Weighted Fourier Phase Slope as a centroiding method in a Shack-Hartmann wavefront sensor: A Z-tilt estimation method in the Fourier domain, optimizable to the system´s geometry

The “Weighted Fourier Phase Slope” (WFPS) Z-tilt estimation method is presented, that operates in the Shack-Hartmann wave-front sensor subpupil image´s Fourier transform domain. It consists of two steps: first, the Fourier phase slopes at a grid of discrete spatial frequencies are directly obtained, without the intermediate step of obtaining the phases; second, they are weighted with a Maximum a Posteriori optimality criterion, dependent upon the system´s geometry, to give the estimated centroid coordinates. The method has been validated by simulations. Centre of Gravity (CoG) and WFPS estimators have been applied to simulated image sequences that follow the Kolmogorov´s statistics, and compared to the actual Z-tilt applied. For typical turbulence conditions, the WFPS shows a better accuracy than CoG, reducing the rms estimation error by a factor of 2.