Shack-Hartmann wavefront sensor sensitivity loss factor estimation in partial correction regime

In typical adaptive optics applications, the atmospheric residual turbulence affects the wavefront sensor response decreasing its sensitivity. On the other hand, wavefront sensors are generally calibrated in diffraction limited condition, and, so, the interaction matrix sensitivity differs from the closed loop one. The ratio between the two sensitivities, that we will call the sensitivity loss factor, has to be estimated to retrieve a well-calibrated measurement. The spots size measurement could give a good estimation, but it is limited to systems with spots well sampled and uniform across the pupil. We present an algorithm to estimate sensitivity loss factor from closed loop data, based on the known parameters of the closed loop transfer functions. Here we preferred for simplicity the Shack-Hartmann WFS, but the algorithm we propose can be extended to other WFSs.