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Instrumentation Concepts Ground-based Optical Telescopes. Keith Taylor (IAG/USP) Aug-Nov, 2008. Atmospheric Turbulence (appreciative thanks to USCS/CfAO). Adaptive Optics. Atmospheric Turbulence: Main Points. - PowerPoint PPT Presentation
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Aug-Nov, 2008 IAG/USP (Keith Taylor)
Instrumentation Concepts
Ground-based Optical Telescopes
Keith Taylor(IAG/USP)
Aug-Nov, 2008
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Adaptive OpticsAdaptive Optics
Atmospheric Turbulence
(appreciative thanks to USCS/CfAO)
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!
Aug-Nov, 2008 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.
Aug-Nov, 2008 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.
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Cloud formations
Indicative of atmospheric turbulence
profiles
Atmospheric Turbulence: Outline
What determines the index of refraction in air?
Origins of turbulence in Earth’s atmosphere
Kolmogorov turbulence models
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Kinetic energy in large scale turbulence cascades to smaller scales Inertial interval
Inner scale l0 2mm. Outer scale L0 10 to 100 m Turbulence distributed within discrete layers The strength of these layers is described by a refractive index
structure function:
The AtmosphereKolmogorov model of
turbulence
J. Vernin, Universite de Nice. Cerro Pachon for Gemini IGPO
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
Aug-Nov, 2008 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.
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Wavefront variance
radians2
• 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)=20D/ r0(2.2 m)=3.5
2 = 1.0039 DT
r0
5/3
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Strehl ratio
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)
R = Peak intensity in a (un)corrected image
Peak intensity in a diffraction limited image
MARTINIWHT, K-band
Uncorrected0.49” FWHM
Corrected0.20” FWHM
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Isoplanatic angle, temporal variation
• Angle over which wavefront distortions are essentially the same:
83
32 5
2 5 / 30
22.91 sec ( )nC h h dh
• 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
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Atmospheric Seeing - Summary
Dependence on Wavelength
56
0 r 56
0 56
0 =0.55m =1.6m =2.2m
r0 10cm 36 53
0 10ms 36ms 53ms
0 5’’ 18’’ 27’’
Turbulence arises in several places
stratosphere
Heat sources w/in dome
boundary layer
~ 1 km
tropopause
10-12 km
wind flow around dome
Within dome: “mirror seeing”
When a mirror is warmer than dome air, convective equilibrium is reached.
Remedies: Cool mirror itself, or blow air over it.
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
credit: M. Sarazin credit: M. Sarazin
convective cells are bad
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Dome seeing(TMT CFD calculations)
Wind velocities
Wind direction
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
Top View -Flow pattern around a
telescope dome
Computational fluid dynamics simulation (D. de Young)
Thermal Emission Analysis: mid-IR
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?
*>15.0¡C
*<1.8¡C
2.0
4.0
6.0
8.0
10.0
12.0
14.0
A good way to find heat sources that can cause turbulence
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.
Boundary layer is much thinner at night
Credits: Stull (1988) and Haggagy (2003)
Surface layer: where viscosity is largest
effect
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
Boundary layer profiles fromacoustic sounders
Turbulence profile
Vertical wind profile
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
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Big Bear Solar
Observatory
QuickTimeª and aYUV420 codec decompressor
are needed to see this picture.
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
Real Kelvin-Helmholtz instability measured by
FM-CW radar
Colors show intensity of radar return signal. Radio waves are backscattered by the turbulence.
Temperature profile in atmosphere
Temperature gradient at low altitudes wind shear will produce index of refraction fluctuations
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
Day
Night NightDayNight Night
Leonardo da Vinci’s view of turbulence
Aug-Nov, 2008 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.
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
Aug-Nov, 2008 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
Aug-Nov, 2008 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).
Aug-Nov, 2008 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.
Kolmogorov turbulence, cartoon
Outer scale L0
ground
Inner scale l0
hconvection
solar
h
Wind shear
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
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
How large is the Outer Scale?
Dedicated instrument, the Generalized Seeing Monitor (GSM), built by Dept. of Astrophysics, Nice Univ.)
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
(cm-1)
Slope = -5/3
Power (arbitrary
units)
Lab experiments agree Air jet, 10 cm diameter (Champagne, 1978) Assumptions: turbulence is homogeneous,
isotropic, stationary in time
Slope -5/3
l0 L0
Credit: Gary Chanan, UCI
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!
Questionable at best
Typical values of CN2
Index of refraction structure function
DN ( r ) = < [ N (x ) - N ( x + r ) ]2 > = CN
2 r 2/3
Night-time boundary layer: CN2 ~ 10-13 - 10-
15 m-2/3
10-14
Paranal, Chile, VLT
Turbulence profiles from SCIDAR
Eight minute time period (C. Dainty, Imperial College)
Siding Spring, Australia Starfire Optical Range, Albuquerque NM
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!
Aug-Nov, 2008 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
Aug-Nov, 2008 IAG/USP (Keith Taylor)
Atmospheric Wavefront Variance after Removal of Zernike Polynomials
j n m Zernike Polynomial Name Resid. Var. (rad2)
1 0 0 1 Constant 1.030 (D/r0)5/3
2 1 1 Tilt 0.582 (D/r0)5/3
3 1 1 Tilt 0.134 (D/r0)5/3
4 2 0 Defocus 0.111 (D/r0)5/3
5 2 2 Astigmatism 0.0880 (D/r0)5/3
6 2 2 Astigmatism 0.0648 (D/r0)5/3
7 3 1 Coma 0.0587 (D/r0)5/3
8 3 1 Coma 0.0525 (D/r0)5/3
9 3 3 0.0463 (D/r0)5/3
10 3 3 0.0401 (D/r0)5/3
23 2 1
2 cos
2 sin
28 3 2 sin
26 sin 2 26 cos2
28 3 2 cos 38 sin3 38 cos3
Piston
Tip-tilt
Gary Chanan, UCI
Astigmatism(3rd order)
Defocus
Trefoil
Coma
Spherical
“Ashtray”
Astigmatism(5th order)
Units: Radians of phase / (D / r0)5/6
Reference: Noll
Tip-tilt is single biggest contributor
Focus, astigmatism, coma also big
High-order terms go on and on….
What is Diffraction?
Slides based on those of James E. Harvey, Univ. of Central Florida, Fall ‘05
Details of diffraction from circular aperture1) Amplitude
2) Intensity
First zero at r = 1.22 / D
FWHM / D
Diffraction pattern from hexagonal Keck
telescope
Ghez: Keck laser guide star AO
Stars at Galactic Center
Considerations in the optical design of AO systems: pupil
relaysPupil Pupil Pupil
Deformable mirror and Shack-Hartmann lenslet array should be “optically conjugate to the telescope pupil.”“optically conjugate to the telescope pupil.”
What does this mean?mean?
Let’s define some terms
“Optically conjugate” = “image of....”
“Aperture stop” = the aperture that limits the bundle of rays accepted by the optical system
“Pupil” = image of aperture stop
optical axis
object space image space
symbol for aperture stopsymbol for aperture stop
So now we can translate: ““The deformable mirror should be optically conjugate to the The deformable mirror should be optically conjugate to the
telescope pupil”telescope pupil”
means
The surface of the deformable mirror is an image of the The surface of the deformable mirror is an image of the telescope pupiltelescope pupil
where
The pupil is an image of the aperture stop The pupil is an image of the aperture stop
In practice, the pupil is usually the primary mirror of the In practice, the pupil is usually the primary mirror of the telescopetelescope
Considerations in the optical design of AO
systems: “pupil relays”Pupil Pupil Pupil
‘PRIMARY MIRROR
Typical optical design of AO system
telescope primary mirror
Science camera
Pair of matched off-axis parabola mirrors
Wavefront sensor (plus
optics)Beamsplitter
Deformable mirror
collimated
More about off-axis parabolas
Circular cut-out of a parabola, off optical axis
Frequently used in matched pairs (each cancels out the off-axis aberrations of the other) to first collimate light and then refocus it
SORL
Aug-Nov, 2008 IAG/USP (Keith Taylor)
High order AO architecture
• Wavefront controller– Typically a deformable mirror (DM)– May not be optically conjugate to an
image of the primary
• Wavefront sensor (WFS)– Shack Hartmann (WFS) or Curvature
Sensor (CS)
• Beamsplitter– Dichroic, multi-dichroic, intensity, spatial
or combination
• Controller– Typically multi-processor or multi-DSP
• Interfaces– Can be complex and include removal of
non-common path errors to science instrumentation (hence an interface to science data path)
• Laser beacons