1. Design and Development of the FSM (Fast steering Secondary Mirror)
Myung Cho, NOAO-GSMTPO
Kwijong Park, KASI
Young-Soo Kim, KASI
October 4, GMT2010: Design and Development of FSM

2. OUTLINE Prior Work: Magellan Secondary Mirror modeling
FSM Configuration
3. Design and Development (work in progress)
4. 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
October 4, GMT2010: Design and Development of FSM

3. 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
25.4m GMT
October 4, GMT2010: Design and Development of FSM

4. 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.
October 4, GMT2010: Design and Development of FSM

5. GMT and GMT FSM Primary: 25.4m (8.4m x 7) GMT F/8 Gregorian beams
Secondary: 3.2m (1.06m x 7)
Shape: Ellipsoid
Focal ratio: F/0.7
Final focal ratio: F/8 Gregorian
GMT F/8 Gregorian beams
Conjugated M1 and M2
October 4, GMT2010: Design and Development of FSM

6. FSM assembly layout
October 4, GMT2010: Design and Development of FSM

7. FSM optical prescription
FSM optical prescription (as of 9/2010):
FSM M2 nominal segment Configuration:
1060mm
175mm
140mm
October 4, GMT2010: Design and Development of FSM

8. FSM Error Budget specification
Error budget: Encircled Energy diameters at 80% (EE80)
Orientation 80% EE Specifications
Zenith ” (arc-seconds)
Horizon ”
Figure error ”
October 4, GMT2010: Design and Development of FSM

9. Assumptions in FE FSM local coordinates 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) = m (from vertex)
Mass=105 kg; Ixx=6.3 kg-m2, Izz=12.3 kg-m2 at CG
CTE = 20 E-9 /’C
Support systems
Axial support = 3 point mount with vacuum
Lateral support = single central flexure Y X
FSM local coordinates
October 4, GMT2010: Design and Development of FSM

10. FSM Support system 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
October 4, GMT2010: Design and Development of FSM

11. Support system – FE modeling
Axial support: Vacuum floating system
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
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
P: Atmosphere pressure
(counter-pressure)
W: Weight
October 4, GMT2010: Design and Development of FSM

12. 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
October 4, GMT2010: Design and Development of FSM

13. 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, GMT2010: Design and Development of FSM

14. FSM: thermal gradient, T(z)
Thermal gradients delta T =1oC/0.1m along Z axis (Optical axis)
(CTE = 20 x /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, GMT2010: Design and Development of FSM

15. 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, GMT2010: Design and Development of FSM

16. Natural mirror mode (low order modes)1 3 4 6 8 10 12 14 16 17 19 21
October 4, GMT2010: Design and Development of FSM

17. Typical Lateral Flexures in trade
Thickness of Disk Flexure
5mm
8.68mm
0.7mm
15mm
10.16mm
100mm
Sample: Section Plane of Lateral Flexure
October 4, GMT2010: Design and Development of FSM

18. 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
Buckling analysis
Stress calculation
Lateral deformation
October 4, GMT2010: Design and Development of FSM

19. Sensitivity: Axial gravity/vacuum
Atmosphere pressure
Gravity
Axial gravity compensated by pressure
Fully Balanced
97% compensation
3% residual by axial support 10N each
RMS=4.1nm surface
3% residual force by lateral support
(work in progress)
RMS=3.8nm surface
Optical Surface deformation maps
October 4, GMT2010: Design and Development of FSM

20. Sensitivity: vacuum seal
Seal force applied along the edge of front surface (Flange)
(currently assumed a uniform distribution)
10 N/m along optical axis
10 N/m along radial direction
RMS=12.2nm surface
RMS=1.0nm surface
Focus corrected
RMS=3.9nm RMS=0.4nm
October 4, GMT2010: Design and Development of FSM

21. 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
October 4, GMT2010: Design and Development of FSM

22. Optical calculations (AXIAL)
Surface error Slope X Slope Y
EE80 diameter
October 4, GMT2010: Design and Development of FSM

23. Optical calculations (LATERAL)
Surface error Slope X Slope Y
October 4, GMT2010: Design and Development of FSM

24. Optical calculations (ZA=60o) (polished and tested at FSM face-up)
Surface error Slope X Slope Y
October 4, GMT2010: Design and Development of FSM

25. Structure Function calculations (ZA=60o)
Structure function of random variable, P(r)
D() = < | P(r+ ) - P(r) |2 >
Phase map
RMS WFE: 11.2 nm
Structure function at ZA=60o: sqrt(D) in WFE
October 4, GMT2010: Design and Development of FSM

26. 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 = arcsec (< 0.020)
Lateral gravity: 6.1nm RMS surface; EE80 = 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 = arcsec (< 0.039)
October 4, GMT2010: Design and Development of FSM

27. 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
October 4, GMT2010: Design and Development of FSM

28. 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, GMT2010: Design and Development of FSM