A mathematical framework for the linear reconstructor problem in adaptive optics

Citation
Mt. Chu et al., A mathematical framework for the linear reconstructor problem in adaptive optics, LIN ALG APP, 316(1-3), 2000, pp. 113-135
Citations number
22
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Mathematics
Journal title
LINEAR ALGEBRA AND ITS APPLICATIONS
ISSN journal
0024-3795 → ACNP
Volume
316
Issue
1-3
Year of publication
2000
Pages
113 - 135
Database
ISI
SICI code
0024-3795(20000901)316:1-3<113:AMFFTL>2.0.ZU;2-4
Abstract
The wave front field aberrations induced by atmospheric turbulence can seve rely degrade the performance of an optical imaging system. Adaptive optics refers to the process of removing unwanted wave front distortions in real t ime, i.e,, before the image is formed, with the use of a phase corrector. T he 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 atmosph eric turbulence effects on the phase of the incoming light wave front. A ph ase computation system, referred to as a reconstructor, transforms the outp ut of a wave front sensor into a set of drive signals that control the shap e 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 ma trix-vector multiply. The matrix associated with the reconstruction algorit hm is called the reconstructor matrix. Since the entire process, from the a cquisition of wave front measurements to the positioning of the surface of the deformable mirror, must be performed at speeds commensurate with the at mospheric 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 inte ractions among main components involved in an adaptive optics imaging syste m, and (ii) to present several ways to estimate the reconstructor matrix ba sed on this framework. The performances of these various reconstruction tec hniques an illustrated using some simple computer simulations. (C) 2000 Els evier Science Inc. All rights reserved.