Compressive Sampling in Intensity Based Control for Adaptive Optics

Abstract

The central problem in Adaptive Optics feedback control is the reconstruction of the aberrated wavefront from wavefront sensor measurements. We recently presented a novel algorithm to compute the wavefront estimate directly from (Shack-)Hartmann intensity images instead of using the classical centroid algorithm to approximate the local wavefront slopes. The novel algorithm allows a distributed linearization of the model describing the imaging process through the use of a B-spline parametrization of the wavefront. This linearization enables the estimation of the wavefront via a linear least-squares solver. A major bottleneck of this new algorithm is the computational complexity that stems from the large number of pixels with each pixel giving rise to one row of the overdetermined set of equations. In this paper, a compression method is proposed to speed up this new reconstruction method by only using a small percentage of the given intensities to make it applicable for real-time Adaptive Optics. Numerical simulations for open- and closed-loop show that reducing the data on the one hand dramatically reduces the number of measurements, but on the other hand does not cause any significant loss in accuracy or robustness of the reconstructed wavefront estimate.