# A mathematical framework for the linear reconstructor problem in adaptive optics

Published

Journal Article

The wave front field aberrations induced by atmospheric turbulence can severely degrade the performance of an optical imaging system. Adaptive optics refers to the process of removing unwanted wave front distortions in real time, i.e., before the image is formed, with the use of a phase corrector. The basic idea in adaptive optics is to control the position of the surface of a deformable mirror in such a way as to approximately cancel the atmospheric turbulence effects on the phase of the incoming light wave front. A phase computation system, referred to as a reconstructor, transforms the output of a wave front sensor into a set of drive signals that control the shape of a deformable mirror. The control of a deformable mirror is often based on a linear wave front reconstruction algorithm that is equivalent to a matrix-vector multiply. The matrix associated with the reconstruction algorithm is called the reconstructor matrix. Since the entire process, from the acquisition of wave front measurements to the positioning of the surface of the deformable mirror, must be performed at speeds commensurate with the atmospheric changes, the adaptive optics control imposes several challenging computational problems. The goal of this paper is twofold: (i) to describe a simplified yet feasible mathematical framework that accounts for the interactions among main components involved in an adaptive optics imaging system, and (ii) to present several ways to estimate the reconstructor matrix based on this framework. The performances of these various reconstruction techniques are illustrated using some simple computer simulations. © 2000 Elsevier Science Inc.

### Full Text

### Duke Authors

### Cited Authors

- Chu, MT; Pauca, VP; Plemmons, RJ; Sun, X

### Published Date

- September 1, 2000

### Published In

### Volume / Issue

- 316 / 1-3

### Start / End Page

- 113 - 135

### International Standard Serial Number (ISSN)

- 0024-3795

### Digital Object Identifier (DOI)

- 10.1016/S0024-3795(00)00019-7

### Citation Source

- Scopus