measurements of the wave-front outer scale at paranal
DESCRIPTION
Measurements of the wave-front outer scale at Paranal. Influence of this parameter in interferometry. R. Conan, A. Ziad, J. Borgnino and F. Martin UMR 6525 Astrophysique, Université de Nice-Sophia Antipolis, F-06108 Nice Cedex 2, France A. Tokovinin - PowerPoint PPT PresentationTRANSCRIPT
Measurements of the wave-front outer scale at Paranal
Measurements of the wave-front outer scale at Paranal
Influence of this parameter in interferometry
R. Conan, A. Ziad, J. Borgnino and F. MartinUMR 6525 Astrophysique, Université de Nice-Sophia Antipolis,F-06108 Nice Cedex 2, France
A. TokovininSternberg Astronomical Institute, Universitestsky prosp., 13,119899 Moscow, Russia
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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The Generalized Seeing MonitorThe Generalized Seeing Monitor
• Four telescopes (Ø=10cm, L-shape layout)
• Simultaneous measurement of one component of the angle of arrival
• Real-time computation of :– the Fried’s parameter : r0
– the spatial coherence outer scale : L0
– the isoplanatic patch : 0
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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GSM at Paranal27 Nov./20 Dec. 1998
GSM at Paranal27 Nov./20 Dec. 1998
• GSM has worked during 19 clear nights
• 1884 measurements of each parameter : – median seeing : 0.9
as,
– median L0 : 22 m,
– median 0 : 1.9 as.
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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Co-phasing & outer scaleTheory
Co-phasing & outer scaleTheory
• Standard deviation of the Optical Path Difference (OPD) : where
is the structure function and
is the spectrum of the phase fluctuations (Von Karman).
)(2
BDOPD
dfDf
DfJBfJfWfBD
2
100
)(2)2(1)(4)(
6/112
0
23/50
10229.0)(
L
frfW
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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Co-phasing & outer scaleTheory
Co-phasing & outer scaleTheory
• Solutions to the structure function– without aperture filtering :
– with aperture filtering :– 1.
– 2.
– 3.
06/5
0
3/5
0
0 22117.0)(
L
BK
L
B
r
LBD
3/1
0
3/5
0
0 49.1188.6)(L
B
r
BBD
LBD
3/5
0
00 17.0)(
r
LBDB
LD
3/11
0
3/5
0
0 06.0)(
L
D
r
DBDBD
L
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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Co-phasing & outer scaleTheory
Co-phasing & outer scaleTheory
• Structure function of the phase fluctuations
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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Co-phasing & outer scaleTheory
Co-phasing & outer scaleTheory
• Isolines of the OPD in units of wavelength as a function of B and L0
• D = 10m and r0 = 10cm
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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Co-phasing & outer scaleApplication to VLTI
Co-phasing & outer scaleApplication to VLTI
• OPD in units of the wavelength
• Diameter : 8.2m• Baselines : 40,
100 and 200 m
• r0 and L0 measured by the GSM
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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OPD residual after correctionby a fringe tracker
OPD residual after correctionby a fringe tracker
• Structure function of the residual phase (residual piston) :
with :
2
),(),()( trtBrBDr
),(),( trtBr TT
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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OPD residual after correctionby a fringe tracker
OPD residual after correctionby a fringe tracker
),,(2)()()( TBCBDBDBDTr
)()(1
)( VtDVtBDT
tdt
TBD
T
)()(1
),,( VtDVtBDT
tdt
TTBC
with
and
• OPD residual = )arg()arg(,,,,,,, 00 BVVBDLrTF
03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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03/29/2000 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000
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SummarySummary
• Longest set of continuous nights of outer scale measurements at Paranal (median L0 : 22 m)
• Derivation of mathematical formulas for OPD with and without the filtering effect of a finite size aperture
• OPD values expected at Paranal (D=8.2m, B=40, 100 and 200m) are 10 times lower than for a model with an infinite L0. The OPD is independent of baseline values.