ao - ForOT Optical Turbulence Forecasts

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CO-PHASED AND COHERENT INTERFEROMETERS Fringe spacing varies with Wavelength ⇒ Colored Fringes Coherence Length = OPD range With high fringe contrast Scan of Delay Line ( = OPD variation) ⇒ Zero <strong>Optical</strong> Path Difference ⇒ “White Light Fringe” (WLF) In the “CO-PHASED MODE” the OPDs in the interferometer arms have to be very close to zero (within fraction of a wavelength) This requires using the WLF on an unresolved star within the Field-Of-View of the interferometer for homothetic interferometers or a differential Delay Line on a nearby star (at VLTI this is done with PRIMA). Fringes are tracked on that star. Because the WLF is used a broad wavelength range can be used (wide color bands) In the “COHERENT MODE” the OPDs in the interferometer have to be within the coherence length (CL). CL = λ * (λ/∆λ) = λ 2 /∆λ. This requires narrow color bands. Fringes have good contrast but cannot be tracked. They may be hidden in photon noise. If at least 3 interferometer arms are used one can use the “Triple Correlation Technique” for the combined image analysis. Average Triple Correlations ⇒“Closure Phases”⇒ Images (as in Radio Interferometers)
TRIPLE CORRELATION/BISPECTRUM ANALYSIS AND CLOSURE PHASE IMAGING ‣ How to derive phase (and amplitude) information in “Coherent” interferometry ‣ No fringe tracking ⇒ fringe positions change rapidly (< second scale) because of atmospheric seeing and instrumental effects. ‣ The same problem was encountered in radio astronomy in radio interferometry many years ago and solved with “CLOSURE PHASE” techniques (R. Jennison, 1958) ‣ It requires the use of at least 3 Interferometer arms ( with 3 telescopes) • Intensity in Short Exposure Combined Image ≡ I(x,x’) (x values are vectors) • Triple Correlation TC( x,x’) ≡ ∫ I(x”) I(x”+x) I(x”+x’) dx” • TC(x,x’) shows 3 correlation peaks at 3 spatial frequencies with observed phases φ, φ’ and φ” each one consisting of the true phase Φ and an atmospheric error ε • So: φ = Φ+ε ; φ’ = Φ+ε’ and φ” = Φ”+ε” where ε” = ε+ε’ • ⇒ Φ + Φ’ -Φ” = φ + φ’ -φ” • Two of the phases e.g. Φ and Φ’ are related to the position of the object. They can be taken as a given like (0,0) ⇒ Φ” (“closure phase”) over distance x” . • There have to be enough photons to allow the determination of φ, φ’ and φ” in the amount of time during which the ε values change by a fraction of 2π . NOTE: COHERENT IMAGING USING CLOSURE PHASES HAS YET NOT BEEN USED
Page 1 and 2: TURBULENCE IN HIGH ANGULAR RESOLUTI
Page 3 and 4: DETRIMENTAL EFFECTS BY THE ATMOSPHE
Page 5 and 6: SO: WHY BOTHER WITH GROUND-BASED TE
Page 7 and 8: HEIGHT VARIATION OF REFRACTIVE INDE
Page 9 and 10: Height (meters) WINTER SUMMER SEEI
Page 11 and 12: “Fried Parameter” r 0 definitio
Page 13 and 14: REMOVING SEEING EFFECTS IN TELESCOP
Page 15 and 16: SOME EXAMPLES OF IMAGES RESTORED BY
Page 17 and 18: INCREASING THE CORRECTED AREA ON TH
Page 19 and 20: SOLAR S-H WAVEFRONT SENSOR FOR ATMO
Page 21 and 22: NAME Balloons SCIDAR G-SCIDAR S-S S
Page 23 and 24: THE MANY FLAVORS OF ADAPTIVE OPTICS
Page 25: MANAGING SEEING EFFECTS IN INTERFER
Page 29: THANK YOU!

ao - ForOT Optical Turbulence Forecasts

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