1. 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 Nice Cedex 2, France
A. Tokovinin
Sternberg Astronomical Institute, Universitestsky prosp., 13,
Moscow, Russia

2. The 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 : q0
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

3. 03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

4. GSM at Paranal 27 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 q0 : 1.9 as.
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

5. Co-phasing & outer scale Theory
Standard deviation of the Optical Path Difference (OPD) : where is the structure function and is the spectrum of the phase fluctuations (Von Karman).
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

6. Co-phasing & outer scale Theory
Solutions to the structure function
without aperture filtering :
with aperture filtering : 1. 2. 3.
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

7. Co-phasing & outer scale Theory
Structure function of the phase fluctuations
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

8. Co-phasing & outer scale Theory
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

9. Co-phasing & outer scale Application 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

10. OPD residual after correction by a fringe tracker
Structure function of the residual phase (residual piston) : with :
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

11. OPD residual after correction by a fringe tracker
with
and
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

12. 03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

13. Summary
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.
03/29/2000
SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000