1. Highlights of CDCSS-UMD Accomplishments
Presentation to Dr. Randy Zachery
Army Research Office
May 25, 2004 at Harvard University

2. Accomplishments Adaptive Optics
- Proof-of-concept experimental demonstration of the liquid crystal light valve (LCLV)-based high resolution wave-front control system (nonlinear Zernike filter realization)
- Simulation results show effectiveness against atmospheric turbulence
- Global nonlinear stability analysis for the continuous system model of the wave-front control system
- Patent disclosure (PS ) jointly to University of Maryland and Army Research Laboratory: Wave-front phase sensors based on optically or electrically controlled phase spatial light modulators for wave-front sensing and control (M.A. Vorontsov, E. W. Justh, L. Beresnev, P. S. Krishnaprasad, J. Ricklin)

3. From nonlinear Zernike filters to high-resolution adaptive optics
Figure on upper left shows a realization of a nonlinear Zernike filter using a liquid crystal light valve device developed at ARL. This is the device that enables direct wave-front sensing (without use of a reference beam). Figure on upper right shows the effect of turbulent distortion (a), corrected in (b), measured via an interferometer. In (c) and (d) the “before” and “after” correction pictures of the Fourier spectrum are displayed, the latter indicating concentration in the zero-order. It took about 34 iterations of the correction algorithm to converge. In the panel on the lower left we see the successive stages of self-organizing behavior (displayed by the iterative correction algorithm), in the Fourier spectrum from initial (a), to 10 iterations (b), to 20 iterations in (c), to finally (d) achieved in 30 iterations with most of the energy concentrated in the zero order component. This corresponds to the near-maximization of Strehl ratio, a key measure of how much of the phase distortion has been corrected. (Details of the technical work have been published in a series of papers in control and optics conferences and in the Journal of the Optical Society of America, series A, and in Automatica, the premier journal of the International Federation of Automatic Control). Figure on lower right shows a conceptualization of the high speed high resolution adaptive optics system with the wave-front correction (green), and wave-front sensing (purple) modules. It is anticipated that the interface will be opto-electronic, with correction actuators similar to the type of micro-mirrors designed, fabricated, and tested by Tom Bifano of the Boston University team.

4. Accomplishments
Modeling, Computation and Control of Magnetostrictive Hysteresis
- Effective numerical computation of magnetostrictive hysteresis in materials such as Terfenol-D using the Landau-Lifshitz-Gilbert (LLG) equation to model ferromagneto-dynamics, and elastic rod theory to model actuator movement
- Hierarchical tree-structured Fast Multipole Algorithm to compute magnetostatic term in effective field, coupled to a new Cayley transform- based geometric integrator for solving the LLG equation, to compute theoretical hysteresis curves
- Modeling of rate-dependent phenomena in hysteretic actuators due to eddy current effects by a novel extension of the Preisach model
- Fast inversion algorithm for Preisach-type model to compute control signals for tracking specified output trajectories.
- New Hamilton-Jacobi theory for robust control of hysteretic systems

5. Sectional view of the Etrema magnetostrictive actuator

6. Higher Order Geometric Integrator— Performance Comparision
Comparison of integration schemes on a 2 by 2 by 4 grid, using the result of RK4 with much smaller stepsize as the benchmark. RK4: Runge-Kutta 4-th order, MP: Mid-point rule. Cay_RK4: Cayley transform with RK4.

7. Higher Order Geometric Integrator— Performance Comparision
Comparison of performance on norm preserving

8. Higher Order Geometric Integrator— Summary of Features
Fast
Explicit
On the right track
Accurate due to high order
Norm preserving