Results 101 to 110 of about 2,467 (209)

Non-imaging optics: Using Laplacian magic windows and Zernike polynomials

, 2019
In this report a semi-analytic solution to the Laplacian magic window is proposed. The Laplacian magic window is a term recently introduced in 2017[2]. When a uniform wavefront hits a refractive surface, it creates an illumination distribution behind the
Buijssen, Niels (author)
core  

Application of Zernike polynomials in solving certain first and second order partial differential equations

, 2022
Integration operational matrix methods based on Zernike polynomials are used to determine approximate solutions of a class of non-homogeneous partial differential equations (PDEs) of first and second order.
Datta, Somantika, Datta, Kanti Bhushan
core  

Ladder operators for generalized Zernike or disk polynomials.

The aim of this work is to report on several ladder operators for generalized Zernike polynomials which are orthogonal polynomials on the unit disk $\mathbf{D}\,=\,\{(x,y)\in \mathbb{R}^2: \; x^2+y^2\leqslant 1\}$ with respect to the weight function $W_{\
Marriaga, Misael E.
core   +2 more sources

WFST Astrometric Calibration. I. Modeling Global Geometric Distortion with Zernike Polynomials

The Astronomical Journal
Accurate modeling of geometric distortion (GD) is essential for precise astrometric calibration in wide-field imaging surveys. We present a self-calibration method based on Zernike polynomials, applied to imaging data from the Wide Field Survey Telescope
Chao Yang, Min Fang, Xian Zhong Zheng, Guoliang Li, Binyang Liu, Zheng Lou, Zhen Wan, Miaomiao Zhang, Tian-Rui Sun, Lulu Fan, Xiaoling Zhang, Xu Kong, Yongquan Xue, Wen Zhao, Bin Li, Wentao Luo, Feng Li, Wei Liu, Jian Wang, Hongfei Zhang, Hao Liu, Qinfeng Zhu, Hairen Wang, Dazhi Yao   +23 more
doaj   +1 more source

Multi-order combined diffractive optical elements for identification of different-magnitude wave aberrations

Компьютерная оптика
In this article, multi-order combined diffractive optical elements (DOEs) matched with a set of wave aberrations and Zernike polynomials are proposed and developed.
P.A. Khorin, A.P. Dzyuba, S.N. Khonina
doaj   +1 more source

Bessel-Zernike Discrete Variable Representation Basis [PDF]

, 2005
The connection between the Bessel discrete variable basis expansion and a specific form of an orthogonal set of Jacobi polynomials is demonstrated. These so-called Zernike polynomials provide alternative series expansions of suitable functions over the ...
Cerjan, C J
core  

Average gradient of Zernike polynomials over polygons. [PDF]

Opt Express, 2020
Akondi V, Dubra A.
europepmc   +1 more source

Zernike functions, rigged Hilbert spaces and potential applications

, 2019
We revise the symmetries of the Zernike polynomials that determine the Lie algebra su(1,1) + su(1,1). We show how they induce discrete as well continuous bases that coexist in the framework of rigged Hilbert spaces. We also discuss some other interesting
Mariano A del Olmo (17504994), Manuel Gadella (8711175), Enrico Celeghini (17504991)   +2 more
core   +1 more source

Zernike Polynomials and Optical Aberration

The Zernike polynomials are commonly used in the analysis of adaptive optics systems. Annular Zernikes are particularly useful for analyzing the aberrations of telescopes with annular pupils (e.g., Cassegrain telescopes).
Bryant, Jeff, Pavlyk, Oleksandr
core   +1 more source

ZernikeViewer: An Open-Source Framework for Fast Simulation and Real-Time Reconstruction of Phase, Fringe, and PSF Maps

Applied System Innovation
Zernike polynomials constitute an essential mathematical basis for representing functions defined over the unit disk. They are widely used in a diverse range of scientific and engineering disciplines, including adaptive optics for characterizing ...
Ilya Galaktionov
doaj   +1 more source