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Description
  • The Zernike polynomials are known in optical physics, and they are used for the various diffractions and aberrations problems of lenses. They are defined on a circle, so that their representation decouples radial and axial coordinates. It is know that the Zernike radial polynomials are represented through Jacobi polynomials. This paper deals with Chebyshev expansions for Jacobi polynomials. We have developed the recursive evaluation for spectral coefficients used in these expansions. These consequently provide a straightforward interpretation of Fourier transform of Zernike polynomials.
  • The Zernike polynomials are known in optical physics, and they are used for the various diffractions and aberrations problems of lenses. They are defined on a circle, so that their representation decouples radial and axial coordinates. It is know that the Zernike radial polynomials are represented through Jacobi polynomials. This paper deals with Chebyshev expansions for Jacobi polynomials. We have developed the recursive evaluation for spectral coefficients used in these expansions. These consequently provide a straightforward interpretation of Fourier transform of Zernike polynomials. (en)
Title
  • Zernike Polynomials and their Spectral Representation
  • Zernike Polynomials and their Spectral Representation (en)
skos:prefLabel
  • Zernike Polynomials and their Spectral Representation
  • Zernike Polynomials and their Spectral Representation (en)
skos:notation
  • RIV/68407700:21260/13:00210962!RIV14-GA0-21260___
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  • P(GAP102/11/1795)
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  • 118692
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  • RIV/68407700:21260/13:00210962
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  • Zernike polynomials; Jacobi polynomials; recursive algorithms; robust representation (en)
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  • [165869409FD9]
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  • Venice
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  • Venice
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  • Proceedings of the 2013 International Conference on Electronics, Signal Processing and Communication Systems (ESPCO 2013)
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  • Sovka, Pavel
  • Vlček, Miroslav
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number of pages
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  • EUROPMENT, European Society for Applied Sciences and Development
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  • 978-1-61804-207-1
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  • 21260
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