Open AccessIntegral-based parallel algorithm for the fast generation of the Zernike polynomials
Author(s) -
Y. H. Hsieh,
Yi–Tao Yu,
YuHung Lai,
M. X. Hsieh,
Yung-Fu Chen
Publication year - 2020
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.380567
Subject(s) - zernike polynomials , algorithm , convergence (economics) , mathematics , graphics , representation (politics) , computer science , optics , physics , computer graphics (images) , wavefront , politics , law , political science , economics , economic growth
The integral representation of the Zernike radial functions is well approximated by applying the Riemann sums with a surprisingly rapid convergence. The errors of the Riemann sums are found to averagely be not exceed 3 ×10 -14 , 3.3×10 -14 , and 1.8×10 -13 for the radial order up to 30, 50, and 100, respectively. Moreover, a parallel algorithm based on the Riemann sums is proposed to directly generate a set of radial functions. With the aid of the graphics processing units (GPUs), the algorithm shows an acceleration ratio up to 200-fold over the traditional CPU computation. The fast generation for a set of Zernike radial polynomials is expected to be valuable in further applications, such as the aberration analysis and the pattern recognition.