Filter-generating system of Zernike polynomials
Filter-generating system of Zernike polynomials
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DOI：
10.1016/j.automatica.2019.108498
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
Barmak Honarvar;J. Flusser;Yifan Zhao;J. Erkoyuncu
中科院分区：
文献类型：
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作者：
Barmak Honarvar;J. Flusser;Yifan Zhao;J. Erkoyuncu
本文提出了一种求二维泽尼克多项式生成函数的新方法。结合广义函数和离散时间系统的方法，我们可以开发出系统生成全阶泽尼克多项式的二维数字系统。基于径向多项式的度和方位阶，建立了径向泽尼克多项式的GF的两种不同的公式。本文用四项递归关系代替一般的三项递归关系，利用单侧二维z变换计算径向泽尼克多项式及其GFs。提出了径向泽尼克多项式生成的时空实现方案。算例给出了一种可靠的求任意度和任意方位阶泽尼克多项式的方法。
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.