Integral-based parallel algorithm for the fast generation of the Zernike polynomials

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 x 10(-14), 3.3 x 10(-14), and 1.8 x 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. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement