Outer Scale DefinitionModel dependant Equivalent (Tatarski)

Infinite φ (κ) α (κ 2 ) −11/6

Von Karman φ (κ) α (κ 2 + (2 π/ L0) 2 ) −11/6

Dθ(LT) = Cθ2 Lθ

2/3 = ∆θ 2

Cθ2 = a2 Lθ

4/3 (grad θ)2

Saturation ∆θ 2

J. Vernin

Von Karman Outer Scale

Equivalent Outer ScaleO.17 m

1.0 m

Ratio = 5.8

dKKKKr

KrrD )(²)

)sin(1()(

0

θθΦ−= ∫

∞

J. Vernin

Abahamid,Jabiri,Vernin et al.(2003),A&A, in press

Avila,Ziad et al.(1997) JOSA,14,3070

Outer Scale Scatter

J. Vernin

Atmospheric Parameters Relevant to AO

To characterize r0 , θFCAO , θPCAO , τAO , d0 one needs to knowvertical profiles of optical turbulence CN

2(h) and windV(h)with 0 < h < 20-30 km

Operational Profilers Prototype Profilers Generalized Scidar

Instrumented balloonsSingle Star Scidar's

Slodar

Other combinations

MASS + DIMM + V(h) from meteo model

J. Vernin

Single Star Scidar basic equation

Pupil plane Virtual plane

Autocorrelation for a layer at altitude i

Gaussian convolution due to wind variations

Impulse response of the receiver

Displacement due to wind speed

)(*)(*),(*),(),(1

τδτστ→→→→→

=

→−= ∑ ivi

N

i i vrrSrGhrCrCi

),( ii hrC→

),( τσivrG

→

)(→rS

)( τδ→→

− ivr

J. Vernin

Single Star Scidar results

J. Vernin

Single Star Scidar vsGeneralized Scidar

Habib, Vernin, Benkhaldoun, Submitted to CRAS Paris

Seeing** (21h09)=0.55”Seeing** (22h54)=0.97”

Seeing* (21h20)=0.85”

* * Scidar * Scidar

J. Vernin

Phase Structure Function at various baselinesCoulman, Vernin, 1991, Appl. Opt.,30,118

Log[ΦN(K)]

K-5/3

Log(K)

III

II

I

I Inertial Isotropic

II

Anisotropic 2D turb.

Spectral Gap

III

Log(ρ)

ρ 2/3

I

II

III

Log D N (ρ) Log D S (ρ)

Log(ρ)

1m 1km 1000km

I

II

III

VI

ρ 2/3

ρ 2/3

ρ 5/3

ρ 5/3

VI Thick atmosphereB > H

Thin atmosphereB < H

J. Vernin

Instruments

NO T H

IN

G

PR

I

O

F

L

E

STurbulent layers

GS MASSGSM DIMM Mast Radio receiver

Balloon

SlodarSSS

Models

Kite

Which model for atmospheric turbulence?

• Verification of the atmosphericturbulence model

• Measurement of atmosphericparameters with the GI2TInterferometer GSM Instrument

Jérome Maire LUAN

Verification of the atmospheric turbulence model

(F. Roddier, progress in Optics1981)

AA longitudinal covariancesmeasured with the GSM for

differents baselines

Phase structure functionreconstructed from GSM data

with σOPD=10λ

Kol

mog

orov

Greenwood-Tarazano

Von Karman

Modèle reconstitué

L0=25m r0=6.4cm

Optical Path Difference in an interferometer

)(2

)()(2

)(2

OPD bDbrrb ϕπλϕϕ

πλσ =+−= &&

[ ] dfDf

DfJfbJffWbD

2

10

)(2)2(1)(4)(

−= ∫ π

πππ ϕϕ

6/11

20

23/50

10229.0)(

−

−

+=

LfrfWϕ

• for the Von Karman model:

R. Conan Thèse de l’Université de Nice Sophia Antipolis (2000)

Estimation of the OPD & turbulence parameters withthe GI2T interferometer

GSM-GI2T observations and first results (06 June 2003)

Comparison r0 GSM et GI2T Comparaison L0 GSM et GI2T

Estimation of the turbulence parameters