Fast and Robust Simulation of Atmospheric Phase Screen by Zernike Polynomials with Recursive Radial Formulas

The Zernike polynomials method is popular in the generation of atmospheric phase screen, but suffers from the high frequency components insufficiency. Hence, the higher terms of Zernike polynomials need to be calculated, creating new problems: computational inefficiency and numerical instability, their causes (calculating the Zernike radial polynomials with the direct method) and consequences are discussed and analyzed in detail in the following paper. Substituting the direct method with a recursive formula can solve these problems. Furthermore, four popular and excellent recursive methods are chosen, and their performances on phase screen generation are studied and discussed with respect to computational efficiency and numerical stability, respectively. The results shows an increase of 10-20 times in computational efficiency for phase screen generation and numerical stability maintained even for the thousands of terms arising from Zernike polynomials since the recursive radial formula is adopted.