Performance of wave-front measurement concepts for GLAO

1. Performance of wave-front measurement concepts for GLAO M. NICOLLE1, T. FUSCO1, V. MICHAU1, G. ROUSSET1, J.-L. BEUZIT2 1ONERA - DOTA, Châtillon, France 2LAOG, Grenoble, France Mail: magali.nicolle@onera.fr

2. Introduction – Analytical criterion – SO & LO Optimization - Conclusion 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.

3. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Altitude D  0 • BUT available phases are: fPUP = f1 + f2 + f3= 3 jsol + j1alt + j2alt +j3alt • We only can measure : Ground Layer turbulence measurement : • 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:

4. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Star Oriented ? Layer Oriented ? Other ? Wave-front measurement concept (measured phases) Number ? Magnitude ? Shack-Hartmann ? Pyramid ? Guides Stars (available phases) Natural ? Artificial ? Other ? A triple problem : Wave-front sensing devices

5. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Tools for GLAO performance analysis : • 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. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated:  Wave-front measurement error: Measured phase: Wave-front measurement Error :

7. Introduction – Analytical criterion – SO & LO Optimization - Conclusion  Wave-front measurement error: FOV 8 arcmin wide, QC VS usual quality criterions for GLAO : • 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; • lWFS: 0.7 µm; • Photon noise only • GS integrated magnitude in R : 12. • GS uniformly spread in FOV; • Phases measurement  Shack-Hartmann slopes.

8. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated Independent from WFMC Phase to be measured Measured phase Secondary Quality criterions on phase :

9. Introduction – Analytical criterion – SO & LO Optimization - Conclusion  1./K QCquantize characteristics:

10. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated Independent from WFMC Phase to be measured Measured phase Star Oriented Layer Oriented Secondary Quality criterions on phase :

11. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Analytical criterion : We measure: DM Pupil COMMAND 1 WFS / GS  Criterion derivation for SO : Detector Noise term: Depends on: Photon Noise term Depends on: Flux per GS • Flux per GS (= flux per WFS) • CCD Read-out noise QCWFMC for Star Oriented:

12. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Analytical criterion : DM Pupil COMMAND 1 WFS only Phases weighted by GS flux 1 WFS Turbulence related term Depends on: Detector Noise term Depends on: Photon Noise term Depends on: Total flux in FOV. • Total flux in FOV, • CCD Read-out noise. • Total flux in FOV, • GS flux dispersion , • Covariance of phase perturbations • From one direction to another. QCWFMC for Layer Oriented:

13. Introduction – Analytical criterion – SO & LO Optimization - Conclusion 4 GS ~30 GS 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; • lWFS: 0.7 µm; • s2det: 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.

14. Introduction – Analytical criterion – SO & LO Optimization - Conclusion We measure: That we can employ as we want.  We can consider : numerical coefficients to be optimized  Criterion derivation for OSO :  hi optimal only if : Star Oriented Optimization: • Linear Matricial equation to invert. • Solution exists.

15. Introduction – Analytical criterion – SO & LO Optimization - Conclusion 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; • lWFS: 0.7 µm; • s2det: 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.

16. Introduction – Analytical criterion – SO & LO Optimization - Conclusion numerical coefficient to be optimized Optical attenuations to be optimized Layer Oriented Optimization: We measure only one integrated phase ! • We can optimize it by attenuating optically some GS; • We can account for the WFS SNR in the use of this phase measurement;  We can consider :

17. Introduction – Analytical criterion – SO & LO Optimization - Conclusion h optimization: • analytical solution exists. li optimization: • NON linear equation to invert. • Multi-variable optimization. Layer Oriented Optimization:  Criterion derivation for OLO :

18. Introduction – Analytical criterion – SO & LO Optimization - Conclusion 4 GS 30 GS Analyse performance SO / LO : Galactic coordinates : (30, 0) 8x8 arcmin FoV

19. Introduction – Analytical criterion – SO & LO Optimization - Conclusion 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.

20. Introduction – Analytical criterion – SO & LO Optimization - Conclusion … 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 ?)

21. Introduction – Analytical criterion – SO & LO Optimization - Conclusion  Wave-front measurement error: FOV 8 arcmin wide, 37 guide stars 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; • lWFS: 0.7 µm; • Photon noise only • GS integrated magnitude in R : 12. • GS uniformly spread in FOV; • Phases measurement  Shack-Hartmann slopes.

22. Introduction – Analytical criterion – SO & LO Optimization - Conclusion QC QCWFMC QCquantize Saturation due to pupil footprints superimposition Splitting of QC:

23. Introduction – Analytical criterion – SO & LO Optimization - Conclusion Phase to be estimated Independent from WFMC Phase to be measured Measured phase Secondary Quality criterions on phase :