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.