1. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 Workshop Leiden 2005 Performance of wave-front measurement concepts for GLAO M. NICOLLE 1, T. FUSCO 1, V. MICHAU 1, G. ROUSSET 1, J.-L. BEUZIT 2 1 ONERA - DOTA, Châtillon, France 2 LAOG, Grenoble, France Mail: magali.nicolle@onera.fr

2. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 2 Workshop Leiden 2005 Outline Problem statement, An analytical criterion for GLAO performance estimation, SO and LO performance analysis, Optimization of SO and LO measurement, Conclusions and future works. Introduction – Analytical criterion – SO & LO Optimization - Conclusion

3. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 3 Workshop Leiden 2005 Ground Layer turbulence measurement : Altitude  PUP =  1 +  2 +  3 = 3  sol +  1 alt +  2 alt +  3 alt  0 0 DD Introduction – Analytical criterion – SO & LO Optimization - Conclusion  GLAO: wide FOV seeing reducer;  Needs a uniform correction in FOV:  That ’s why we want to measure only the boundary layer,  A solution for that is to estimate:  We only can measure :  BUT available phases are:

4. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 4 Workshop Leiden 2005 Wave-front sensing devices Shack-Hartmann ? Other ? Pyramid ? A triple problem : Number ? Magnitude ? Natural ? Artificial ? Star Oriented ?Layer Oriented ?Other ? Introduction – Analytical criterion – SO & LO Optimization - Conclusion Guides Stars (available phases) Wave-front measurement concept (measured phases)

5. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 5 Workshop Leiden 2005 Tools for GLAO performance analysis : Introduction – Analytical criterion – SO & LO Optimization - Conclusion Two models have been used:  Numerical model, for both study of Guides Stars impact and WFMC performance:  Simulates uniform, random or Galactic-model based Guide Stars fields;  Simulates Star Oriented and Layer Oriented WFMC;  Complex turbulence profile;  Decomposition of phases onto Zernike polynomials;  Simulates photon and detector noises;  Modal optimization;  Computes long exposure PSF, encircled energy, residual phase variances.  Analytical model, for WFMC performance analysis:  Based on an analytical criterion  Considered variable: phase slopes as measured by Shack-Hartmann WFS

6. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 6 Workshop Leiden 2005  Wave-front measurement error: Wave-front measurement Error : Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated: Measured phase:

7. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 7 Workshop Leiden 2005 QC VS usual quality criterions for GLAO : Introduction – Analytical criterion – SO & LO Optimization - Conclusion  Wave-front measurement error: Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; WFS : 0.7 µm; Photon noise only GS integrated magnitude in R : 12. GS uniformly spread in FOV; Phases measurement  Shack-Hartmann slopes. Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; WFS : 0.7 µm; Photon noise only GS integrated magnitude in R : 12. GS uniformly spread in FOV; Phases measurement  Shack-Hartmann slopes. FOV 8 arcmin wide,

8. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 8 Workshop Leiden 2005 Secondary Quality criterions on phase : Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated Measured phase Independent from WFMC Phase to be measured

9. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 9 Workshop Leiden 2005 QC quantize characteristics: Introduction – Analytical criterion – SO & LO Optimization - Conclusion  1./  K 

10. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 10 Workshop Leiden 2005 Secondary Quality criterions on phase : Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated Measured phase Independent from WFMC Phase to be measured Star OrientedLayer Oriented

11. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 11 Workshop Leiden 2005 QC WFMC for Star Oriented: Introduction – Analytical criterion – SO & LO Optimization - Conclusion Analytical criterion :  Criterion derivation for SO : Photon Noise term Depends on: Flux per GS Flux per GS (= flux per WFS) CCD Read-out noise Detector Noise term: Depends on: COMMAND Pupil 1 WFS / GS DM We measure:

12. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 12 Workshop Leiden 2005 QC WFMC for Layer Oriented: DM COMMAND Pupil 1 WFS Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phases weighted by GS flux 1 WFS only Photon Noise term Depends on: Total flux in FOV. Total flux in FOV, CCD Read-out noise. Detector Noise term Depends on: Turbulence related term Depends on: Total flux in FOV, GS flux dispersion, Covariance of phase perturbations From one direction to another. Analytical criterion :

13. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 13 Workshop Leiden 2005 Performance analysis for SO / LO : Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; l WFS : 0.7 µm; s 2 det : 3 e - (when simulated); Galactic coordinates : lat = 30°, lon = 0°; Repartition of GS mag. simulated from Besançon Model; At least 4 GS in Technical FoV; Phases measurement  Shack-Hartmann slopes. Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; l WFS : 0.7 µm; s 2 det : 3 e - (when simulated); Galactic coordinates : lat = 30°, lon = 0°; Repartition of GS mag. simulated from Besançon Model; At least 4 GS in Technical FoV; Phases measurement  Shack-Hartmann slopes. Introduction – Analytical criterion – SO & LO Optimization - Conclusion 4 GS ~30 GS

14. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 14 Workshop Leiden 2005 Star Oriented Optimization: We measure:That we can employ as we want.  We can consider :  Criterion derivation for OSO :   i optimal only if :  Linear Matricial equation to invert.  Solution exists. numerical coefficients to be optimized Introduction – Analytical criterion – SO & LO Optimization - Conclusion

15. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 15 Workshop Leiden 2005 Performance analysis for SO / LO : Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; l WFS : 0.7 µm; s 2 det : 1 e - (when simulated); Galactic coordinates : lat = 30°, lon = 0°; Repartition of GS mag. simulated from Besançon Model; At least 4 GS in Technical FoV; Phases measurement  Shack-Hartmann slopes. Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; l WFS : 0.7 µm; s 2 det : 1 e - (when simulated); Galactic coordinates : lat = 30°, lon = 0°; Repartition of GS mag. simulated from Besançon Model; At least 4 GS in Technical FoV; Phases measurement  Shack-Hartmann slopes. Introduction – Analytical criterion – SO & LO Optimization - Conclusion

16. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 16 Workshop Leiden 2005 Layer Oriented Optimization: We measure only one integrated phase !  We can consider :  We can optimize it by attenuating optically some GS;  We can account for the WFS SNR in the use of this phase measurement; numerical coefficient to be optimizedOptical attenuations to be optimized Introduction – Analytical criterion – SO & LO Optimization - Conclusion

17. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 17 Workshop Leiden 2005 Layer Oriented Optimization:  Criterion derivation for OLO : Introduction – Analytical criterion – SO & LO Optimization - Conclusion  analytical solution exists.  optimization:  NON linear equation to invert.  Multi-variable optimization.  i  optimization:

18. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 18 Workshop Leiden 2005 Analyse performance SO / LO : Introduction – Analytical criterion – SO & LO Optimization - Conclusion 4 GS 30 GS Galactic coordinates : (30, 0) 8x8 arcmin FoV

19. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 19 Workshop Leiden 2005 Conclusions … Study of the influence of GS number and repartition on GLAO performance uniformity Performance analysis for both SO and LO WFMC:  Analytical modelization and definition of a quality criterion based on phase measurement error for SO and LO WFMC,  SO performance is mainly limited by Detector noise,  LO performance is mainly limited by GS flux dispersion; Optimisation of both SO and LO measurements:  SO: numerical optimization  LO: both numerical and optical optimizations;  Identical performance of SO and LO in photon noise,  Slight gain for LO in detector noise,  Very small dependency of the errors with respect to GS number. Introduction – Analytical criterion – SO & LO Optimization - Conclusion

20. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 20 Workshop Leiden 2005 … And future works :  GLAO:  Global optimization of  Complete Sky coverage study,  Scaling to ELT,  MCAO: Generalization to Multiple FOV concept,  Real data process (MAD results ?) Introduction – Analytical criterion – SO & LO Optimization - Conclusion

21. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 21 Workshop Leiden 2005 Wave-front measurement Error : Introduction – Analytical criterion – SO & LO Optimization - Conclusion  Wave-front measurement error: Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; WFS : 0.7 µm; Photon noise only GS integrated magnitude in R : 12. GS uniformly spread in FOV; Phases measurement  Shack-Hartmann slopes. Conditions of the numerical simulation : Technical FoV : 8 arcmin; Seeing : 0.9 arcsec @ 0.5 µm; Turbulence profile : 60% in pupil plane, 40% in altitude; WFS : 0.7 µm; Photon noise only GS integrated magnitude in R : 12. GS uniformly spread in FOV; Phases measurement  Shack-Hartmann slopes. FOV 8 arcmin wide, 37 guide stars

22. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 22 Workshop Leiden 2005 Splitting of QC: Introduction – Analytical criterion – SO & LO Optimization - ConclusionQC QC quantize QC WFMC Saturation due to pupil footprints superimposition

23. Comète axe 2 - TC1 : RSA n°2 - SPART/S t Cloud - 080304 23 Workshop Leiden 2005 Secondary Quality criterions on phase : Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated Measured phase Independent from WFMC Phase to be measured