Post on 02-Jan-2016
description
transcript
Cn2 profile measurement from Shack-Hartmann data
Clélia Robert, Nicolas Védrenne,Vincent Michau, Jean-Marc Conan
2
A new method to profile Cnn2
Cn² ?
Cn² ?
Cn² ?
Cn² ?
Cn² ?
Cn² ?
3
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
Measurement of Cn² profile
4
Cn2 Profile
Profile from Observatoire de Haute Provence (ballon sonde)
Profile knowledge:
High variability
Need of profilemonitoring
Dimensioning systemsEvaluation of performancesA priori for servo-loop laws
How to measure ?
5
MASS (V. Kornilov, A. Tokovinin) SSCIDAR (D. Garnier)
More operations needed(mode: « generalized»)
No sensitivity to law altitude layers (no propagation)
intensité dans la pupille
Spectral analysis of scintillation structures
TF
(λh)-(1/2)
PSDχ(ν)
ν
h
More uncertainties
Principles of Cn2 profiling : single source
Single source: low vertical resolution
6
Principles of Cn2 profiling : multiple source
Slopes: Cross-correlations of wavefront slopes: SLODAR (R.W. Wilson)
What about simultaneous exploitation of slopes and intensities ?
h
θ
Intensities: Cross-correlations of scintillation indices: G-SCIDAR (J. Vernin, V.A. Klueckers)
θ X h
7
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
Measurement of Cn² profile
8
Shack Hartmann Wavefront sensor
SH data:
sm(θ) = wavefront slopes averaged on subaperture at rm
im(θ) = averaged intensity of the incident wave on subaperture at rm
m
x
yrm
αα
9
Correlations of data (intensities & slopes):
h
10
Propagation + subaperture averaging
m
h
rm
Correlations of data (intensities & slopes):
Small perturbation approximation (Rytov regime, σχ
2 < 0.3)
11
Propagation + subaperture averaging
θ
m
h
rm θh – rm
Correlations of data (intensities & slopes):
12
Propagation + subaperture averaging
dmn
θ
m n
h
Correlations of data (intensities & slopes):
13
Propagation + subaperture averaging
dmn
θ
m n
h
θh
Correlations of data (intensities & slopes):
Altitude of maximum sensitivity
14
Propagation + moyenne sur la sous-pupille
dmn
θ
m n
h
θh
Correlations of data (intensities & slopes):
unknown WeightingMeasurement
15
Correlations of Shack-Hartmann data
Slopes
Coupling
Intensities
SLODAR
SCIDAR, MASS Shack-Hartmann ++ !!
16
Complementarity of measurements
D= 0.4 m,16 x 16, λ = 0.5 μm
Simultaneous exploitation: better sensitivity
80 %
15 %
5 %
Slopes Intensities
Se:
dy
n
m
dmn
dx
dy
Shack-Hartmann:
Law layers High layers
sensitivity:
17
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
Measurement of Cn² profile
18
Problem statement
Estimated covariances:
SH data: sm(θ), im(θ): xki
: covariance of detection noise (bias)
: statistical noise on
Direct problem:
: weighting functions
Multiple sourcesSingle source
ou
Pseudo data
19
Inversion of direct problem
CalibrationSubtraction of detection
noise bias
Pseudo-data:
Covariance matrixCnoise
Limited statistic(convergence noise)
Noise treatment:
Minimisation of J with positivity constraint
: regularisation parameter (depends on h)
Criterion to minimise relatively to S (Cn2 profile)
-1
Data likelihood A priori
20
I. Motivation and techniques
II. Shack-Hartmann data
III. Exploitation to measure Cn2 profile
IV. Numerical validation
Measurement of Cn² profile
21
Simulation:
Data: sm(θ), im(θ)
16 x 16, d = 2.5 cm, λ = 0.5 μm (D = 40 cm)Shack-Hartmann:
Object model: binary starθ = 10 arcsec.
Code PILOTSimulation of turbulent screens
+ Diffractive propagation
32 layers/ 400 frames
+
+
22
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 Cn
2 profile measurement », OL, octobre 2007
23
Conclusion and perspectives:
Proposition of two original methods to profile Cn2
New exploitation of the Shack-Hartmann
Sensitivity
Validated numerically
Study of nois effect (photons, detector, quantification)
Processing of real data (SLODAR)
Determination of wind profile
Calibration
Adaptation to close binary, moon edge, sun edge
Influence of external scale?