Filter-generating system of Zernike polynomials

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dc.contributor.authorHonarvar Shakibaei Asli, Barmak
dc.contributor.authorFlusser, Jan
dc.contributor.authorZhao, Yifan
dc.contributor.authorErkoyuncu, John Ahmet
dc.date.accessioned2019-08-09T10:34:23Z
dc.date.available2019-08-09T10:34:23Z
dc.date.issued2019-07-24
dc.description.abstractThis work proposes a new approach to find the generating function (GF) of the Zernike polynomials in two dimensional form. Combining the methods of GFs and discrete-time systems, we can develop two dimensional digital systems for systematic generation of entire orders of Zernike polynomials. We establish two different formulas for the GF of the radial Zernike polynomials based on both the degree and the azimuthal order of the radial polynomials. In this paper, we use four terms recurrence relation instead of the ordinary three terms recursion to calculate the radial Zernike polynomials and their GFs using unilateral 2D Z-transform. A spatio-temporal implementation scheme is developed for generation of the radial Zernike polynomials. The case study shows a reliable way to evaluate Zernike polynomials with arbitrary degrees and azimuthal orders.en_UK
dc.identifier.citationHonarvar Shakibaei Asli B, Flusser J, Zhao Y, Erkoyuncu J. (2019) Filter-generating system of Zernike polynomials, Automatica, Volume 108, October 2019, Article Number 108498en_UK
dc.identifier.cris24086674
dc.identifier.issn0005-1098
dc.identifier.urihttps://doi.org/10.1016/j.automatica.2019.108498
dc.identifier.urihttps://dspace.lib.cranfield.ac.uk/handle/1826/14420
dc.language.isoenen_UK
dc.publisherElsevieren_UK
dc.rightsAttribution 4.0 International*
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.subjectOpticsen_UK
dc.subjectZernike polynomialsen_UK
dc.subjectFilter-generating systemsen_UK
dc.subjectGenerating functionen_UK
dc.subjectZ-transformen_UK
dc.titleFilter-generating system of Zernike polynomialsen_UK
dc.typeArticleen_UK

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