Design and Development of the FSM
(Fast steering Secondary Mirror)
Myung Cho, NOAO-GSMTPO
Kwijong Park, KASI
Young-Soo Kim, KASI
October 4, 2010
GMT2010: Design and Development of FSM
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OUTLINE
1.
2.
3.
4.
Prior Work: Magellan Secondary Mirror modeling
FSM Configuration
Design and Development (work in progress)
GMT FSM Performance Predictions
a. Gravity Analysis
b. Thermal Analysis
c. Natural Frequency analysis
d. Lateral support flexure analysis
e. Sensitivity analysis
f. Zenith Angle effects
5. Summary and Conclusion
6. Next Steps
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GMT2010: Design and Development of FSM
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Magellan Heritage
Magellan heritage:
 Magellan secondary mirror
GMT
Primary: 25.4m (8.4m x 7)
Secondary: 3.2m (1.06m x 7)
Shape: Ellipsoid
Focal ratio: F/0.7
Final focal ratio: F/8
Magellan telescope
Primary: 6.5m
Secondary: 1.3m
Shape: Paraboloid
Focal ratio: F/1.25
Final focal ratio: F/11.0
※ Gregorian
6.5m Magellan telescope
October 4, 2010
25.4m GMT
GMT2010: Design and Development of FSM
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Magellan M2 Assembly
Secondary Mirror Assembly of Magellan telescope
For GMT FSM design and development, take a
conservative engineering approach; utilize concepts
established from the F/11 M2 of Magellan telescope.
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GMT2010: Design and Development of FSM
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GMT and GMT FSM
Primary: 25.4m (8.4m x 7)
Secondary: 3.2m (1.06m x 7)
Shape: Ellipsoid
Focal ratio: F/0.7
Final focal ratio: F/8 Gregorian
October 4, 2010
GMT F/8 Gregorian beams
Conjugated M1 and M2
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FSM assembly layout
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FSM optical prescription
 FSM optical prescription (as of 9/2010):
 FSM M2 nominal segment Configuration:
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GMT2010: Design and Development of FSM
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175mm
140mm
1060mm
FSM Error Budget specification
Error budget: Encircled Energy diameters at 80% (EE80)
Orientation
Zenith
Horizon
Figure error
October 4, 2010
80% EE Specifications
0.020” (arc-seconds)
0.030”
0.039”
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Assumptions in FE
• Finite Element mirror model
• 3D solid elements
• Center mirror of the FSM array (on-axis)
• Clear aperture in the optical surface evaluations:
OD=1060mm
• Solid Zerodur concave lightweight (63%)
•
•
•
•
•
Nominal mirror thickness: 140mm
RADCV=4.2m; sag=0.031m
Center of gravity (CG) = 0.0205m (from vertex)
Mass=105 kg; Ixx=6.3 kg-m2, Izz=12.3 kg-m2 at CG
CTE = 20 E-9 /’C
Y
X
• Support systems
• Axial support = 3 point mount with vacuum
• Lateral support = single central flexure
FSM local coordinates
October 4, 2010
GMT2010: Design and Development of FSM
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FSM Support system
• Three axial support (defining points) mounted
at the mirror back surface
• Axial supports oriented parallel to the optical
axis (vertical, Z-axis)
• Axial gravity is fully compensated by a
vacuum system at Zenith
• Lateral gravity is held by a flexure at the mirror
center position on the M2 CG plane.
FSM support system
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Support system – FE modeling
 Axial support: Vacuum floating system
W: Weight
 Atmospheric pressure was applied on the
entire front surface of the FSM from the
vacuum
 Magnitude of the atmospheric pressure is
equivalent to the axial gravity of FSM
P: Atmosphere pressure
(counter-pressure)
 Reaction force at the three axial supports is
to be zero; therefore, the FSM is floating
 This floating axial system provides a low
surface error in Zenith.
 Lateral support: Flexure system
 FSM gravity is held by a flexure at the mirror
center location
 Line of action is on the mirror CG plane
 No axial force is to be induced at Horizon
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Mirror Blank Optimization
Four different configurations (depth effect):
1. Gravity print-through
2. Natural Frequency
A. 100mm : 78.8kg
Baseline: favorable configuration for
stiffness and stress requirements
B. 120mm : 84.1kg
Depth=140mm
Face sheet
thickness=20mm
Mass=105kg
C. 140mm : 89.3kg
D. 150mm : 91.9kg
E. 150mm (rib = 10mm) : 118.4kg
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GMT2010: Design and Development of FSM
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FSM: Gravity Print-through
Lateral Gravity (Gy)
Axial Gravity (Gz+vacuum)
RAW
(un-corrected))
P.T.T
corrected
PTT: RMS=6.1 nm surface
PTT: RMS=3.8 nm surface
Optical Surface deformation maps
October 4, 2010
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FSM: thermal gradient, T(z)
Thermal gradients delta T =1oC/0.1m along Z axis (Optical axis)
(CTE = 20 x 10-9 /oC)
P.T.T corrected
Displacement in Z: Max.= 18 nm; PV=35 nm
PV=22nm; RMS=6.3nm surface
Mechanical and Optical surface deformations
October 4, 2010
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Natural Frequency (first mode)
1st Mode Shape: Astigmatism at 720 Hz
1st natural frequency mode with free-free condition
Mirror mass = 105 Kg in the FE model
October 4, 2010
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Natural mirror mode (low order modes)
1
3
4
6
8
10
12
14
16
17
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16
Typical Lateral Flexures in trade
Thickness of Disk Flexure
5mm
0.7mm
8.68mm
15mm
10.16mm
100mm
Sample: Section Plane of Lateral Flexure
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Lateral Flexure Trade study
Stress analysis of lateral flexure was performed initially based on
thickness and materials provided by GMTO. Further assumptions
were made for parametric study. This work is in progress.
Typical results during trade study in static, buckling and non-linear analysis
y
x
Stress calculation
October 4, 2010
Lateral deformation
GMT2010: Design and Development of FSM
Buckling analysis
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Sensitivity: Axial gravity/vacuum
Gravity
Axial gravity compensated by pressure
Atmosphere pressure
97% compensation
Fully Balanced
3% residual by axial support 10N each
RMS=4.1nm surface
RMS=3.8nm surface
3% residual force by lateral support
(work in progress)
Optical Surface deformation maps
October 4, 2010
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Sensitivity: vacuum seal
Seal force applied along the edge of front surface (Flange)
(currently assumed a uniform distribution)
10 N/m along optical axis
RMS=12.2nm surface
10 N/m along radial direction
RMS=1.0nm surface
Focus corrected
October 4, 2010
RMS=3.9nm
RMS=0.4nm
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Zenith Angle Dependence
Gravity Print-through effects from Zenith angle variations
• Print-through from Zenith variation
• Combination of optical surfaces from Axial
and Lateral cases
• Axial support print-through
• RMS surface 3.8 nm
• Lateral support print-through
• RMS surface 6.1 nm
• RMS calculations based on surface
polished out at FSM face-up
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Optical calculations (AXIAL)
Surface error
Slope Y
AXIAL
RMS surface error
RMS surface X_slope
RMS surface Y_slope
EE80 diameter
3.8
0.035
0.035
0.007
Slope X
nm
micro_rad
micro_rad
arcsec
EE80 diameter
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Optical calculations (LATERAL)
Surface error
Slope Y
LATERAL
RMS surface error
RMS surface X_slope
RMS surface Y_slope
EE80 diameter
October 4, 2010
6.1
0.082
0.139
0.005
Slope X
nm
micro_rad
micro_rad
arcsec
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Optical calculations (ZA=60o)
(polished and tested at FSM face-up)
Surface error
Slope Y
Zenith Angle at 60
RMS surface error
RMS surface X_slope
RMS surface Y_slope
EE80 diameter
October 4, 2010
5.6
0.073
0.121
0.005
Slope X
nm
micro_rad
micro_rad
arcsec
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Structure Function calculations (ZA=60o)
Structure function of random variable, P(r)
D() = < | P(r+ ) - P(r) |2 >
Phase map
Structure function at ZA=60o: sqrt(D) in WFE
RMS WFE: 11.2 nm
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Summary and Conclusion
 FSM mirror blank optimum configuration:
 D=1.06m; depth=140mm; face plate thickness=20mm; mass=105kg
 Lightweight glass or glass ceramic mirror
 FSM support system provides adequate optical performances:
 Gravity print-through effects: – met error budget
 Axial gravity: 3.8nm RMS surface; EE80 = 0.007 arcsec (< 0.020)
 Lateral gravity: 6.1nm RMS surface; EE80 = 0.005 arcsec (< 0.020)
 FSM thermal effects were accessed:
 Thermal soak, thermal gradients
 Natural frequency analysis for FSM mirror blank:
 Lowest mode is at 720 hz (astigmatic mode) – stiff mirror
 Optical performances at various Zenith angles: – met error budget
 Assume: FSM figured and tested at its face up position
 At ZA=60 degrees: EE80 = 0.005 arcsec (< 0.039)
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Next Step
 FSM performance evaluations
 Support sensitivity
 Vacuum seals and seal force sensitivity
 FSM mirror support system trade study
 Axial support :
 Vacuum support
 Lateral support :
 Lateral support diaphragm/flexure
 Stiffness of axial and lateral supports
 Work with GMTO for Magellan Secondary mirror engineering
document:
 Lateral support flexure and bonding procedure
 Vacuum
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Acknowledgments
The authors gratefully acknowledge the support of the GMT Office,
Matt Johns and Stephen Shectman. This work was partially
contributed by the scientists and engineers from the KASI and
KRISS of Korea. Students of the University of Arizona are also
greatly acknowledged.
The individual contributors are:
Il Kweon Moon, Andrew Corredor, Christoph Dribusch,
Ju-Heon Koh, Eun-Kyung Kim.
October 4, 2010
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