Some computational problems arising in adaptive optics imaging systems

• Published in: Journal of computational and applied mathematics 2000-11, Vol.123 (1), p.467-487
• Main Authors: Plemmons, Robert J., Pauca, Victor P.
• Format: Article
• Language: English
• Subjects: Adaptive optics control; Covariance matrix computations; Eigenvalues; Fast Hankel transforms; Imaging through turbulence; Structured matrices
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(00)00410-6

Recently there has been growing interest and progress in using numerical linear algebra techniques in adaptive optics imaging control computations. Real-time adaptive optics is a means for enhancing the resolution of ground based, optical telescopes beyond the limits previously imposed by the turbulent atmosphere. An adaptive optics system automatically corrects for light distortions caused by the medium of transmission. The system measures the characteristics of the phase of the arriving wavefront and corrects for the degradations by means of one or more deformable mirrors controlled by special purpose computers. No attempt is made in this paper to give a comprehensive survey of recent numerical linear applications in optical imaging. Rather, two fairly representative applications are discussed in some detail. The following research topics in the area of adaptive optics control systems, each involving the formulation and numerical solution of difficult problems in numerical linear algebra, are described: (1) Jacobi-like eigenvalue computations for multiple bandwidth deformable mirror control methods, and (2) covariance matrix computations for performance modeling of adaptive optics systems using fast Hankel transforms.