ShackHartmann tomographic wavefront reconstruction using LGS: Analysis of spot elongation and fratri

1
Shack-Hartmann tomographic wavefront
reconstruction using LGS Analysis of spot
elongation and fratricide effect

• Clélia Robert1, Jean-Marc Conan1, Damien
  Gratadour2,
• Thierry Fusco1,Cyril Petit1, Jean-François
  Sauvage1, Nicolas Muller1

1 ONERA, 2 Obs. Meudon (LESIA)
2
Expected Noise for LGS-HO-WFS

• Backscattering of the laser in the Sodium layer
  at an altitude of 90 km
• Laser emission10 km thickness
• Paralax effect on ELT
• Spot elongation 10 " _at_ 42 m
• Anisoplanatism effects
• Non-uniformity of the Na density profile
• Rayleigh scattering

10 km
Sodium
90 km
20 km
Turbulence
3
Outline

• Modal wavefront tomography model description
• Central/Edge LGS launching
• Impact of fratricide effect
• Number of reconstructed layers
• Up to 32 m telescope
• Conclusion perspectives

4
Multi-LGS wavefront reconstruction

• Model of measurements

Wavefront sensor(Shack-Hartmann)

• Minimum Variance (MAP)

Errors correlated on x and y
Covariance of the errors (centred)

• Propagation of multi-LGS slope noise

• Modal matrix-based simulation tool for
  tomography noise wavefront error (WFE)

5
Principle of tomographic simulations
10 km LGS thickness -gt 5 km,
6 LGS altitude 45 km
12 scaling
The atmosphere is not scaled vertically!
21m
Sketches courtesy R. Myers

• Telescope diameter 21 m, 42x42 sous-pupilles,
  central occultation factor 0.3
• No distorsion of Sodium profile
• Images elongated Gaussian, subap. FoV 10x10
  arcsec2, pixscale0.75
• Modal (KL) matrix-based MAP wavefront
  reconstruction with analytical WCoG
• Tip/tilt LGS measurement, plane waves (!)

6
Impact of launching scheme Central (M2) vs edge
(M1)

• Downscaled simulation (12)
• Telescope 21m 0.5 m subap
• 6 LGS on 1 min ring (MAORY-like)
• Medium LGS flux
• 500 photons/subap/frame
• 3 e- RON

no fratricide effect
Tomographic performance M1 M2 about 59
nm Even a small gain for edge launching
Edge launching gives more uniform propagation
onto modes !
7
Spot elongation launch from M1 side why does it
work?
Side launch
Central launch
Lowest elongation where the layer is seen only
once
Information redundancy for large elongated spots
Schematic sketch with 3 LGSs
Courtesy M. Tallon al.
8
Modeling of fratricide background

• performed by D. Gratadour (LESIA) based on Gemini
  code
• code has been validated with experimental data
  (Gemini...)
• common activity for MAORY / ATLAS / EAGLE studies
• Currently used for LGS tomography analysis (see
  next slides)
• Will be used for Optimal LGS WFS algorithm
  definition WFS design (correlation)

Examples of fratricide effects 21 m / 6 LGS
(launch behind M2)
9
MAORY-like case with fratricide

• Downscaled simulation
• Telescope 21m 0.5 m subap
• 6 LGS on 1 min ring
• Medium LGS flux
• 500 photons/subap/frame 3 e- RON

rms error 20 smaller with edge launching
10
Summary of fratricide effect impact

• Downscaled simulation
• Telescope 21m 0.5 m subaperure
• 6 LGS on xx arcmin ring

Quite uniform and moderate impact for each LGS
asterism (in quadratic difference)
11
Impact of the number of reconstructed layers

• ATLAS project
• LGS asterism 4.2 arcmin

WFE stable with 10 reconstructed layers in a 10 m
telescope simulation Impact of Cn2 profile
uncertainties in altitude and strength ??
12
Up to 32 m telescope simulation

• Fast memory efficient developments for 42m
  simulations
• Modal KL matrix-based MAP reconstruction, sparse
  matrices multiplication and storage
• WFE still grows up in a 32 m telescope case More
  unseen modes up to 2600 KL involved

Medium LGS flux, 2 reconstructed layers, with
spider
13
Conclusion

• Development of a fast memory efficient modal
  matrix-based MAP reconstructor using analytical
  WCoG 1,2
• 1 Sandrine Thomas et al, MNRAS 2008, 2
  Laura Schreiber et al, MNRAS 2009
• Edge launching is better than central launching
• RMS error 20 smaller when fratricide effect is
  accounted for
• warning LGS spot anisoplanatism neglected
• WFS noise model slope equivalent uniform noise
• factor 2 reduction in noise variance wrt
  simplistic single LGS channel not regularized
  reconstruction
• even with relaxed requirement on photon flux
  (typically 500 ph/subap/frame with 3 e- RON)
• Confirmed on 32m case
• Pupil segmentation (spider, fratricide effect)
  has limited effect with regularized
  reconstruction (MAP)

14
Perspectives

• Fast modal reconstructor development
• Spherical versus plane waves tomography
  comparison with zonal E2E tool Fourier codes
  (Cyril Petit presentation)
• LGS tomography activity gives updated slope
  equiv. uniform noise for Fourier code update of
  MAORY / ATLAS / EAGLE projects
• (presentations of Diolaiti, Fusco, Rousset)
• Analysis of LGS spot anisoplanatism (phase and
  scintillation)
• 3 Scintillation and phase anisoplanatism in
  Shack-Hartmann wavefront sensing.
• Clélia Robert et al. JOSA A, Vol. 23, Issue 3,
  pp. 613-624 (2006).
• Impact through tomographic reconstruction see
  Nicolas Mullers Poster
• Impact of Cn2 profile uncertainties in altitude
  and strength
• (presentations of Conan, Fusco)

15
Calculation of the LGS spot elongation
qe q2 - q1
r
r
h2.
h1 .
1
h2
h1
r

h2
h1
When focalised at 90 km height and with 10 km
thickness LGS lauched at 21m with 2 arcmin from
optical axis has a spot elongation of 5 arcsec
in the telescope focal plane
r
16
What do we want to learn ?

• Is LS estimator sufficient ?
• Errors non uniform
• Is WLS estimator better ?
• Errors non uniform
• Correlation on the errors
• Kolmogorov a priori useful?
• MAP (MMSE)
• Use of multi-LGS ?
• GLAO, MCAO, MOAO, LTAO

y
x
Errors correlated on x and y

17
Pure wavefront reconstruction methods

• Model of measurements

Wavefront sensor(Shack-Hartmann, Fried
?geometry, )

• Least Squares

covariance of the errors (centred)

• Weighted Least Squares

• Minimum Variance (MAP)

18
Propagation of multi-LGS slope noise

• Phase estimators LS, WLS, uniform noise MAP,
  MAP
• Telescope diameter from 4,2 m to 42m cases
• subap FoV 10", seeing 1.2",
• OPD without elongation 1 rad2/subap./LGS _at_ 589
  nm
• Estimation of WFE (nm) in SFoV directions
  (bias2 noise_variance)

3 LGS
3 LGS
Validation OK in a GLAO configuration as Tallon
(SPIE 08) alias multi-LGS with pupil-only
turbulence! (no anisoplanatism)
19
Impact of fratricide effect

• Downscaled E2E simulation
• Telescope 21m 0.5 m subap
• 6 LGS on 1 min ring (MAORY-like)
• low LGS flux
• 250 photons/subap/frame 0 e- RON

WFE 15 nm 80 nm compared to 65 nm
20
Summary of fratricide effect impact

• Downscaled E2E simulation
• Telescope 21m 0.5 m subaperure
• 6 LGS on xx arcmin ring

21
Impact of pupil segmentation

• Downscaled E2E simulation
• Telescope 21 m 0.5 m subap
• 6 LGS on 1 arcmin ring (MAORY-like)
• homothetic spider
• Thickness respected 1 sub-aperture

8-arms spider
no fratricide effect
Medium LGS flux, WFE 2 nm
22
MAORY-like case with fratricide spider effects

• Downscaled E2E simulation
• Telescope 21 m 0.5 m subap
• 6 LGS on 1 min ring
• Medium LGS flux
• 500 photons/subap/frame 3 e- RON
• homothetic spider
• Thickness respected 1 sub-ap
• 3 reconstructed layers

rms error 30 smaller with edge
launching Absolute error value estimated in 32 m
telescope case Uniform performance in MAORY FoV
23
Estimation of WFS error through tomographic
reconstruction

• Impact of 3D phase and scintillation
  anisoplanatism
• synergy with Nicolas Muller PhD _at_ Onera
• Analytical expression exists for 2D object
• 3 Scintillation and phase anisoplanatism in
  Shack-Hartmann wavefront sensing.
• Clélia Robert et al. JOSA A, Vol. 23, Issue 3,
  pp. 613-624 (2006).
• gt estimation at sub-aperture level for largest
  elongations (worst case)
• Account for 3D shape of the spot through
  propagation code (PILOT)
• on downscaled cases no difference with 2D
  object
• First results show that it is not negligible on
  very elongated spots in edge launching. So
  serious? these data are also almost discarded
  because of poor SNR
• Impact through tomographic reconstruction see
  Poster

unit nm rms of sub-ap edge OPD along elongated
axis central launching 30 nm edge launching
93 nm
24
Estimation of WFS error through tomographic
reconstruction

• Impact of LGS noise signature on modal
  tomographic reconstruction
• Account for spot elongation pattern related to
  the laser launching option
• Reconstruction using MAP estimator
• on downscaled cases 21m , LGS angle and height
  scaled with D, 3 layers ...
• Various spot position estimators (WCoG)
• Account for additive fratricide background
• Account for pupil segmentation (spider)
• Analysis of LGS spot anisoplanatism (phase and
  scintillation)
• 3 Scintillation and phase anisoplanatism in
  Shack-Hartmann wavefront sensing.
• Clélia Robert et al. JOSA A, Vol. 23, Issue 3,
  pp. 613-624 (2006).
• Impact through tomographic reconstruction see
  Nicolas Mullers Poster

25
Impact of the number of reconstructed layers

• ATLAS
• Two LGS asterisms 3 arcmin and 4.2 arcmin
• 3 and 5 reconstructed layers