Open AccessResolving capacity of the circular Zernike polynomials
Author(s) -
М. В. Свечников,
Н. И. Чхало,
М. Н. Торопов,
Н. Н. Салащенко
Publication year - 2015
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.23.014677
Subject(s) - zernike polynomials , jacobi polynomials , spectrum (functional analysis) , mathematics , approximation theory , orthogonal polynomials , gegenbauer polynomials , set (abstract data type) , polynomial , square (algebra) , difference polynomials , connection (principal bundle) , classical orthogonal polynomials , mathematical analysis , optics , geometry , physics , computer science , quantum mechanics , wavefront , programming language
Circular Zernike polynomials are often used for approximation and analysis of optical surfaces. In this paper, we analyse their lateral resolving capacity, illustrating the effects of a lack of approximation by a finite set of polynomials and answering the following questions: What is the minimum number of polynomials that is necessary to describe a local deformation of a certain size? What is the relationship between the number of approximating polynomials and the spatial spectrum of the approximation? What is the connection between the mean-square error of approximation and the number of polynomials? The main results of this work are the formulas for calculating the error of fitting the relief and the connection between the width of the spatial spectrum and the order of approximation.