Truncation robust centroiding for wavefront sensors

In the new generation of giant telescopes with high resolution images, the atmospheric turbulence has become an obstacle to the precision of the results. The use of adaptive optics is now crucial for wavefront correction in such telescopes. The most commonly used sensor in adaptive optics is the Shack-Hartmann Wavefront Sensor. Composed of an array of lenses, it uses a reference, normally a star, to sample the wavefront tilts in the primary aperture. By processing the tilts at each sub-aperture, it is possible to estimate the overall disturbance. Since adaptive optics systems require high luminous intensity, it is common to use artificial guide stars. These stars are generated by a laser focused on the sodium layer in the upper atmosphere. Due to the optical geometry, the laser guide star generates an elongated spot when imaged by a sub-aperture. In giant telescopes larger than 20 meters in diameter, the spot elongation is so large that classical centroiding techniques provide poor results, especially in the presence of spot truncation at the edge of the sub-aperture. Such peculiarities, in addition to the temporal variation of the atmospheric sodium profile, make it difficult to determine the displacement of the image reference and, consequently, to determine the wavefront disturbance. In this work, we propose a method capable of determining the centroid of the elongated spots even in the presence of truncation. The key ideas are to model the observed images with Poisson noise and to employ a Grid Search strategy to determine the position of the spot. Finally, we show that the proposed method provides better results when compared to current methods.