. Examples are given to show the excellent fitting results with the polynomials.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Volume7426
DOIs
StatePublished - 2009
EventOptical Manufacturing and Testing VIII - San Diego, CA, United States
Duration: Aug 4 2009Aug 5 2009

Other

OtherOptical Manufacturing and Testing VIII
CountryUnited States
CitySan Diego, CA
Period8/4/098/5/09

Fingerprint

Orthonormal
Unit circle
Null
polynomials
Polynomials
Set of vectors
Polynomial
Justify

Keywords

  • Aberration
  • Mapping distortion
  • Optical testing

ASJC Scopus subject areas

  • Applied Mathematics
  • Computer Science Applications
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

Cite this

Zhao, C., & Burge, J. H. (2009). Orthonormal vector polynomials in a unit circle, application: Fitting mapping distortions in a null test. In Proceedings of SPIE - The International Society for Optical Engineering (Vol. 7426). [74260V] https://doi.org/10.1117/12.828288

Orthonormal vector polynomials in a unit circle, application : Fitting mapping distortions in a null test. / Zhao, Chunyu; Burge, James H.

Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7426 2009. 74260V.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Zhao, C & Burge, JH 2009, Orthonormal vector polynomials in a unit circle, application: Fitting mapping distortions in a null test. in Proceedings of SPIE - The International Society for Optical Engineering. vol. 7426, 74260V, Optical Manufacturing and Testing VIII, San Diego, CA, United States, 8/4/09. https://doi.org/10.1117/12.828288
Zhao C, Burge JH. Orthonormal vector polynomials in a unit circle, application: Fitting mapping distortions in a null test. In Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7426. 2009. 74260V https://doi.org/10.1117/12.828288
Zhao, Chunyu ; Burge, James H. / Orthonormal vector polynomials in a unit circle, application : Fitting mapping distortions in a null test. Proceedings of SPIE - The International Society for Optical Engineering. Vol. 7426 2009.
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