May 2001 Venice Workshop 1

The Statistics of Isoplanatic Angle The Statistics of Isoplanatic Angle and Adaptive Optics Time Constant and Adaptive Optics Time Constant

derived from DIMM dataderived from DIMM data

Marc Sarazin (1) and Andrei Tokovinine (2)

(1) European Southern Observatory(2) Cerro Tololo Inter-American Observatory

May 2001 Venice Workshop 2

List of List of ThemesThemes

How to find the ideal site...and keep it good?How to find the ideal site...and keep it good?

• Optical Propagation through Turbulence– Mechanical and Thermal– Index of Refraction– Signature on ground based observations– Correction methods

• Integral Monitoring Techniques– Seeing Monitoring– Scintillation Monitoring

• Profiling Techniques– Microthermal Sensors– Scintillation Ranging

• Modelling Techniques

May 2001 Venice Workshop 3

Automated DIMM OperationAutomated DIMM Operation

35cm Telescope for the 35cm Telescope for the automated DIMM at the automated DIMM at the

VLT ObservatoryVLT Observatory• Pixel size=0.7”Pixel size=0.7”• Pupil Diameter=11cm Pupil Diameter=11cm • Pupil Separation=20cm Pupil Separation=20cm • Exposure Time=5msExposure Time=5ms• 600 frames/mn600 frames/mn

May 2001 Venice Workshop 4

Fried parameter: ( meter, ^6/5)

Seeing: (arcsec, ^-0.2) 0

98.0)(r

FWHM

53

0

22

0 )()sec(2

423.0)(

dhhCr n

Optical PropagationOptical Propagation

The Signature of Atmospheric TurbulenceThe Signature of Atmospheric Turbulence

May 2001 Venice Workshop 5

53

0

22

0 )()()sec(2

91.2)( 35

dhhChv n

53

0

22

0 )()sec(2

91.2)( 35

dhhCh n

Correlation time:

Isoplanatic angle:

High Resolution ImagingHigh Resolution Imaging

May 2001 Venice Workshop 6

Statistics of Tau0Statistics of Tau0

Comparison of

wavefront velocity V0 and 200mb

wind speed during Paranal and Gemini balloon campaigns

V0 = 0.4 V200mb

May 2001 Venice Workshop 7

Statistics of Tau0Statistics of Tau0

Estimate of the coherence time

from 200mb wind velocity during Paranal and Gemini

balloon campaigns

V0fit= Max(Vground, 0.4 V200mb )

Tau0fit=0.31 r0/ V0fit

May 2001 Venice Workshop 8

Statistics of Tau0Statistics of Tau0

The error on the estimate

of the coherence time from 200mb wind velocity

increases when low level turbulence dominates (Paranal and Gemini balloon campaigns)

Hbar =0.314 r0 / Theta0

Venice Workshop 9

Statistics of Tau0 Statistics of Tau0

Geographical Location and 200mb wind velocity16 years statistics ( line:0, dash:180, tr:La Silla, dia:Paranal, sq:Mauna Kea)

May 2001 Venice Workshop 10

Statistics of tau0 Statistics of tau0

16-year average 200mb wind velocity at known observatories

(Latitude and Longitude +/- 2.5 degree)

Observatory June December mean Jun+DecChirripo (Costa Rica) 17.8 10.3 14.1 Mauna Kea 19.5 24.7 22.1Gamsberg (Nam) 32.0 20.0 26.0Paranal 34.5 22.2 28.4La Silla 36.0 27.6 31.8La Palma 24.0 42.6 33.3Maidanak (Uz) 27.1 49.6 36.4San Pedro Martir 23.0 63.3 43.2

May 2001 Venice Workshop 11

0

22

35

0 )(2

91.2 35

dhhCh n

Isoplanatic angle at zenith:

Measuring teta0 with a DIMMMeasuring teta0 with a DIMM

Scintillation index at zenith:

0

2 )()( dhhChWs n

May 2001 Venice Workshop 12

58530 cos s

Measuring teta0 with a DIMMMeasuring teta0 with a DIMM

Choose an aperture such as: 35)( hhW

and

May 2001 Venice Workshop 13

Statistics of Theta0Statistics of Theta0

Chromatic effects

Comparison of scintillation index and isoplanatic angle for Paranal

Cn2 profiles at various wavelengths

(0,4, 0.5, 0.7, and 0.9 micron, top to bottom)

The dispersion from the linear relation is about 5%. The chromatic error at 0.5 micron is

[+2%,-5%] from 0.4 to 0.9 micron.

May 2001 Venice Workshop 14

Statistics of Theta0Statistics of Theta0

Time Averaging Effects

True bias from 200mb wind speed for Paranal Cn2 profiles compared

to bias calculated from a single-layer model

The best agreement is obtained using half the wind velocity at 200mb. The mean correction due to time averaging was 12% in 2000 with

the 5ms Paranal DIMM

May 2001 Venice Workshop 15

Statistics of Tau0 and Theta0Statistics of Tau0 and Theta0

Statistical Distribution of the seeing at Paranal in

2000

mean r0=11.6cm

for photometric sky observations at 0.5 micron and at zenith, averaged

over 10mn

May 2001 Venice Workshop 16

Statistics of Tau0 Statistics of Tau0

Statistical Distribution of

the coherence time at Paranal in 2000

mean tau0=3.9ms

for photometric sky observations at 0.5 micron and at zenith, averaged

over 10mn

May 2001 Venice Workshop 17

Statistics of Theta0Statistics of Theta0

Statistical Distribution of the isoplanatic angle at

Paranal in 2000

mean Theta0=2.6”

for photometric sky observations at 0.5 micron and at zenith, averaged

over 10mn

May 2001 Venice Workshop 18

Statistics of Tau0 and Teta0Statistics of Tau0 and Teta0

Statistical Distribution of the isoplanatic angle at Paranal in 2000 for high and low wind speed at

the tropopause

The mean Theta0 increases by 10% for each 10m/s

speed decrease

The mean Tau0 is 30% larger for the best 50%

values of Theta0

May 2001 Venice Workshop 19

Statistics of tau0 and theta0Statistics of tau0 and theta0

Paranal 2000

measurements at zenith, 0.5 micron, 10mn average

Parameter best 5% best 20% 50% meanSeeing, arcsec 0.43 0.56 0.75 0.86200mb wind, m/s 12 19 29 32 Tau0, ms 8.5 5.8 3.6 3.9Theta0, arcsec 4.1 3.3 2.6 2.6