ONE-DIMENSIONAL RANDOM WALKS Definition 1. A random walk ...
Outer Scale Definition - ESO · Outer Scale Definition Model dependant Equivalent (Tatarski) ......
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Outer Scale Definition Model dependant Equivalent (Tatarski) Infinite φ (κ29 α (κ 2 29 -11/6 Von Karman φ (κ) α (κ 2 + (2 π/ L 0 29 2 29 -11/6 D θ (L T ) = C θ 2 L θ 2/3 = ∆θ 2 C θ 2 = a 2 L θ 4/3 (grad θ) 2 Saturation ∆θ 2 J. Vernin Von Karman Outer Scale Equivalent Outer Scale O.17 m 1.0 m Ratio = 5.8 dK K K Kr Kr r D ) ( ² ) ) sin( 1 ( ) ( 0 θ θ Φ - = ∫ ∞
Transcript of Outer Scale Definition - ESO · Outer Scale Definition Model dependant Equivalent (Tatarski) ......
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
