The Complete Basis Set of The Orthonormal Vector Polynomials in A unit Annular Circular Pupil | ||
| Albahir journal | ||
| Article 1, Volume 4, Issue 7, December 2016, Pages 67-81 | ||
| Authors | ||
| Sundus Y. Hasan; Thill A. Kadhum and | ||
| Abstract | ||
| In this paper, a complete set of the orthonormal vector polynomials in a unit annular pupil were derived by finding, first a set of orthogonal functions that represent vector quantities which can be generated from the gradients of annular Zernike polynomials ZP, and the orthogonality is made by MATLAB code using Gram Schmidt orthogonalization method. A relation of these polynomials with the circular ZP and circular ZP gradients are represented also in this work. Then, to complete the basis, a complementary set of functions were added that have zero divergence, those which are defined locally as a rotation or curl. | ||
| Keywords | ||
| Orthonormal vector polynomials; Annular Zernike polynomials ZP; Gram Schmidt orthogonalization method | ||
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