Orthogonality of Zernike Polynomials
نویسندگان
چکیده
Zernike polynomials are an orthogonal set over a unit circle and are often used to represent surface distortions from FEA analyses. There are several reasons why these coefficients may lose their orthogonality in an FEA analysis. The effects, their importance, and techniques for identifying and improving orthogonality are discussed. Alternative representations are presented.
منابع مشابه
Representation of Videokeratoscopic Height Data Using a Set of Discrete Tchebichef Orthogonal Polynomials
The continuous orthogonal polynomials, such as Zernike and pseudo-Zernike, are often used as an expansion of corneal height data. However, the use of continuous polynomials has some limitations due to the discretization. It is because that the integrals are usually approximated by discrete summations, and this process not only leads to numerical errors, but also severely affects some analytical...
متن کاملUse of Zernike Polynomials and SPGD Algorithm for Measuring the Reflected Wavefronts from the Lens Surfaces
Recently, we have demonstrated a new and efficient method to simultaneously reconstruct two unknown interfering wavefronts. A three-dimensional interference pattern was analyzed and then Zernike polynomials and the stochastic parallel gradient descent algorithm were used to expand and calculate wavefronts. In this paper, as one of the applications of this method, the reflected wavefronts from t...
متن کاملUtilizing the Discrete Orthogonality of Zernike Functions in Corneal Measurements
The optical behaviour of the human eye is often characterized with the Zernike coefficients. Great number of measurements and statistical data are available for individuals and for various groups of people concerning the Zernike coefficients of their eyes. Although, these coefficients were obtained from measurements at discrete points and via computations using some discretization of the contin...
متن کاملاصلاح توام نقص ابیراهی لنز دوربین و خطای خروج از مرکز تصویر با بهرهگیری از مدل اصلاح شده زرنیک
Reduction of the quality of the image formed by an optical system is a function of different parameters such as lens aberrations, CCD digitization errors, and the errors of system assembling. Assembling errors usually consist of two types: 1) the prism error, which is the error of non-orthogonality of the optical axis and the image plane 2) the de-centering error, which is error of not passing ...
متن کاملImage analysis by Krawtchouk moments
In this paper, a new set of orthogonal moments based on the discrete classical Krawtchouk polynomials is introduced. The Krawtchouk polynomials are scaled to ensure numerical stability, thus creating a set of weighted Krawtchouk polynomials. The set of proposed Krawtchouk moments is then derived from the weighted Krawtchouk polynomials. The orthogonality of the proposed moments ensures minimal ...
متن کامل