Adaptive Optics in the VLT and ELT eraAdaptive Optics in the VLT and ELT era

Laser Guide Stars Laser Guide Stars

François WildiObservatoire de Genève

Outline of this short lectureOutline 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 Laser guide stars: Main points of this lecturethis 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 Two types of laser guide stars in use today: “Rayleigh” and use today: “Rayleigh” and “Sodium”“Sodium”

• Sodium guide stars: excite atoms in “sodium layer” at altitude of ~ 95 km

• Rayleigh guide stars: Rayleigh scattering from air molecules sends light back into telescope, h ~ 10 km

• Higher altitude of sodium layer is closer to sampling the same turbulence that a star from “infinity” passes through

Telescope

Turbulence

8-12 km

~ 95 km

Reasons why laser guide stars Reasons why laser guide stars can’t do as well as bright natural can’t do as well as bright natural guide starsguide 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

Cone effectCone effect

90 k

m

“Missing” Data

Scattering: 2 different physical Scattering: 2 different physical processes 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 ScatteringRayleigh 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 Dependence of Rayleigh scattering on altitude where the scattering on altitude where the scattering occursscattering occurs

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

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

BRnmol 3.6 10 31

P(z)

T (z) 4.0117 m-1 sr-1

Rayleigh laser guide stars use Rayleigh laser guide stars use timing of laser pulses to detect timing of laser pulses to detect light from light from zz

• 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 z at altitude z

Rayleigh laser guide starsRayleigh laser guide stars

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

• MMT LGS. current

Sodium Resonance FluorescenceSodium 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, h ~ 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: The atmospheric sodium layer: altitude ~ 95 km , thickness ~ 10 altitude ~ 95 km , thickness ~ 10 kmkm

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

• Thought to be deposited as smallest meteorites burn up

Credit: Clemesha, 1997

Credit: Milonni, LANL

Rayleigh scattering vs. sodium Rayleigh scattering vs. sodium resonance fluorescenceresonance fluorescence

• 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.

(nkT )nMg n(z)no exp-

Mg zkT

• Atmosphere has ~ exponential density profile:

Real data: Kumar et al. 2007

Image of sodium light taken from Image of sodium light taken from telescope very close to main telescope very close to main telescopetelescope

Rayleigh scattered lightfrom low altitudes

Light from Na layer at ~ 100 km

Max. altitude of Rayleigh ~ 35 km

Overview of sodium physicsOverview 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 Sodium abundance varies with seasonseason

• 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 Can see vertical distribution of Na atoms by looking at laser return atoms by looking at laser return from side viewfrom side view

Propagation direction

~ 105 km

~ 95 km

Time variation of Na density Time variation of Na density profiles over periods of 4 - 5 hoursprofiles over periods of 4 - 5 hours

Night 1: single peaked Night 2: double peaked

At La Palma, Canary Islands

Next: discuss line profile of DNext: discuss line profile of D22 line, and saturation of Na line, and saturation of Na resonance transitionresonance 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 Doppler Broadening dominates line shapeshape

• For gas in equilibrium @ temp. T, fraction of atoms with velocities between v and dv is given by Boltzmann distribution:

• For atom moving at velocity v towards source, frequency of the 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 (vx) dv

xn

m2kT

1/2

exp -mv

x2

2kT

dvx

0-rk

rv

0 1

vc

vc

0-1

f d n

mc2

2kTo

1/2

exp -mc2 -o 2

2kTo2

exp-mc2

D-o 2

2kTo2

12

Dmc2

2kTo

0.5

ln 2

Shape of Doppler-broadened Shape of Doppler-broadened sodium:sodium:Na DNa D22 line in mesosphere, T ~ 200 line in mesosphere, T ~ 200 KK

• 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?

~ 2.5 GHz

-3 -2 -1 0 1 2

2

0

4

6

8

10

12

Answer: ~ 250 velocity Answer: ~ 250 velocity groups within the Doppler groups within the Doppler profileprofile

Result of previous calculation: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 CW lasers produce more return/watt than pulsed lasers because of lower than pulsed lasers because of lower peak powerpeak power

Keck requirement:0.3 ph/ms/cm2

3

3

• Lower peak power less saturation

Laser guide stars: Main points so Laser guide stars: Main points so farfar

• 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 TECHNOLOGYLASER TECHNOLOGY

Types of lasers: OutlineTypes 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 General comments on guide star laserslasers

• 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 Lasers used for Rayleigh guide starsstars

• 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 lasersCurrent 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 Rayleigh guide stars in planning stars in planning stagestage

• 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 Lasers used for sodium guide starsstars

• 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 lasersDye 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 Two types of dye lasers used for sodium laser guide starssodium 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

specially-shaped 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 starsDye 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 starKeck laser guide star

Keck dye laser architectureKeck 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, ChilePARSEC 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 Solid-State Lasers for Na Guide Stars: Sum frequency mixing Stars: Sum frequency mixing conceptconcept

• Two diode laser pumped Nd:YAG lasers are sum-frequency combined in a non-linear crystal

– 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)

(1.06 m)-1 + (1.32 m)-1 = (0.589 m)-1

Air Force Research Lab’s sum-Air Force Research Lab’s sum-frequency laser is the farthest frequency laser is the farthest along, right nowalong, 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 Air Force Research Lab laser seems most efficient at producing return from most efficient at producing return from Na layerNa 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 Future lasers: all-fiber laser (Pennington, LLNL and ESO)(Pennington, LLNL and ESO)

• Example of a fiber laser

Potential advantages of fiber Potential advantages of fiber laserslasers

• 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 LGSWORKING WITH LGS

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

from A. Tokovinin

Effective isoplanatic angle for Effective isoplanatic angle for image motion: “isokinetic angle”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 Sky coverage is determined by distribution of (faint) tip-tilt starsdistribution of (faint) tip-tilt stars

• Keck: >18th magnitude

1

0

271 degrees of freedom5 W cw laser

Galactic latitude = 90°Galactic latitude = 30°

From Keck AO book

LGS Hartmann spots are LGS Hartmann spots are elongatedelongated

Sodium layer

Laser projectorTelescope

Image of beam as it lights up sodium layer = elongated spot

Elongation in the shape of Elongation in the shape of the LGS Hartmann spotsthe LGS Hartmann spots

Off-axis laser

projector

Keck pupil

Representative elongated Hartmann

spots

Keck: Subapertures farthest from Keck: Subapertures farthest from laser launch telescope show laser laser launch telescope show laser spot elongationspot elongation

Image: Peter Wizinowich, Keck

LGS spot elongation due to off-LGS spot elongation due to off-axis projection hurts system axis projection hurts system performanceperformance

Ten meter telescope

From Keck AO book

For ELT’s new CCD geometry for For ELT’s new CCD geometry for WFS being developed to deal with WFS being developed to deal with spot elongationspot elongation

CW Laser Pulsed Laser

Sean Adkins, Keck

Polar Coordinate DetectorPolar 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 ConceptPixel Island Concept

ØS3

ØS2

ØS1

ØI1

ØI2

ØI3

ØFS1

ØFS2

ØFS3

Output gate

Video “column” bus

Output select

Shift register

Summing well

2-stage O/P amp

Imaging area

Frame store

Typical subaperture

Dump drain

ØS3

““Cone effect” or “focal Cone effect” or “focal anisoplanatism” for laser guide anisoplanatism” for laser guide starsstars

• Two contributions:

– Unsensed turbulence above height of guide star

– Geometrical effect of unsampled turbulence at edge of pupil

from A. Tokovinin

Cone effect, continuedCone effect, continued

• Characterized by parameter d0

• Hardy Sect. 7.3.3 (cone effect = focal

anisoplanatism)

• FA2 = ( D / d0)5/3

Dependence of dDependence of d00 on beacon on beacon altitudealtitude

• One Rayleigh beacon OK for D < 4 m at = 1.65 micron

• One Na beacon OK for D < 10 m at = 1.65 micron

from Hardy

Effects of laser guide star on Effects of laser guide star on overall AO error budgetoverall 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 tilt

2 = ( / tilt )5/3

– New: focus anisoplanatism FA2 = ( D / d0 )5/3

– Laser spot larger than NGS meas2 ~ ( b /

SNR )2

Main PointsMain 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