scholarly journals Complete Modal Representation with Discrete Zernike Polynomials - Critical Sampling in Non Redundant Grids

10.5772/24631 ◽  
2011 ◽  
Author(s):  
Rafael Navarro ◽  
Justo Arines
Keyword(s):  
Zernike Polynomials

On the circle polynomials of Zernike and related orthogonal sets

1954 ◽  
Vol 50 (1) ◽  
pp. 40-48 ◽  
Author(s):  
A. B. Bhatia ◽  
E. Wolf
Keyword(s):  
Unit Circle ◽  
Generating Functions ◽  
Legendre Polynomials ◽  
Phase Contrast ◽  
Diffraction Theory ◽  
Zernike Polynomials ◽  
Optical Aberrations ◽  
Orthogonal Set ◽  
Complete Orthogonal Set ◽  
Explicit Expressions

ABSTRACTThe paper is concerned with the construction of polynomials in two variables, which form a complete orthogonal set for the interior of the unit circle and which are ‘invariant in form’ with respect to rotations of axes about the origin of coordinates. It is found that though there exist an infinity of such sets there is only one set which in addition has certain simple properties strictly analogous to that of Legendre polynomials. This set is found to be identical with the set of the circle polynomials of Zernike which play an important part in the theory of phase contrast and in the Nijboer-Zernike diffraction theory of optical aberrations.The results make it possible to derive explicit expressions for the Zernike polynomials in a simple, systematic manner. The method employed may also be used to derive other orthogonal sets. One new set is investigated, and the generating functions for this set and for the Zernike polynomials are also given.

scholarly journals Phase Only Pupil Filter Design Using Zernike Polynomials

2016 ◽  
Vol 20 (1) ◽  
pp. 101-106 ◽  
Author(s):  
Jiang Liu ◽  
Erlong Miao ◽  
Yongxin Sui ◽  
Huaijiang Yang
Keyword(s):  
Filter Design ◽  
Zernike Polynomials
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