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Adaptive Optics in the VLT and ELT era
Laser Guide Stars
François Wildi
Observatoire de Genève
Outline of this short lecture
• Why are laser guide stars needed?
• Principles of laser scattering in the atmosphere
• What is the sodium layer? How does it behave?
• Physics of sodium atom excitation
• Lasers used in astronomical laser guide star AO
• Wavefront errors for laser guide star AO
Laser guide stars: Main points of this
lecture
• Laser guide stars are needed because there aren’t enough bright
natural guide stars in the sky
– Hence YOUR favorite galaxy probably won’t have a bright
enough natural guide star nearby
• Solution: make your own guide star
– Using lasers
– Nothing special about coherent light - could use a flashlight
hanging from a “giant high-altitude helicopter”
– Size on sky has to be  diffraction limit of a WFS sub-aperture
• Laser guide stars have PROS and CONS:
– Pluses: can put them anywhere, can be bright
– Minuses: NGS give better AO performance than LGS even when
both are working perfectly. High-powered lasers are tricky to
build and work with. Laser safety is added complication.
Two types of laser guide stars in use
today: “Rayleigh” and “Sodium”
• Sodium guide stars: excite
atoms in “sodium layer” at
altitude of ~ 95 km
~ 95 km
• Rayleigh guide stars:
Rayleigh scattering from air
molecules sends light back
into telescope, h ~ 10 km
8-12 km
• Higher altitude of sodium
layer is closer to sampling
the same turbulence that a
star from “infinity” passes
through
Turbulence
Telescope
Reasons why laser guide stars can’t do
as well as bright natural guide stars
1) Laser light is spread out by turbulence on the way up.
– Spot size is finite (0.5 - 2 arc sec)
– Can increase measurement error of wavefront sensor
» Harder to find centroid if spot is larger
2) For Rayleigh guide stars, some turbulence is above altitude where
light is scattered back to telescope. Hence it can’t be measured.
3) For both kinds of guide stars, light coming back to telescope is
spherical wave, but light from “real” stars is plane wave
– Implications: some of the turbulence around the edges of the
pupil isn’t sampled well
90 km
Cone effect
“Missing” Data
Scattering: 2 different physical processes
• Rayleigh Scattering (Rayleigh beacon)
– Elastic scattering from atoms or molecules in
atmosphere. Works for broadband light, no change
in frequency
• Resonance Scattering (Sodium Beacon)
– Line radiation is absorbed and emitted with no
change in frequency.
Rayleigh Scattering
• Due to interactions of the electromagnetic wave from
the laser beam with molecules in the atmosphere.
• The light’s electromagnetic fields induce dipole
moments in the molecules, which then emit radiation at
same frequency as the exciting radiation (elastic
scattering).
Dependence of Rayleigh scattering on
altitude where the scattering occurs
• Product of Rayleigh scattering cross section with
density of molecules is
 n
R
B mol
 3.6  10
31
P(z) 4.0117 -1 -1

m sr
T (z)
where P(z) is the pressure in millibars at altitude z,
and T(z) is temperature in degrees K at altitude z
• Because pressure P(z) falls off exponentially with
altitude, Rayleigh beacons are generally limited to
altitudes below 8 - 12 km
Rayleigh laser guide stars use timing of
laser pulses to detect light from Dz
• Use a pulsed laser, preferably at a
short wavelength (UV or blue or
green) to take advantage of -4
• Cut out scattering from altitudes
lower than z by taking advantage of
light travel time z/c
• Only open shutter of your wavefront
sensor when you know that a laser
pulse has come from the desired
scattering volume Dz at altitude z
Rayleigh laser guide stars
• GLAS
Rayleigh
laser guide
star, La
Palma.
Current.
• MMT LGS.
current
Sodium Resonance Fluorescence
• Resonance scattering occurs when incident laser is tuned
to a specific atomic transition.
• Absorbed photon raises atom to an excited state. Atom
then emits photon of the same wavelength via
spontaneous or stimulated emission, returning to the
lower state that it started from.
• Can lead to large absorption and scattering cross-sections.
• Layer in mesosphere ( h ~ 95 km, Dh ~ 10 km) containing
alkali metals, sodium (103 - 104 atoms/cm3), potassium,
calcium
• Strongest laser return is from D2 line of Na at 589 nm.
The atmospheric sodium layer:
altitude ~ 95 km , thickness ~ 10 km
Credit: Clemesha, 1997
Credit: Milonni, LANL
• Layer of neutral sodium atoms in mesosphere (height ~ 95 km)
• Thought to be deposited as smallest meteorites burn up
Rayleigh scattering vs. sodium resonance
fluorescence
• Atmosphere has ~ exponential density profile:
 Mg z 
 kT 
 (nkT )  nMg  n(z)  no exp- 
• M = molecular mass, n =
number density, T =
temperature, k = Planck’s
constant, g = gravitational
acceleration
• Rayleigh scattering dominates
over sodium fluorescence
scattering below h = 75 km.
Real data:
Kumar et al. 2007
Image of sodium light taken from
telescope very close to main telescope
Light from Na layer
at ~ 100 km
Max. altitude of
Rayleigh ~ 35 km
Rayleigh scattered light
from low altitudes
Overview of sodium physics
• Column density of sodium atoms is relatively low
– Less than 600 kg in whole Earth’s sodium layer!
• When you shine a laser on the sodium layer, the optical
depth is only a few percent. Most of the light just
keeps on going upwards.
• Natural lifetime of D2 transition is short: 16 nsec
• Can’t just pour on more laser power, because sodium D2
transition saturates:
– Once all the atoms that CAN be in the excited state
ARE in the excited state, return signal stops
increasing even with more laser power
Sodium abundance varies with season
• At University of Illinois: factor
of 3 variation between
December-January (high) and
May-June (low)
• In Puerto Rico (Arecibo): smaller
seasonal variation. Tropical vs.
temperate?
Can see vertical distribution of Na atoms
by looking at laser return from side view
~ 105 km
~ 95 km
Propagation
direction
Time variation of Na density profiles
over periods of 4 - 5 hours
Night 1: single peaked
Night 2: double peaked
At La Palma, Canary Islands
Next: discuss line profile of D2 line, and
saturation of Na resonance transition
• Line profile determines what the linewidth of the laser
should be, to get best return signal
• Line profile and atomic physics determine “saturation
level”:
– Beyond a certain incident laser flux, all the atoms
that CAN be in the upper state ARE in the upper
state.
– Laser return signal no longer increases as you
increase incident laser power above the power
corresponding to saturation.
Doppler Broadening dominates line shape

• For gas in equilibrium @ temp. T,
2
-mv
 m  1/2


x  dv

fraction of atoms with velocities f (v ) dv  n 
exp 
 2 kT 
x
x
x
 2kT 


between v and dv is given by


Boltzmann distribution:
 

v
 c    -1
 0

r r

v
• For atom moving at velocity v
    0 - k  v   0  1 

towards source, frequency of the
c 

radiation is shifted by:
• Rewrite in frequency space as:
• HWHM can be found from
distribution in frequency space:
• For sodium atom at 200 K,
Doppler width is ~ 1 GHz: 100 X
larger than natural linewidth.
f  d 
n


 1/2
2
 mc

exp
 2kT  
o





2
2
 -mc  -  o 

2kT  o2 




2

2
 -mc  D -  o 

exp 


2kT  o2



 mc2 

D  
 2kT  o 
1
2
0.5
ln 2

Shape of Doppler-broadened sodium:
Na D2 line in mesosphere, T ~ 200 K
• 1.8 GHz separation between 2
peaks due to hyperfine
splitting of ground state
• FWHM ~ 2.5 GHz
• Question: if each naturally
broadened line is 10 MHz wide
(natural linewidth), how many
velocity groups are there
within FWHM?
12
10
8
6
4
2
Answer: ~ 250 velocity
groups within the Doppler
profile
~ 2.5 GHz
0
-3
-2
-1
0
1
2
Result of previous calculation:
• If sodium layer is illuminated with a single frequency
laser tuned to the peak of the D2 line only a few per
cent (of order 10 MHz/1GHz) of the atoms travel in a
direction to interact at all with the radiation field.
• These atoms interact strongly with the radiation until
they collide or change direction.
• Use multi-frequency laser in order to excite many
velocity groups at once.
• Bottom line: Saturation occurs at about Nsat = a few x
1016 photons/sec.
CW lasers produce more return/watt than
pulsed lasers because of lower peak power
• Lower peak
power  less
saturation
3
3
Keck requirement:
0.3 ph/ms/cm2
Laser guide stars: Main points so far
• Laser guide stars are needed because there aren’t enough bright
natural guide stars in the sky
– Hence YOUR favorite galaxy probably won’t have a bright
enough natural guide star nearby
• Solution: make your own guide star
– Using lasers
– Nothing special about coherent light - could use a flashlight
hanging from a “giant high-altitude helicopter”
– Size on sky has to be  diffraction limit of a WFS sub-aperture
• Rayleigh scattering: from ~10 km, doesn’t sample turbulence as
well as resonant scattering from Na layer at ~100 km. But lasers
are cheaper and easier to build.
• Sodium laser guide stars: must deal with saturation of atomic
transition. Means you should minimize peak laser power. Some
aspects of optimizing the Na return are not yet understood.
LASER TECHNOLOGY
Types of lasers: Outline
• Principle of laser action
• Lasers used for Rayleigh guide stars
– Serious candidates for use with Ground Layer AO
– Doubled or tripled Nd:YAG
– Excimer lasers
• Lasers used for sodium guide stars
– Dye lasers (CW and pulsed)
– Solid-state lasers (sum-frequency)
– Fiber lasers
General comments on guide star lasers
• Typical average powers of a few watts to 20 watts
– Much more powerful than typical laboratory lasers
• Class IV lasers (a laser safety category)
– “Significant eye hazards, with potentially
devastating and permanent eye damage as a result
of direct beam viewing”
– “Able to cut or burn skin”
– “May ignite combustible materials”
• These are big, complex, and can be dangerous. Need
a level of safety training not usual at astronomical
observatories until now.
Lasers used for Rayleigh guide stars
• Rayleigh x-section ~ -4  short wavelengths better
• Commercial lasers are available
– Reliable, relatively inexpensive
• Examples:
– Frequency-doubled or tripled Nd:YAG lasers
» Nonlinear crystal doubles the frequency of 1.06
micron light, to yield 532 nm light; quite efficient
– Excimer lasers: not so efficient
» Example: Univ. of Illinois,  = 351 nm
» Excimer stands for excited dimer, a diatomic molecule
usually of an inert gas atom and a halide atom, which
are bound only when in an excited state.
Current Rayleigh guide star lasers
• SOAR: SAM
– Frequency tripled Nd:YAG, λ = 355 nm, 8W, 10 kHz
rep rate
• MMT Upgrade:
– Two frequency doubled Nd:YAG, λ = 532 nm, 30 W
total, 5 kHz rep rate
• William Herschel Telescope: GLAS. Either:
– Yb:YAG “disk laser” at λ = 515 nm, 30 W, 5 kHz, or
– 25W pulsed frequency-doubled Nd:YLF (or YAG)
laser, emitting at λ = 523 (or 532) nm
– Both are in the literature. Not sure which was
chosen.
Rayleigh guide stars
in planning stage
• LBT (planned):
– Possibly 532nm Nd
in hybrid design
with lower power Na
laser at 589nm
– Cartoon courtesy of
Sebastian Rabien
and Photoshop
Lasers used for sodium guide stars
• 589 nm sodium D2 line doesn’t correspond to any
common laser materials
• So have to be clever:
– Use a dye laser (dye can be made to lase at a range
of frequencies)
– Or use solid-state laser materials and fiddle with
their frequencies somehow
» Sum-frequency crystals (nonlinear index of refraction)
Dye lasers
• Dye can be “pumped” with
different sources to lase at
variety of wavelengths
• Messy liquids, some flammable
• Poor energy efficiency
• You can build one at home!
– Directions on the web
• High laser powers require
rapid dye circulation,
powerful pump lasers
Two types of dye lasers used for sodium
laser guide stars
• Dye solution is circulated from a large reservoir to the (small)
lasing region. Types of lasing region:
• Free-space dye jet
– Dye flows as a sheet-like stream in open air from a speciallyshaped nozzle
– Can operate CW (“continuous wave”) - always “on”
– Average power limited to a few watts per dye jet
• Contained in a glass cell
– Dye can be at pressure >> atmospheric
– Very rapid dye flow  can remove waste heat fast  can
operate at higher average power
Dye lasers for guide stars
• Single-frequency continuous wave (CW): always “on”
– Modification of commercial laser concepts
– At Subaru (Mauna Kea, HI); PARSEC laser at VLT in Chile
– Advantage: avoid saturation of Na layer
– Disadvantage: hard to get one laser dye jet to > 3 watts
• Pulsed dye laser
– Developed for DOE - LLNL laser isotope separation program
– Lick Observatory, then Keck Observatory
– Advantage: can reach high average power
– Disadvantages: potential saturation, less efficient excitation of
sodium layer
• Efficiency: dye lasers themselves are quite efficient, but their
pump lasers are frequently not efficient
Keck laser guide star
Keck dye laser architecture
• Dye cells (589 nm) on
telescope pumped by
frequency doubled Nd:YAG
lasers on dome floor
• Light transported to
telescope by optical fibers
• Dye master oscillator, YAG
lasers in room on dome
floor (Keck)
• Main dye laser on telescope
• Refractive launch telescope
PARSEC dye laser at the VLT, Chile
• Under the Nasmyth platform
• More compact than Lick and Keck lasers (I think...)
Solid-State Lasers for Na Guide Stars:
Sum frequency mixing concept
• Two diode laser pumped Nd:YAG lasers are sum-frequency combined in
a non-linear crystal
(1.06 mm)-1 + (1.32 mm)-1 = (0.589 mm)-1
– Advantageous spectral and temporal profile
– Potential for high beam quality due to non-linear mixing
– Good format for optical pumping with circular polarization
• Kibblewhite (U Chicago and Mt Palomar), Telle (Air Force Research
Lab), Coherent Technologies Incorporated (for Gemini N and S
Observatories and Keck 1 Telescope)
Air Force Research Lab’s sum-frequency
laser is the farthest along, right now
• Sum-frequency generation
using nonlinear crystal is
done inside resonant cavity
– Higher intensity, so
increased efficiency of
nonlinear frequency
mixing in crystal
– Laser producing 50W of
589 nm light!
Telle and Denman, AFRL
Air Force Research Lab laser seems most
efficient at producing return from Na layer
• Why?
– Hillman has theory based on atomic physics: narrow
linewidth lasers should work better
– Avoid Na atom transitions to states where the atom
can’t be excited again
• More work needs to be done to confirm theory
• Would have big implications for laser pulse format
preferred in the future
Future lasers: all-fiber laser
(Pennington, LLNL and ESO)
• Example of a fiber laser
Potential advantages of fiber lasers
• Very compact
• Uses commercial parts from telecommunications
industry
• Efficient:
– Pump with laser diodes - high efficiency
– Pump fiber all along its length - excellent surface to
volume ratio
• Disadvantage: has not yet been demonstrated at the
required power levels at 589 nm
WORKING WITH LGS
Laser guide star AO needs to use a faint
tip-tilt star to stabilize laser spot on sky
from A. Tokovinin
Effective isoplanatic angle for image
motion: “isokinetic angle”
• Image motion is due to low order modes of turbulence
– Measurement is integrated over whole telescope
aperture, so only modes with the largest
wavelengths contribute (others are averaged out)
• Low order modes change more slowly in both time and
in angle on the sky
• “Isokinetic angle”
– Analogue of isoplanatic angle, but for tip-tilt only
– Typical values in infrared: of order 1 arc min
Sky coverage is determined by
distribution of (faint) tip-tilt stars
• Keck: >18th magnitude
1
Galactic latitude = 90°
Galactic latitude = 30°
271 degrees of freedom
5 W cw laser
0
From Keck AO book
LGS Hartmann spots are elongated
Sodium layer
Telescope
Laser projector
Image of beam as it lights up
sodium layer = elongated spot
Elongation in the shape of the LGS
Hartmann spots
Representative
elongated Hartmann
spots
Off-axis
laser
projector
Keck pupil
Keck: Subapertures farthest from laser
launch telescope show laser spot elongation
Image: Peter Wizinowich, Keck
LGS spot elongation due to off-axis
projection hurts system performance
From Keck AO book
Ten meter telescope
For ELT’s new CCD geometry for WFS
being developed to deal with spot
elongation
CW Laser
Pulsed Laser
Sean Adkins, Keck
Polar Coordinate Detector
• CCD optimized for LGS AO wavefront sensing on an
Extremely Large Telescope (ELT)
– Allows good sampling of a CW LGS image along the
elongation axis
– Allows tracking of a pulsed LGS image
– Rectangular “pixel islands”
– Major axis of rectangle aligned with axis of
elongation
Pixel Island Concept
Dump drain
Imaging
area
Output gate
Summing
well
Video
“column”
bus
ØI1
ØI2
ØI3
Frame
store
ØFS1
ØFS2
ØFS3
ØS3
Output
select
2-stage O/P amp
ØS3
ØS2
ØS1
Shift register
Typical subaperture
“Cone effect” or “focal anisoplanatism”
for laser guide stars
• Two contributions:
– Unsensed turbulence
above height of guide star
– Geometrical effect of
unsampled turbulence at
edge of pupil
from A. Tokovinin
Cone effect, continued
• Characterized by parameter d0
• Hardy Sect. 7.3.3 (cone effect = focal anisoplanatism)
• FA2 = ( D / d0)5/3
Dependence of d0 on beacon altitude
from Hardy
• One Rayleigh beacon OK for D < 4 m at  = 1.65 micron
• One Na beacon OK for D < 10 m at  = 1.65 micron
Effects of laser guide star on overall AO
error budget
• The good news:
– Laser is brighter than your average natural guide star
» Reduces measurement error
– Can point it right at your target
» Reduces anisoplanatism
• The bad news:
– Still have tilt anisoplanatism
– New: focus anisoplanatism
– Laser spot larger than NGS
tilt2 = (  / tilt )5/3
FA2 = ( D / d0 )5/3
meas2 ~ ( b / SNR )2
Main Points
• Rayleigh beacon lasers are relatively straightforward to
purchase, but limited to medium sized telescopes due
to focal anisoplanatism
• Sodium layer saturates at high peak laser powers
• Sodium beacon lasers are harder:
– Dye lasers (today) inefficient, hard to maintain
– Solid-state lasers are better
– Fiber lasers may be better still
• Added contributions to error budget from LGS’s
– Tilt anisoplanatism, cone effect, larger spot