P. Piatrou and L. Gilles (lgilles@mtu.edu) are with the Department of Electrical and Computer Engineering, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan 49931-1295.
Piotr Piatrou and Luc Gilles, "Robustness study of the pseudo open-loop controller for multiconjugate adaptive optics," Appl. Opt. 44, 1003-1010 (2005)
Robustness of the recently proposed “pseudo open-loop control” algorithm against various system errors has been investigated for the representative example of the Gemini-South 8-m telescope multiconjugate adaptive-optics system. The existing model to represent the adaptive-optics system with pseudo open-loop control has been modified to account for misalignments, noise and calibration errors in deformable mirrors, and wave-front sensors. Comparison with the conventional least-squares control model has been done. We show with the aid of both transfer-function pole-placement analysis and Monte Carlo simulations that POLC remains remarkably stable and robust against very large levels of system errors and outperforms in this respect least-squares control. Approximate stability margins as well as performance metrics such as Strehl ratios and rms wave-front residuals averaged over a 1-arc min field of view have been computed for different types and levels of system errors to quantify the expected performance degradation.
Brice Le Roux, Jean-Marc Conan, Caroline Kulcsár, Henri-François Raynaud, Laurent M. Mugnier, and Thierry Fusco J. Opt. Soc. Am. A 21(7) 1261-1276 (2004)
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Single-mirror shifts are done in the 45° direction. Three-mirror shifts are done in the 60 deg, 150 deg, and 300 deg directions, respectively. Norms of shifts are quoted as a fraction of LGS WFSs’ subaperture size (0.5 m). Three-mirror rotations are taken to be clockwise on DMs 1 and 3 and anticlockwise on DM 2. DMs mismagnification is the same for each mirror.
Table 4
Approximate Stability Margins for Misalignments in WFSs
Shifts in WFSs are done in the 0 deg, 45 deg, 135 deg, 225 deg, and 315 deg directions for the LGS WFSs and in the 0 deg, 90 deg, 180 deg, and 270 deg directions for the tip-tilt WFSs. Norms of shifts are quoted as a fraction of LGS WFSs’ subaperture size (0.5 m).
WFS rotation is done clockwise on all sensors.
WFS mismagnification is the same for each sensor.
Table 5
Average Strehl Ratios Obtained for Various Types and Degrees of System Errorsa
System-error type
J band (1.25 μm)
Perfect alignment
0.53
0.33
0.25
10% shift in all DMs
0.51
0.32
0.24
10% shift in all WFSs
0.52
0.32
0.25
30% shift in all DMs
0.47
0.27
0.18
30% shift in all WFSs
0.41
0.22
0.18
0.01-rad rotation in DMs
0.53
0.33
0.24
0.05-rad rotation in DMs
0.45
0.25
0.19
0.03-rad rotation in WFSs
0.50
0.32
0.21
0.06-rad rotation in WFSs
0.43
0.25
0.18
1% overmagnification in DMs
0.50
0.34
0.23
5% overmagnification in DMs
0.45
0.29
0.17
1% overmagnification in WFSs
0.54
0.32
0.25
5% overmagnification in WFSs
0.37
0.16
0.12
25-mas tilt in all DMs
0.51
0.33
0.22
75-mas tilt in all DMs
0.46
0.19
0.16
2.5-mas tilt in all WFSs
0.53
0.31
0.26
12.5-mas tilt in all WFSs
0.37
0.14
0.13
1% actuator command noise
0.53
0.34
0.22
5% actuator command noise
0.13
0.07
0.06
First, second, and third numbers correspond, respectively, to the center, middle of the right side, and upper-right corner of the field of view.
Tables (5)
Table 1
Six-Layer Turbulence Model Used in the Simulation of the Gemini-South 8-m Telescope MCAO System
Single-mirror shifts are done in the 45° direction. Three-mirror shifts are done in the 60 deg, 150 deg, and 300 deg directions, respectively. Norms of shifts are quoted as a fraction of LGS WFSs’ subaperture size (0.5 m). Three-mirror rotations are taken to be clockwise on DMs 1 and 3 and anticlockwise on DM 2. DMs mismagnification is the same for each mirror.
Table 4
Approximate Stability Margins for Misalignments in WFSs
Shifts in WFSs are done in the 0 deg, 45 deg, 135 deg, 225 deg, and 315 deg directions for the LGS WFSs and in the 0 deg, 90 deg, 180 deg, and 270 deg directions for the tip-tilt WFSs. Norms of shifts are quoted as a fraction of LGS WFSs’ subaperture size (0.5 m).
WFS rotation is done clockwise on all sensors.
WFS mismagnification is the same for each sensor.
Table 5
Average Strehl Ratios Obtained for Various Types and Degrees of System Errorsa
System-error type
J band (1.25 μm)
Perfect alignment
0.53
0.33
0.25
10% shift in all DMs
0.51
0.32
0.24
10% shift in all WFSs
0.52
0.32
0.25
30% shift in all DMs
0.47
0.27
0.18
30% shift in all WFSs
0.41
0.22
0.18
0.01-rad rotation in DMs
0.53
0.33
0.24
0.05-rad rotation in DMs
0.45
0.25
0.19
0.03-rad rotation in WFSs
0.50
0.32
0.21
0.06-rad rotation in WFSs
0.43
0.25
0.18
1% overmagnification in DMs
0.50
0.34
0.23
5% overmagnification in DMs
0.45
0.29
0.17
1% overmagnification in WFSs
0.54
0.32
0.25
5% overmagnification in WFSs
0.37
0.16
0.12
25-mas tilt in all DMs
0.51
0.33
0.22
75-mas tilt in all DMs
0.46
0.19
0.16
2.5-mas tilt in all WFSs
0.53
0.31
0.26
12.5-mas tilt in all WFSs
0.37
0.14
0.13
1% actuator command noise
0.53
0.34
0.22
5% actuator command noise
0.13
0.07
0.06
First, second, and third numbers correspond, respectively, to the center, middle of the right side, and upper-right corner of the field of view.