Transcript Diapositive 1

Cn2 profile measurement from Shack-Hartmann
data
Clélia Robert, Nicolas Védrenne,Vincent Michau, Jean-Marc Conan
Cn² ?
Cn² ?
Cn² ?
Cn² ?
Cn² ?
Cn² ?
A new method to profile Cn2
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Measurement of Cn² profile
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
3
Cn2 Profile
Profile knowledge:
Dimensioning systems
Evaluation of performances
A priori for servo-loop laws
Profile from Observatoire de
Haute Provence (ballon sonde)
High variability
Need of profile
monitoring
How to measure ?
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Principles of Cn2 profiling : single source
Spectral analysis of scintillation structures
PSDχ(ν)
TF
h
ν
intensité dans
la pupille
No sensitivity to law altitude layers
(no propagation)
(λh)-(1/2)
More operations needed
(mode: « generalized»)
MASS (V. Kornilov, A. Tokovinin)
SSCIDAR (D. Garnier)
Single source: low vertical resolution
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More uncertainties
Principles of Cn2 profiling : multiple source
θ
θXh
h
Intensities:
Cross-correlations of scintillation indices: G-SCIDAR
(J. Vernin, V.A. Klueckers)
Slopes:
Cross-correlations of wavefront slopes: SLODAR (R.W. Wilson)
What about simultaneous exploitation of
slopes and intensities ?
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Measurement of Cn² profile
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
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Shack Hartmann Wavefront sensor
α
α
y
rm
x
SH data:
sm(θ) = wavefront slopes averaged on subaperture at rm
im(θ) = averaged intensity of the incident wave on subaperture at rm
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m
Correlations of data (intensities & slopes):
h
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Correlations of data (intensities & slopes):
rm
Propagation + subaperture averaging
h
Small perturbation approximation
(Rytov regime, σχ2 < 0.3)
m
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Correlations of data (intensities & slopes):
θ
θh – rm
rm
Propagation + subaperture averaging
h
m
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Correlations of data (intensities & slopes):
θ
Propagation + subaperture averaging
h
n
m
dmn
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Correlations of data (intensities & slopes):
θ
Propagation + subaperture averaging
h
θh
Altitude of maximum sensitivity
n
m
dmn
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Correlations of data (intensities & slopes):
θ
Propagation + moyenne sur la sous-pupille
h
θh
n
m
dmn
Measurement
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unknown
Weighting
Correlations of Shack-Hartmann data
Slopes
SLODAR
Intensities
SCIDAR,
MASS
Coupling
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Shack-Hartmann ++ !!
Complementarity of measurements
Slopes
Intensities
n
Shack-Hartmann:
dmn
D= 0.4 m,16 x 16, λ = 0.5 μm
dy
dy
m
sensitivity:
dx
Law layers
High layers
5%
Se:
15 %
80 %
Simultaneous exploitation: better sensitivity
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Measurement of Cn² profile
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
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Problem statement
Estimated covariances:
SH data: sm(θ), im(θ): xki
Pseudo data
ou
Single source
Multiple sources
Direct problem:
: weighting functions
: covariance of detection noise (bias)
: statistical noise on
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Inversion of direct problem
Pseudo-data:
Calibration
Noise treatment:
Subtraction of detection
noise bias
Limited statistic
(convergence noise)
Covariance
matrix
Cnoise
Criterion to minimise relatively to S (Cn2 profile)
-1
Data likelihood
: regularisation parameter (depends on h)
Minimisation of J with positivity constraint
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A priori
Measurement of Cn² profile
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
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Simulation:
θ = 10 arcsec.
Object model: binary star
+
Code PILOT
Simulation of turbulent screens
+
Diffractive propagation
32 layers/ 400 frames
+
Shack-Hartmann:
16 x 16, d = 2.5 cm, λ = 0.5 μm (D = 40 cm)
Data: sm(θ), im(θ)
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Preliminary results
N. Védrenne, V. Michau, C. Robert, J.-M Conan, « Improvements in Cn2 profile monitoring with a Shack-Hartmann wavefront sensor », Proc. SPIE Vol. 6303,
septembre 2006.
N. Védrenne, V. Michau, C. Robert, J.-M Conan, « Full exploitation of Shack-Hartmann data for Cn2 profile measurement », OL, octobre 2007
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Conclusion and perspectives:
Proposition of two original methods to profile Cn2
New exploitation of the Shack-Hartmann
Sensitivity
Validated numerically
Processing of real data (SLODAR)
Study of nois effect (photons, detector, quantification)
Calibration
Adaptation to close binary, moon edge, sun edge
Determination of wind profile
Influence of external scale?
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