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Performance of wave-front measurement Performance of wave-front measurement concepts for GLAO 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

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OutlineOutline

• 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

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Ground Layer turbulence measurement : Ground Layer turbulence measurement :

Altitude

PUP = 1 + 2 + 3 = 3 sol + 1

alt + 2alt +3

alt

0

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:

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5 Wave-front sensing devices

Shack-Hartmann ?

Other ?

Pyramid ?

A triple problem :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)

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Tools for GLAO performance analysis :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

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Wave-front measurement error:

Wave-front measurement Error :Wave-front measurement Error :

Introduction – Analytical criterion – SO & LO Optimization - Conclusion

Phase to be estimated:

Measured phase:

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QC VS usual quality criterions for GLAO :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.

FOV 8 arcmin wide,

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Secondary Quality criterions on phase :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

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QCQCquantize quantize characteristics:characteristics:

Introduction – Analytical criterion – SO & LO Optimization - Conclusion

1./K

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Secondary Quality criterions on phase :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 Oriented Layer Oriented

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QCQCWFMCWFMC for Star Oriented: for Star Oriented:

Introduction – Analytical criterion – SO & LO Optimization - ConclusionAnalytical criterion :

Criterion derivation for SO :

Photon Noise termDepends on: Flux per GS • Flux per GS (= flux per WFS)

• CCD Read-out noise

Detector Noise term:Depends on:

COMMANDPupil

1 WFS / GS

DM We measure:

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QCQCWFMCWFMC for Layer Oriented: for Layer Oriented:

DM

COMMANDPupil

1 WFS

Introduction – Analytical criterion – SO & LO Optimization - Conclusion

Phases weighted by GS flux 1 WFS only

Photon Noise termDepends on:

Total flux in FOV. •Total flux in FOV,• CCD Read-out noise.

Detector Noise termDepends on:

Turbulence related termDepends on:

• Total flux in FOV, • GS flux dispersion ,• Covariance of phase perturbations From one direction to another.

Analytical criterion :

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Performance analysis for SO / LO :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; s2

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

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Star Oriented Optimization: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

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Performance analysis for SO / LO :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; s2

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

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Layer Oriented Optimization: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 optimized Optical attenuations to be optimized

Introduction – Analytical criterion – SO & LO Optimization - Conclusion

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Layer Oriented Optimization: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:

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Analyse performance SO / LO :Analyse performance SO / LO :

Introduction – Analytical criterion – SO & LO Optimization - Conclusion

4 GS 30 GS

Galactic coordinates : (30, 0)8x8 arcmin FoV

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Conclusions …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

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… … And future works :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

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Wave-front measurement Error :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.

FOV 8 arcmin wide,37 guide stars

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Splitting of QC:Splitting of QC:

Introduction – Analytical criterion – SO & LO Optimization - Conclusion

QCQC

QCQCquantizequantize

QCQCWFMCWFMC

Saturation due to pupil footprints superimposition

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Secondary Quality criterions on phase :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