The University of Montana
Department of Mathematical Sciences

Technical report #15/2007

An Analysis of Methods for Wavefront Reconstruction from Gradient Measurements in Adaptive Optics

Johnathan M. Bardsley
Department of Mathematical Sciences
University of Montana, Missoula, MT 59812-0864, USA
email:bardsleyj@mso.umt.edu

Abstract

The use of adaptive optics (AO) in ground-based astronomy is becoming increasingly mainstream. While classical methods, such as de- convolution, remove the blur in an image only after it has been collected, AO systems seek to remove phase error in incoming wavefronts prior to image formation, resulting in higher resolution images. If the phase error is known, it can be removed via the creation of a counter wavefront using, e.g., a deformable mirror. In the AO systems used on ground-based tele- scopes, an estimate of the phase error is typically obtained by solving an inverse problem involving measurements of the wavefront gradient. The standard approach for obtaining phase estimates from measurements of its gradient is least squares. However, a more robust solution can be ob- tain if a minimum variance, or penalized least squares, approach is taken instead. In this paper, we will perform a theoretical analysis of these approaches in a continuous, i.e. function space, setting.

Keywords:adaptive optics, wavefront reconstruction, partial diŽerential equations, variational methods.

AMS Subject Classification:35A15

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