A multi-input multi-output surface shape control system model is developed to study wavefront aberration correction. The plant model represents a deformable mirror and utilizes a finite element model that is validated using an actual prototype deformable mirror and an interferometer system. The sensor model is based on a Shack-Hartmann sensor, and the controller model is based on a least squares approach. The control system model is used to compare an available Gaussian model with the validated finite element model. Results clearly show the efficacy of the approach and the superiority of the finite element based method. The control approach is expected to be implemented on the adaptive optics system of the National Ignition Facility.

1.
Apollonov
,
V. V.
,
Vdovin
,
G. V.
,
Ivanova
,
E. A.
,
Prokhorov
,
A. M.
, and
Shetkin
,
S. A.
,
1990
, “
Analytic Model of an Adaptive Mirror in the Form of a Thin Plate with Discrete Actuators
,”
Sov. J. Quantum Electron.
,
20
(
11
), pp.
1414
1418
.
2.
Creedon
,
J. F.
, and
Lindgren
,
A. G.
,
1970
, “
Control of the Optical Surface of a Thin, Deformable Primary Mirror with Application to an Orbiting Astronomical Observatory
,”
Automatica
,
6
, pp.
643
660
.
3.
Chiarappa
,
D. J.
, and
Claysmith
,
C. R.
,
1981
, “
Deformable Mirror Surface Control Techniques
,”
J. Guid. Control Dyn.
,
4
(
1
), pp.
7
34
.
4.
Ealey
,
M. A.
,
1991
, “
Active and Adaptive Optical Components: The Technology and Future Trends
,”
Active and Adaptive Optical Components, SPIE
1543
, pp.
2
34
.
5.
Dimitriadis, E. K., and Fuller, C. R., 1989, “Investigation of Active Control of Sound Transmission Through Elastic Plates Using Piezoelectric Actuators.” AIAA 27th Aerospace Sciences Conference, Reno, Nevada, Jan. 8–12, Paper 89–106.
6.
Walker
,
L. A.
, and
Yaneskek
,
P. P.
,
1976
, “
The Damping of the Plate Vibrations by Means of Multiple Active Control Systems
,”
J. Sound Vib.
,
46
, pp.
177
193
.
7.
Livne, E., and Li, W. L., 1995, “Aeroservoelastic aspects of Wing/Control Surface Platform Shape Optimization,” 55(2), pp. 302–311.
8.
Junkins, J. L., 1990, Mechanics and Control of Large Flexible Structures, American Institute of Aeronautics and Astronautics, Inc.
9.
Meirovitch, L., 1990, Dynamics and Control of Structures, Wiley, NY.
10.
Tyson, R. K., 1998, Principles of Adaptive Optics, Academic Press, NY.
11.
Salmon
,
J. T.
,
Bergum
,
J. W.
,
Kartz
,
M. W.
,
Presta
,
R. W.
, and
Swift
,
C. D.
,
1993
, “
Wavefront Correction System Based on an Equilateral Triangular Arrangement of Actuators
,”
SPIE
,
1920
, pp.
20
28
.
12.
Furber
,
M. E.
,
Blaszak
,
D. D.
, and
Pieri
,
M. R.
,
1994a
, “
Correctability Modeling of a Large Deformable Mirror
,”
Adaptive Optics in Astronomy, SPIE
,
2201
, pp.
856
866
.
13.
Shishakov
,
K. V.
, and
Shmal’gauzen
,
V. I.
,
1992
, “
Optimization of Surface Shape Control in Feedback Systems
,”
Automation and Remote Control
, No.
53
, pp.
1866
1871
.
14.
Bushnell
,
D.
,
1979
, “
Control of Surface Configuration by Application of Concentrated Loads
,”
AIAA J.
,
7
(
1
), pp.
71
77
.
15.
Lyakhov
,
D. M.
,
1994
, “
Optimizing the Control of the Shape of the Optical Surface of Plates with Point Connections
,”
J. Opt. Technol.
,
61
(
7
), pp.
518
522
.
16.
Bigelow
,
B. C.
,
Bingham
,
R. G.
, and
Walker
,
D. D.
,
1994
, “
Optimizing a Deformable Secondary Mirror for Adaptive Optics
,”
Adaptive Optics in Astronomy, SPIE
,
2201
, pp.
800
810
.
17.
Ealey
,
M. A.
, and
Wellman
,
J. A.
,
1991
, “
Deformable Mirrors: Design Fundamentals, Key Performance Specifications and Parametric Trades
,”
Active and Adaptive Optical Components, SPIE
,
1543
, pp.
36
51
.
18.
Hiddleston
,
H. R.
,
Lyman
,
D. D.
, and
Schafer
,
E. L.
,
1991
, “
Comparisons of Deformable Mirror Models and Influence Functions
,”
SPIE
Vol.
1542
Active and Adaptive Optical Systems,
20
33
.
19.
Lawry, M. H., 1997, SDRC Master Series Student Guide, SDRC.
20.
Russell
,
R.
,
1996
, “
Don’t Trust the Pretty Pictures,” Machine Design CAM/CAD Industry Report, May.
21.
Zacharias, R., Bliss, E., Feldman, M., Gray, A., Henesian, M., Koch, J., Lawson, J., Sacks, R., Salmon, T., Toeppen, J., Van Atta, L., and Winters, S., 1998, “The National Ignition Facility Wavefront Control System,” Solid State Lasers for Application to Inertial Confinement Fusion, Montery CA. June.
22.
Furber
,
M. E.
,
Cox
,
C. D.
,
Blaszak
,
D. D.
, and
Houghton
,
C. D.
,
1994
, “
Interferometric Measurement and Analysis of Influence Functions for a Large Deformable Mirror
,”
Adaptive Optics in Astronomy, SPIE
,
2201
, pp.
788
799
.
23.
Cielinski
,
A. J.
,
1991
, “
Wavefront Control Model of A Beam Control Experiment
,”
SPIE
,
1542
, Active and Adaptive Optical Systems, pp.
434
448
.
You do not currently have access to this content.