Anisotropic diffusion based on Fermi-Dirac distribution function and its application in the Shack-Hartman wavefront sensor

Abstract

In this study, the anisotropic diffusion technique is applied to estimate spots in the noise signals of the Shack-Hartmann wavefront sensor. Based on the analysis of the classical anisotropic diffusion function and on an improved algorithm, a diffusion function is proposed based on the Fermi-Dirac distribution. It is proved mathematically that the new function has a higher convergence speed and a better performance. Monte Carlo simulations are used to verify the applicability of the new function subject to the noise limit and signal level. The simulation and experimental results show that the anisotropic diffusion algorithm can effectively filter out the noise. The integrity of the spots can be maintained, and the centroid detection accuracy and signal-to-noise ratio are also improved.