Spline-based wavefront reconstruction for Shack-Hartmann measurements

In the coming decade, a new generation of extremely large-scale ground-based astronomical telescopes will see first light. It is well known that increasing the size of the telescope aperture is only beneficial if the adaptive optics (AO) system, which compensates for turbulence-induced wavefront aberrations, scales accordingly. For the extreme-AO (XAO) system of the future European Extremely Large Telescope (E-ELT), in the order of 10^4–10^5 unknown phase points have to be estimated at kHz range frequencies to update the actuator commands of the corrective device, consisting of a deformablemirror (DM).
The work on fast algorithms for wavefront reconstruction (WFR) for real-time application has therefore been extensive. Conventional WFR algorithms estimate the unknown wavefront from wavefront sensor (WFS) measurements. They are generally based on a linear relationship between the unknown wavefront and the sensor read out, and assume one of the two following principles. Zonal methods represent the wavefront as discrete phase points in terms of which the sensor model is formulated, leading to a per se local phase-measurement relationship. The second group of modal methods expands the wavefront with a set of globally defined polynomials which results in a sensormodel that acts on the entire sensor domain.