2 October 1998 Performance modeling of adaptive-optics imaging systems using fast Hankel transforms
Author Affiliations +
Abstract
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. One approach for linear performance modeling of closed-loop adaptive-optics system involves calculating very large covariance matrices whose components can be represented by sums of Hankel transform based integrals. In this paper we investigate approximate matrix factorizations of discretizations of such integrals. Two different approximate factorizations based upon representations of the underlying Bessel function are given, the first using a series representation due to Ellerbroek and the second an integral representations. The factorizations enable fast methods for both computing and applying the covariance matrices. For example, in the case of an equally spaced grid, it is shown that applying the approximated covariance matrix to a vector can be accomplished using the derived integral-based factorization involving a 2D fast cosine transform and a 2D separable fast multiple method. The total work is then O(N log N) where N is the dimensions of the covariance matrix in contrast to the usual O(N2) matrix-vector multiplication complexity. Error bounds exist for the matrix factorizations. We provide some simple computations to illustrate the ideas developed in the paper.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Victor Paul Pauca, Brent L. Ellerbroek, Nikos P. Pitsianis, Robert J. Plemmons, Xiaobai Sun, "Performance modeling of adaptive-optics imaging systems using fast Hankel transforms", Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); doi: 10.1117/12.325694; https://doi.org/10.1117/12.325694
PROCEEDINGS
9 PAGES


SHARE
RELATED CONTENT

Modeling of the SAAO adaptive optics system
Proceedings of SPIE (May 04 2000)
Spatial Interferometry With The European VLT
Proceedings of SPIE (August 20 1986)
Compact active high-resolution imaging system
Proceedings of SPIE (October 07 2008)
Adaptive optics technology for Fourier telescopy
Proceedings of SPIE (November 29 2012)
High-speed seeing measurements at the Keck Telescope
Proceedings of SPIE (May 31 1994)
Adaptive optics for the SALT
Proceedings of SPIE (July 15 2008)
Perspective in adaptive optics for ELT
Proceedings of SPIE (April 22 2008)

Back to Top