Order N reconstructor algorithms for Adaptive Optics.

Michael Flanagan

43 E. Lanikaula St, Hilo, HI, 96720


We apply multigrid methods for the fast solution of large scale problems in Adaptive Optics. Adaptive Optics (AO) is a technique for removing the blurring effects in optical systems. It has important uses in medical imaging as well as astronomical telescopes. In astonomy, AO senses incoming light that has been distorted--due to atmospheric turbulence--and corrects the distortions using a deformable mirror. Of great practical importance is the ability to evaluate the linear map from sensor measurements to mirror deformations (called the reconstructor matrix) within the 5-10 millisecond time scale of the turbulence. For 30+ meter telescopes now being developed, the reconstructor matrix will have tens or even hundreds of thousands of unknowns. In this talk we will describe the special structure of the reconstructor matrix, and we will present a multigrid algorithm for the fast evaluation of this matrix. Classically, least squares reconstruction algorithms are used. We present the model with regularization. We will discuss issues such as the sensor/actuator geometries that affect the performance of the multigrid algorithm. Incorporating Kolmogorov statistics into the least squares reconstruction as a regularizing term will be described.