Cn2 profile measurement from Shack-Hartmann data

Clélia Robert, Nicolas Védrenne,Vincent Michau, Jean-Marc Conan

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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

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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 ?

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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

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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

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I. Motivation and techniques

II. Shack-Hartmann data

III. Exploitation to measure Cn2 profile

IV. Numerical validation

Measurement of Cn² profile

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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

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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)

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Propagation + subaperture averaging

θ

m

h

rm θh – rm

Correlations of data (intensities & slopes):

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Propagation + subaperture averaging

dmn

θ

m n

h

Correlations of data (intensities & slopes):

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Propagation + subaperture averaging

dmn

θ

m n

h

θh

Correlations of data (intensities & slopes):

Altitude of maximum sensitivity

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Propagation + moyenne sur la sous-pupille

dmn

θ

m n

h

θh

Correlations of data (intensities & slopes):

unknown WeightingMeasurement

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Correlations of Shack-Hartmann data

Slopes

Coupling

Intensities

SLODAR

SCIDAR, MASS Shack-Hartmann ++ !!

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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:

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I. Motivation and techniques

II. Shack-Hartmann data

III. Exploitation to measure Cn2 profile

IV. Numerical validation

Measurement of Cn² profile

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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

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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

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I. Motivation and techniques

II. Shack-Hartmann data

III. Exploitation to measure Cn2 profile

IV. Numerical validation

Measurement of Cn² profile

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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

+

+

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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 Cn

2 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

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?