1. Trade Study Report: Fixed vs. Variable LGS Asterism
V. Velur
Caltech Optical Observatories
Pasadena, CA

2. Outline Introduction Assumptions Observing scenarios and assumptions
Narrow fields
High red-shift galaxies (studied with d-IFU)
Cost implications
Optomechanical
RTC
Conclusions
Other issues raised by this trade study

3. Introduction NGAO point design retreat WBS Dictionary Approach
Identified the need for both narrow-field and wide-field asterism configurations
Natural question: “Should the point design have fixed or continuously variable asterism radius?”
WBS Dictionary
Consider the cost/benefit of continually varying the LGS asterism radius vs. a fixed number of radii (e.g. 5", 25", 50"). Complete when LGS asterism requirements have been documented
Approach
Evaluate the benefit based on WFE for two science cases[1] (resource limited)
Estimate cost impact at highest subsystem level (ballpark)

4. Assumptions 5 LGS’s in a quincunx 3 NGS’s randomly distributed
Field of regard varies with observing scenario
Two use TT sensors, one is a TTFA sensor
Other assumptions (atmospheric turbulence, noise, laser return, etc.) per NGAO June ‘06 proposal

5. Observing Scenario I: Narrow fields
Potential advantages of variable asterism radius
Better tomographic information over a given field of regard
-> Better MOAO correction of science targets
-> Better tip/tilt correction for higher sky coverage
Evaluation procedure
Assume science target is on-axis (near central LGS)
For various sky coverage values the system performance is optimized.
WFE vs. (off axis)TT star magnitude is plotted for the case where the TT star is corrected using MOAO.
This case is fairly representative of KBO, Galactic center and Io science cases.

6. Observing Scenario I: Narrow fields
Potential advantages of variable asterism radius
Better tomographic correction of TT and TTFA stars provides better Strehl ratio on-axis for a given sky coverage
Evaluation procedure
Assume science target is on-axis (near central LGS)
For various sky coverage values, optimize system performance to compare continuously variable and discrete (5”, 25”, 50”) asterism radii
WFE vs. (off axis) TT star magnitude is plotted for the case where the TT star is corrected using MOAO

7. 10% sky coverage case

8. 40% sky coverage case

9. 60% sky coverage case

10. Observing Scenario II: High red-shift galaxies
Potential advantages of variable asterism radius
Better tomographic (MOAO) correction of science target, assuming constant correction within the asterism and natural anisoplanatic fallout without
Evaluation procedure
Assume TT/TTFA field of regard is 30 arcsec and brightest TT is mV = 17 (this corresponds to 10% sky coverage).
Vary the science target position between 0” and 150” from quincunx center
Optimize system performance to compare continuously variable and discrete (5”, 25”, 50”) asterism radii

11. High red-shift galaxies

12. Example implementation for this study (assumes telecentricity)

13. Optomechanical Implications
Discrete asterism
Requires HO WFS positioner that is repeatable upon asterism reconfiguration
To change from a 5 to 50 arcsec quincunx we need 40 mm travel at the focal plane.
Continuous asterism
Requires HO WFS positioner with higher accuracy
The accuracy of getting LGS spots on the HOWFS is a combination of the stage position and the amount of asterism deformation that we can tolerate
The minimum error allocated for LGS asterism deformation in the NGAO proposal is 5 nm
This corresponds to ± 0.1 arcsec change in radius of the entire asterism! The HO WFS positioner need only position to this accuracy.
This is ~70 micron accuracy over the necessary travel range.
This assumes that the uplink tip/tilt (UTT) has 0.1 arcsec (Ball Aerospace has mirrors can provide arcsec on sky) resolution on sky.
This loose tolerance would enable us to position the HO WFS continuously without much difficulty.
Stronger cost driver will probably be the required angular tolerances of matching the incoming beam

14. RTC Implications Discrete asterism Continuous asterism
Requires reconstructors for the three asterisms, updated according to changing Cn2(h)
Continuous asterism
Requires reconstructors updated according to asterism radius and changing Cn2(h)
Question is: How do you choose the asterism radius?
Need some auxiliary process and/or measurement
Differential cost for estimating, setting, logging, and perhaps defending the choice of radius and corresponding reconstructor unknown

15. Conclusions Continuously variable asterism
There is little performance benefit in narrow field performance
There is significant performance benefit for d-IFU science when the mismatch between asterism and target radius exceeds 20 arcsec
There is little cost overhead in optomechanical hardware
Real-time and supervisory control software costs will dominate
Software costs allowing, we should assume continuously variable asterism in the system design

16. Other important considerations
There are many concerns pertaining to LGS HO WFS focus requirements
LGS (differential) defocus between the 5 beacons due to projection geometry
LGS defocus due to global Na layer shifts
LGS defocus due to Na layer density fluctuations.
LGS HO WFS would benefit from a telecentric optical space
Chief ray always parallel to the optical axis
Would save us the job of registering each WFS to the DM as the asterism geometry changes

17. References R. Dekany, Private communication
R. Flicker , Private communication

18. Backup Slides

19. HO WFS Positional Accuracy Tolerance: WFE as a result of LGS deformation corresponding to “best condition” narrow field case [2]
WFE [nm]
Asterism radius [arcsec] (w/ perfect asterism corresponding to lowest error)

20. 5 ATS-1000 stages would be ideal for continuously variable asterism.
Stage costs
5 ATS-1000 stages would be ideal for continuously variable asterism.

21. Newport stages
Depending on the WFS optical tolerances on the angle of the incoming beam, this could be as low as $10,000-$20,000. The cost driver for the stages would be the WFS’s angular sensitivity.