Instrumentation Concepts Ground-based Optical Telescopes

1. IAG/USP (Keith Taylor)‏ Instrumentation ConceptsGround-based Optical Telescopes Keith Taylor (IAG/USP) Aug-Nov, 2008

2. Atmospheric Turbulence (appreciative thanks to USCS/CfAO) Adaptive Optics IAG/USP (Keith Taylor)‏

3. Atmospheric Turbulence: Main Points • The dominant locations for index of refraction fluctuations that affect astronomers are the atmospheric boundary layer and the tropopause • Atmospheric turbulence (mostly) obeys Kolmogorov statistics • Kolmogorov turbulence is derived from dimensional analysis (heat flux in = heat flux in turbulence)‏ • Structure functions derived from Kolmogorov turbulence are  r2/3 • All else will follow from these points!

4. IAG/USP (Keith Taylor)‏ Kolmogorov Turbulence • Atmospheric refractive index inhomogeneities warp the wave front incident on the telescope pupil. • These inhomogeneities appear to be associated with atmospheric turbulence • Thermal gradients • Humidity fluctuations • Wind shear and associated hydrodynamic instabilities • Image quality is directly related to the statistics of the perturbations of the incoming wave front • The theory of seeing combines • Theory of atmospheric turbulence • Optical physics • Predict the modifications to the image caused by refractive index gradients.

5. IAG/USP (Keith Taylor)‏ Modeling the atmosphere • Random fluctuations in the motion of the atmosphere occur predominantly due to: • Drag encountered by the air flow at the Earth's surface and resultant wind shear • Differential heating of different portions of the Earth's surface and the resultant thermal convection • Phase changes involving release of heat (condensation/crystallization) and subsequent changes in temperature and velocity fields • Convergence and interaction of air masses with various atmospheric fronts; • Obstruction of air flows by mountain barriers that generate wavelike disturbances and vortex motions on their leeside. • The atmosphere is difficult to study due to the high Reynolds number (Re ~ 106 ), a dimensionless quantity, that characterizes the ratio of inertial to viscous forces.

6. IAG/USP (Keith Taylor)‏ Cloud formations Indicative of atmospheric turbulence profiles

7. Atmospheric Turbulence: Outline • What determines the index of refraction in air? • Origins of turbulence in Earth’s atmosphere • Kolmogorov turbulence models

8. IAG/USP (Keith Taylor)‏ The AtmosphereKolmogorov model of turbulence • Kinetic energy in large scale turbulence cascades to smaller scales • Inertial interval • Inner scale l0 ­ 2mm. Outer scale L0­10 to 100 m • Turbulence distributed within discrete layers • The strength of these layers is described by a refractive index structure function: • Strength of turbulence can be described by a single parameter, r0 , Fried’s parameter • Fried parameter is the diameter of a circular aperture over which the wavefront phase variance equals 1 rad2 J. Vernin, Universite de Nice. Cerro Pachon for Gemini IGPO

9. IAG/USP (Keith Taylor)‏ Cn2 profiles Median seeing conditions on Mauna Kea are taken to be ro ~ 0.23 meters at 0.55 microns. The 10% best seeing conditions are taken to be ro ~ 0.40 meters. A set of SCIDAR data taken by Francois Roddier et al. (1990 SPIE Vol 1236 485) on Mauna Kea.

10.  DT  5/3 r0 Wavefront variance radians2 2 = 1.0039 • This gives the phase variance over a telescope of diameter DT • A phase variance of less than ~ 0.2 gives diffraction limited performance • There are 3 regimes • DT < r0 Diffraction dominates • DT ~ r0 - 4r0 Wavefront tilt (image motion) dominates • DT >> r0 Speckle (multiple tilts across the telescope aperture) dominates 4m telescope: D/ r0(500nm)=20 D/ r0(2.2 m)=3.5 IAG/USP (Keith Taylor)‏

11. IAG/USP (Keith Taylor)‏ Strehl ratio Corrected0.20” FWHM Uncorrected0.49” FWHM • There are two components of the PSF for 2 < 2 radians2 • So ‘width’ of the image is not a useful parameter, use height of PSF: • Strehl ratio: • For small 2 : R ~ exp (-2) MARTINIWHT, K-band

12. Isoplanatic angle, temporal variation • Angle over which wavefront distortions are essentially the same: • It is possible to perform a similar turbulence weighted integral of transverse wind speed in order to derive an effective wind speed and approximate timescale of seeing • τ0 is the characteristic timescale of turbulence • Note the importance of Cn2(h) in both cases IAG/USP (Keith Taylor)‏

13. IAG/USP (Keith Taylor)‏ Atmospheric Seeing - Summary Dependence on Wavelength

14. tropopause 10-12 km wind flow around dome boundary layer ~ 1 km Turbulence arises in several places stratosphere Heat sources w/in dome

15. Remedies: Cool mirror itself, or blow air over it. Within dome: “mirror seeing” • When a mirror is warmer than dome air, convective equilibrium is reached. credit: M. Sarazin credit: M. Sarazin convective cells are bad To control mirror temperature: dome air conditioning (day), blow air on back (night), send electric current through front Al surface-layer to equalize temperature between front and back of mirror

16. IAG/USP (Keith Taylor)‏ Dome seeing(TMT CFD calculations) Wind direction Wind velocities

17. Local “Seeing” -Flow pattern around a telescope dome Cartoon (M. Sarazin): wind is from left, strongest turbulence on right side of dome Computational fluid dynamics simulation (D. de Young) reproduces features of cartoon

18. Top View -Flow pattern around a telescope dome Computational fluid dynamics simulation (D. de Young)

19. Thermal Emission Analysis: mid-IR A good way to find heat sources that can cause turbulence VLT UT3, Chile • 19 Feb. 1999 • 0h34 Local Time • Wind summit: 4m/s • Air Temp summit: 13.8C • Here ground is warm, top of dome is cold. Is this a setup for convection inside the dome?

20. Boundary layers: day and night • Wind speed must be zero at ground, must equal vwind several hundred meters up (in the “free” atmosphere)‏ • Boundary layer is where the adjustment takes place • Where atmosphere feels strong influence of surface • Quite different between day and night • Daytime: boundary layer is thick (up to a km), dominated by convective plumes rising from hot ground. Quite turbulent. • Night-time: boundary layer collapses to a few hundred meters, is stably stratified. Perturbed if winds are high.

21. Boundary layer is much thinner at night Surface layer: where viscosity is largest effect Credits: Stull (1988) and Haggagy (2003)‏

22. Convection takes place when temperature gradient is steep • Daytime: ground is warm, air is cooler • If temperature gradient between ground and ~ 1 km is steeper than the “adiabatic gradient,” a warm volume of air that is raised upwards will find itself still with cooler surroundings, so it will keep rising • These warm volumes of air carry thermal energy upwards: convective heat transport

23. Boundary layer profiles fromacoustic sounders Turbulence profile Vertical wind profile

24. Boundary layer has strongest effect on astronomical seeing • Daytime: Solar astronomers have to work with thick and messy turbulent boundary layer • Big Bear Observatory • Night-time: Less total turbulence, but still the single largest contribution to “seeing” • Neutral times: near dawn and dusk • Smallest temperature difference between ground and air, so wind shear causes smaller temperature fluctuations

25. IAG/USP (Keith Taylor)‏ Big Bear Solar Observatory

26. Wind shear mixes layers with different temperatures • Wind shear  Kelvin Helmholtz instability • If two regions have different temperatures, temperature fluctuations T will result Computer simulation

27. Real Kelvin-Helmholtz instability measured by FM-CW radar • Colors show intensity of radar return signal. • Radio waves are backscattered by the turbulence.

28. Temperature profile in atmosphere Temperature gradient at low altitudes  wind shear will produce index of refraction fluctuations

29. Turbulence strength vs. time of day Theory for different heights: Theory vs. data Balance heat fluxes in surface layer. Credit: Wesely and Alcaraz, JGR (1973)‏ Day Night Day Night Night Day Night

30. Leonardo da Vinci’s view of turbulence

31. IAG/USP (Keith Taylor)‏ Reynolds number • When the average velocity (va) of a viscous fluid of characteristic size (l) is gradually increased, two distinct states of fluid motion are observed:  • Laminar (regular and smooth in space and time) at very low va • Unstable and random at va greater than some critical value.

32. Reynolds number • Re = Reynolds number = v L /  • Here L is a typical length scale, v is a typical velocity,  is the viscosity • Re ~ inertial stresses / viscous stresses 0 - 1 Creeping flow 1 - 100 Laminar flow, strong Re dependence 100 - 1,000 Boundary layer 1,000 - 10,000 Transition to slightly turbulent 104 - 106 Turbulent, moderate Re dependence > 106 Strong turbulence, small Re dependence

33. IAG/USP (Keith Taylor)‏ Effects of variations in Re • When Re exceeds critical value a transition of the flow from laminar to turbulent or chaotic occurs. • Between these two extremes, the flow passes through a series of unstable states. • High Re turbulence is chaotic in both space and time and exhibits considerable spatial structure

34. IAG/USP (Keith Taylor)‏ Velocity fluctuations • The velocity fluctuations occur on a wide range of space and time scales formed in a turbulent cascade. • Kolmogorov turbulence model states that energy enters the flow at low frequencies at scale length L0. • The size of large-scale fluctuations, referred to as large eddies, can be characterized by their outer scale length  L0. (spatial frequency  kL0= 2/L0) • These eddies are not universal with respect to flow geometry; they vary according to the local conditions. • A mean value  L0 = 24m from the data obtained at Cerro Paranal, Chile (Conan et al. 2000).

35. IAG/USP (Keith Taylor)‏ Energy transportto smaller scales • The energy is transported to smaller and smaller loss-less eddies until • At  Re ~ 1 the KE of the flow is converted into heat by viscous dissipation • The small-scale fluctuations with sizes l0 < r < L0 is the inertial subrange have scale-invariant behavior, independent of the flow geometry. • Energy is transported from large eddies to small eddies without piling up at any scale.

36. solar Outer scale L0 Inner scalel0 h Wind shear convection h Kolmogorov turbulence, cartoon ground

37. Kolmogorov turbulence, in words • Assume energy is added to system at largest scales - “outer scale” L0 • Then energy cascades from larger to smaller scales (turbulent eddies “break down” into smaller and smaller structures). • Size scales where this takes place: “Inertial range”. • Finally, eddy size becomes so small that it is subject to dissipation from viscosity. “Inner scale” l0 • L0 ranges from 10’s to 100’s of meters; l0 is a few mm

38. Breakup of Kelvin-Helmholtz vortex • Computer simulation • Start with large coherent vortex structure, as is formed in K-H instability • Watch it develop smaller and smaller substructure • Analogous to Kolmogorov cascade from large eddies to small ones • From small k to large k

39. How large is the Outer Scale? • Dedicated instrument, the Generalized Seeing Monitor (GSM), built by Dept. of Astrophysics, Nice Univ.)‏

40. Outer Scale ~ 15 - 30 m, from Generalized Seeing Monitor measurements • F. Martin et al. , Astron. Astrophys. Supp. v.144, p.39, June 2000 • http://www-astro.unice.fr/GSM/Missions.html

41. Lab experiments agree • Air jet, 10 cm diameter (Champagne, 1978)‏ • Assumptions: turbulence is homogeneous, isotropic, stationary in time Credit: Gary Chanan, UCI Slope -5/3 Power (arbitrary units)‏ Slope = -5/3 l0 L0  (cm-1)‏

42. Questionable at best Assumptions of Kolmogorov turbulence theory • Medium is incompressible • External energy is input on largest scales (only), dissipated on smallest scales (only)‏ • Smooth cascade • Valid only in inertial range L0 • Turbulence is • Homogeneous • Isotropic • In practice, Kolmogorov model works surprisingly well!

43. 10-14 Typical values of CN2 • Index of refraction structure function DN ( r ) = < [ N (x ) - N ( x + r ) ]2 > = CN2 r 2/3 • Night-time boundary layer: CN2 ~ 10-13 - 10-15 m-2/3 Paranal, Chile, VLT

44. Turbulence profiles from SCIDAR Eight minute time period (C. Dainty, Imperial College)‏ Starfire Optical Range, Albuquerque NM Siding Spring, Australia

45. Atmospheric Turbulence:Main Points • The dominant locations for index of refraction fluctuations that affect astronomers are the atmospheric boundary layer and the tropopause • Atmospheric turbulence (mostly) obeys Kolmogorov statistics • Kolmogorov turbulence is derived from dimensional analysis (heat flux in = heat flux in turbulence)‏ • Structure functions derived from Kolmogorov turbulence are  r2/3 • All else will follow from these points!

46. IAG/USP (Keith Taylor)‏ Wavefronts • Zernike polynomials are normally used to describe the actual shape of an incoming wavefront • Any wavefront can be described as a superposition of zernike polynomials

47. Atmospheric Wavefront Variance after Removal of Zernike Polynomials IAG/USP (Keith Taylor)‏

48. Gary Chanan, UCI Piston Tip-tilt

49. Astigmatism (3rd order)‏ Defocus

50. Trefoil Coma