instrumentation concepts ground-based optical telescopes

Aug-Nov, 2008 IAG/USP (Keith Taylor)

Instrumentation Concepts

Ground-based Optical Telescopes

Keith Taylor(IAG/USP)

Aug-Nov, 2008


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!


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.


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.


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


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


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.


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


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


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


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


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


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


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


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


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).


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!


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


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


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

instrumentation concepts ground-based optical telescopes

Documents

origins of turbulence

wavefront phase variance

refractive index gradients

atmospheric boundary

earths surface

resultant wind

interaction of air masses

wavefront variancethis