Jacobi-like method for a control algorithm in adaptive-optics imaging

Nikos P. Pitsianis; Brent L. Ellerbroek; Charles Van Loan; Robert J. Plemmons

doi:10.1117/12.325691

2 October 1998 Jacobi-like method for a control algorithm in adaptive-optics imaging

Nikos P. Pitsianis, Brent L. Ellerbroek, Charles Van Loan, Robert J. Plemmons

Proceedings Volume 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII; (1998) https://doi.org/10.1117/12.325691
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1998, San Diego, CA, United States

Abstract

A study is made of a non-smooth optimization problem arising in adaptive-optics, which involves the real-time control of a deformable mirror designed to compensate for atmospheric turbulence and other dynamic image degradation factors. One formulation of this problem yields a functional f(U) equals (Sigma) _iequals1ⁿ max_j[(U^TM_jU)_ii] to be maximized over orthogonal matrices U for a fixed collection of n X n symmetric matrices M_j. We consider first the situation which can arise in practical applications where the matrices M_j are nearly pairwise commutative. Besides giving useful bounds, results for this case lead to a simple corollary providing a theoretical closed-form solution for globally maximizing f if the M_j are simultaneously diagonalizable. However, even here conventional optimization methods for maximizing f are not practical in a real-time environment. The genal optimization problem is quite difficult and is approached using a heuristic Jacobi-like algorithm. Numerical test indicate that the algorithm provides an effective means to optimize performance for some important adaptive-optics systems.

Citation Download Citation

Nikos P. Pitsianis, Brent L. Ellerbroek, Charles Van Loan, and Robert J. Plemmons "Jacobi-like method for a control algorithm in adaptive-optics imaging", Proc. SPIE 3461, Advanced Signal Processing Algorithms, Architectures, and Implementations VIII, (2 October 1998); https://doi.org/10.1117/12.325691

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