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Measurements of the wave-front outer scale at Paranal

Explore the influence of wave-front outer scale measurements in interferometry at Paranal. The study includes the Generalized Seeing Monitor (GSM) and co-phasing theories related to Optical Path Difference (OPD) and phase fluctuations. Discover the observation results and mathematical derivations for OPD values with and without aperture filtering at Paranal, shedding light on the significance of spatial coherence outer scale (L0) in astronomical observations.

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Measurements of the wave-front outer scale at Paranal

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  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-06108 Nice Cedex 2, France A. Tokovinin Sternberg Astronomical Institute, Universitestsky prosp., 13, 119899 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 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

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

  4. 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 q0 : 1.9 as. SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

  5. 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). SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

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

  7. Co-phasing & outer scaleTheory • Structure function of the phase fluctuations SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

  8. Co-phasing & outer scaleTheory • Isolines of the OPD in units of wavelength as a function of B and L0 • D = 10m and r0 = 10cm SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

  9. 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 SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

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

  11. OPD residual after correctionby a fringe tracker • OPD residual = with and SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

  12. 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 timeslower than for a model with an infinite L0. The OPD is independent of baseline values. SPIE's International Symposium - Astronomical Telescopes and Instrumentation 2000

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