Wave-front slope estimation

The conventional way of measuring the average slope of the phase of a wave front is from the centroid of the image formed at the focal plane. We show the limitations of using the centroid and present an optimal estimator along with the derivation of its lower error bound for a diffraction-limited image. The method is extended to slope estimation in the case of a random aberration introduced by atmospheric turbulence. It was found that the variance of the error of the slope estimator can be improved significantly at low turbulence levels by using the minimum mean-square-error estimator instead of the centroid.