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```					      Lecture 10:

Laser Guide Stars, Part 2

Claire Max
Astro289C
May 6, 2010

Page 1
Outline of laser guide star topics

 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

Page 2
Two types of laser guide stars in use
today: “Rayleigh” and “Sodium”

• Sodium guide stars: excite
atoms in “sodium layer” at                 ~ 95 km
altitude of ~ 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                 Turbulence
through
Telescope
Page 3
Laser beacon geometry causes
measurement errors

Credit: Hardy
Page 4
Solution: make your own guide star using
a laser beam

• Point the laser beam directly at YOUR favorite
astronomical target

• Use scattering of laser light by the atmosphere to
create an “artificial” guide star

• Next we will discuss the physical mechanisms that
cause the laser light to scatter back down into your
telescope’s wavefront sensor

Page 5
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.

Page 6
Regardless of the type of scattering...

Number of photons detected =

(number of transmitted photons

x probability that a transmitted photon is scattered

x probability that a scattered photon is collected

x probability that a collected photon is detected)

+ background photons (noise)

Page 7
Amount of Photon Scattering

nph = # of photons
sbeam = laser beam cross-
section
nmol = density of scatterers
sB = scattering cross-section

• # molecules hit by laser beam in volume sbeam Dz = nmol sbeam Dz
• Percentage of beam scattered = [ nmol sbeam Dz ] sB /s beam
• Total number of photons scattered = ( EL / h ) ( nmol sB Dz )
• EL and  are laser’s energy and frequency, h is Planck’s constant

Page 8
Percentage of photons collected

• Assuming uniform emission
photons are uniformly
distributed over an area
2p p
 R2 sin d d  4p R2
0 0

• Percentage of photons
collected = AR / ( 4 p R2)

Page 9
LIDAR Equation
(LIght Detection And Ranging)

Transmission thru optics
Number of
Fraction      and atmosphere, detector
photons
of beam              efficiency 
detected in
range interval Dz        scattered


AR 
N(z) 
 EL 
 h 
       s n (z)Dz 
B   mol



 4p z2 


T T2   N
opt   Atm        B

Initial                    Fraction               Background
number of              of scattered photons          photons
photons                that are collected
Page 10
Rayleigh Scattering

• Due to interactions of the electromagnetic wave from
the laser beam with molecules in the atmosphere.

• The light’s electromagnetic fields induce oscillating
dipole moments in the molecules, which then emit
(elastic scattering).

Page 11
Rayleigh Scattering cross section

• Rayleigh backscattering cross section is

ds R   p    5.5  10 28
s 
R
                cm 2 sr 1
           
B                              4
d         
0.55  m
where  is laser wavelength

• Scattering  - 4  use shorter wavelength lasers for better
scattering efficiency

• Why sunsets look red:

Page 12
Dependence of Rayleigh scattering on
altitude where the scattering occurs

• Product of Rayleigh scattering cross section with
density of molecules is

P(z) 4.0117 -1 -1
s n
R
B mol    3.6  10   31
     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

Page 13
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
Page 14
Rayleigh laser guide stars

• GLAS Rayleigh
laser guide star,
La Palma.
Current.

• Starfire Optical
Range Rayleigh
Guide Star (with           MMT laser guide
sodium laser
too!), NM.                  star, Arizona.
Quite a few                    Current.
years ago.
Page 15
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.
Page 16
The atmospheric sodium layer:
altitude ~ 95 km , thickness ~ 10 km

Credit: Clemesha, 1997

Credit: Peter Milonni, LANL

• Layer of neutral sodium atoms in mesosphere (height ~ 95 km)

• Thought to be deposited as smallest meteorites burn up
Page 17
Rayleigh scattering compared with sodium
resonance fluorescence

• Atmosphere has ~ exponential density profile:

 Mg z 
 (nkT )  nMg  n(z)  no exp- 
 kT  
Cartoon
• 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.
Page 18
Rayleigh scattering compared with sodium
resonance fluorescence

• Atmosphere has ~ exponential density profile:

 Mg z 
 (nkT )  nMg  n(z)  no exp- 
 kT  

• M = molecular mass, n =                       Real data:
number density, T =                        Kumar et al. 2007

temperature, k = Planck’s
constant, g = gravitational
acceleration

• Rayleigh scattering dominates
over sodium fluorescence
scattering below h ~ 75 km.
Page 19
Image of sodium light taken from a small
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

Page 20
Can model Na D2 transition as a two-level
atom (one valence electron)

Hyperfine
splitting

Hyperfine
splitting (not
to scale)

• Hyperfine splitting: spins of valence electron and nucleus
are (or are not) aligned

• Separation between upper three hyperfine states is small

• Separation bet. two ground states is large: 1.8 GHz
Page 21
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 doesn’t
increase as you add more laser power

Page 22
Sodium abundance varies with season

• Equatorial regions:
density is more
constant over the
year, but peak is
lower
• Temperate regions:
lowest density in
summer
– Chemical
reactions at
bottom of layer:
Na  sodium
bicarbonate
Page 23
Variability during night (UBC Na Lidar,
Thomas Pfrommer)

Page 24
Atomic processes for two-level atom

• Einstein, 1916: atom interacts with light in 3 ways
– Spontaneous emission
 dN1 
             A21 N 2
 dt  spont


– Stimulated emission
 dN1                                              Graphics
            B21 N 2U  
 dt  stim
                                              credit:
Wikipedia
– Absorption
 dN1 
 B12 N1U  

 dt  abs


N1 , N 2 = density of atoms in states 1 and 2; U   = radiation density
Page 25
Saturation effects in the Na layer, from
Ed Kibblewhite’s chapter

• Consider a two level atom which initially has a ground
state n containing Nn atoms and an empty upper state m.
The atom is excited by a radiation field tuned to the
transition

 = Em- En/h,             h >> kT

• In equilibrium      Bnm U() Nn = AmnNm +Bmn U() Nm

Amn is Einstein's A coefficient (= 1/lifetime in upper state).
Bnm = Bmn = Einstein’s B coefficient.                    U()
is the radiation density in units of Joules/cm3 Hz

Page 26
Check units:

(cm3 Hz / erg) sec-1   # atoms

Bnm U() Nn = Amn Nm + Bmn U() Nm

ergs / cm3 Hz       sec-1 per atom

Page 27
Saturation, continued

• Solve for Nm = Nn Bnm U() / [ Bnm U() + Amn]

• If we define the fraction of atoms in level m as f and the fraction in level n
as ( 1 - f ) we can rewrite this equation as

f = Bmn U() (1 - f ) / (Bmn U() + Amn)

f = 1/[2 + Amn/ BmnU()]

• This equation shows that at low levels of radiation U() the fraction of atoms
in the upper level is Bmn U() / Amn

• As the radiation density increases, fraction of atoms in upper level saturates
to a maximum level of 1/2 for an infinite value of U ().

• Define a saturation level as radiation field generating 1/2 this max:

Usat()   = Amn/2Bmn

Page 28
Usat is not a cliff: fraction in upper state
keeps increasing for U >> Usat
Fraction in upper state vs. U/Usat

0.50

0.45

0.40
Fraction in upper state

0.35

0.30

0.25

0.20

0.15
linear response to increased laser power
0.10

0.05

0.00
0   1     2        3       4      5      6         7   8   9   10

U/Usat
Page 29
Saturation, continued

• The ratio Amn/Bmn is known from Planck's black body formula
and is equal to 8ph3/c3 joules cm-3 Hz

• The intensity of the radiation field I (  ) is related to U (  ) by

I () = U (  ) c watts/cm2 Hz

Isat  9.48 mW/cm2 for linearly polarized light

• In terms of photons Nsat = a few x 1016 photons/sec.

Page 30
CW lasers produce more return/watt than
pulsed lasers because of lower peak power

• Lower peak
3
power  less
saturation

Keck requirement:
3
0.3 ph/ms/cm2

CW = “continuous wave” = always “on”
Page 31
Types of lasers: Outline

• Principle of laser action

• Lasers used for Rayleigh guide stars

• Lasers used for sodium guide stars

Page 32
Overall layout (any kind of laser)

Page 33
Principles of laser action

Stimulated
emission

Mirror
Page 34
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.
Page 35
Lasers used for Rayleigh guide stars

• Rayleigh x-section ~ -4  short wavelengths better

• Commercial lasers are available
– Reliable, relatively inexpensive

Page 36
Frequency doubled Nd:YAG lasers

• Nd:YAG means “neodimium-doped
yttrium aluminum garnet”

• Nd:YAG emits at 1.06 micron

• Use nonlinear crystal to convert two
1.06 micron photons to one 0.53
micron photon (2 X frequency)

• Example: Coherent’s Verdi laser
– Pump light: from laser diodes
– Very efficient
– Available up to 18 Watts
– Pretty expensive
» It’s always worrisome when
price isn’t listed on the web!
Page 37
Current Rayleigh guide star lasers

• SOAR: SAM
– Frequency tripled Nd:YAG, λ = 0.35 m, 8W, 10 kHz
rep rate
– Two frequency doubled Nd:YAG, λ = 0.53 m, 30 W
total, 5 kHz rep rate (multiple guide stars)
• William Herschel Telescope: GLAS
– Yb:YAG “disk laser” at λ = 515 nm, 18 W, 5 kHz

Page 38
Rayleigh guide stars
in planning stage

• Large Binocular
Telescope:
– Possibly 532nm
(doubled Nd:YAG) in
hybrid design with
lower power Na
laser at 589nm
– Cartoon courtesy of
Sebastian Rabien
and Photoshop!

Page 39
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)
» Raman scattering
» ...

Page 40
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
Page 41
Dye lasers for guide stars

• Single-frequency continuous wave (CW): always “on”
– Modification of commercial laser concepts
– 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
• Low Efficiency: dye lasers themselves are quite efficient, but their pump
lasers are frequently not efficient

Page 42
Lick Observatory

Photo by Dave Whysong, NRAO   Page 43
Keck laser guide star

Page 44
Galactic Center with Keck laser
guide star AO

Keck laser guide star AO     Best natural guide star AO

Andrea Ghez, UCLA group
Page 45
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 m)-1 + (1.32 m)-1 = (0.589 m)-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 and Denman (Air Force Research
Lab), Coherent Technologies Incorporated (for Gemini N and S Observatories and
Keck 1 Telescope)

Page 46
Page 47
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

Page 48
Future lasers: all-fiber laser
(Pennington, LLNL and ESO)

• Example of a fiber laser

Page 49

• 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

• Two types of fiber lasers have been demonstrated at
the required power levels at 589 nm (Toptica in
Europe, Jay Dawson at LLNL)

Page 50

Page 51
Laser guide star AO needs to use a faint
tip-tilt star to stabilize laser spot on sky

from A. Tokovinin                               Page 52
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

Page 53
Tip-tilt mirror and sensor configuration

Telescope

Deformable mirror            Tip-tilt mirror

Beam splitter                        Wavefront sensor

Tip-tilt sensor          Beam splitter

Imaging camera

Page 54
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
Page 55
“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   Page 56
Cone effect, continued

• Characterized by parameter d0

• Hardy Sect. 7.3.3 (cone effect = focal anisoplanatism)

sFA2 = ( D / d0)5/3
• Typical sizes of d0 ~ a few meters to 20 meters

Page 57
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
Page 58
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

– Still have tilt anisoplanatism      stilt2 = (  / tilt )5/3
– New: focus anisoplanatism           sFA2 = ( D / d0 )5/3
– Laser spot larger than NGS          smeas2 ~ ( b / SNR )2

Page 59
Compare NGS and LGS performance

• Measurements: Keck LGS
Page 60
Main Points

• Rayleigh beacon lasers are straightforward to purchase,
but single beacons are 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

Page 61
Gemini North laser in action!

Page 62
LGS Hartmann spots are elongated

Sodium layer

Telescope             Laser projector

Image of beam as it lights up
sodium layer = elongated spot
Page 64
Elongation in the shape of the LGS
Hartmann spots

Representative
elongated Hartmann
Off-axis
spots
laser
projector

Keck pupil
Page 65
Keck: Subapertures farthest from laser
launch telescope show laser spot elongation

Image: Peter Wizinowich, Keck
Page 66
New CCD geometry for WFS being
developed to deal with spot elongation

CW Laser                Pulsed Laser

Page 67
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

Page 68

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