Filter-generating system of Zernike polynomials. (October 2019)

• Record Type: Journal Article
• Authors: Honarvar Shakibaei Asli, Barmak; Flusser, Jan; Zhao, Yifan; Erkoyuncu, John Ahmet
• Is Part Of: Automatica. Volume 108(2019)
• Publication Date: 2019-10
• Subjects: Optics -- Zernike polynomials -- Filter-generating systems -- Generating function -- Z-transform; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2019.108498
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: This 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.