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					      Lecture 10:

Laser Guide Stars, Part 2

         Claire Max
        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
                                                   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-
                                    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
  over 2p steradians, scattered
  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)
  where AR is receiver area

                                   Page 9
 LIDAR Equation
 (LIght Detection And Ranging)

                                         Transmission thru optics
   Number of
                          Fraction      and atmosphere, detector
                          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
  radiation at same frequency as the exciting radiation
  (elastic scattering).

                                                    Page 11
Rayleigh Scattering cross section

• Rayleigh backscattering cross section is

             ds R   p    5.5  10 28
         s 
                                           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
         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.

• 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,
• 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  
• M = molecular mass, n =
  number density, T =
  temperature, k = Planck’s
  constant, g = gravitational

• 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

• 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)


                                              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
                              • Temperate regions:
                                lowest density in
                                 – Chemical
                                   reactions at
                                   bottom of layer:
                                   Na  sodium
                                             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:
    – 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

       = 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



Fraction in upper state





                                         linear response to increased laser power


                                 0   1     2        3       4      5      6         7   8   9   10

                                                                                                     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
                                            power  less

                                          Keck requirement:
                                            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


                                          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

   – Frequency tripled Nd:YAG, λ = 0.35 m, 8W, 10 kHz
     rep rate
• MMT Upgrade:
   – 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
   – 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
• 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

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

• Example of a fiber laser

                                 Page 49
 Potential advantages of fiber lasers

• Very compact

• Uses commercial parts from telecommunications

• 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
Questions about lasers?

                          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


           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


                                          Galactic latitude = 90°
                                          Galactic latitude = 30°

                                     271 degrees of freedom
                                          5 W cw laser


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

• The bad news:
   – 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!

• Download movie from class website

                                      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

elongated Hartmann

                     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

                 Sean Adkins, Keck
                                             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

                                                    Page 68