1. Adaptive Optics in the VLT and ELT era Laser Guide Stars François Wildi Observatoire de Genève

2. 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

3. 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.

4. 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 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

5. 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

6. Cone effect 90 km “Missing” Data

7. 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.

8. 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).

9. Dependence of Rayleigh scattering on altitude where the scattering 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

10. Rayleigh laser guide stars use timing of laser pulses to detect light from  z 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

11. Rayleigh laser guide stars GLAS Rayleigh laser guide star, La Palma. Current. MMT LGS. current

12. Sodium Resonance Fluorescence 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,  h ~ 10 km) containing alkali metals, sodium (10 3 - 10 4 atoms/cm 3 ), potassium, calcium Strongest laser return is from D 2 line of Na at 589 nm.

13. The atmospheric sodium layer: altitude ~ 95 km, thickness ~ 10 km 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

14. Rayleigh scattering vs. sodium resonance 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. Atmosphere has ~ exponential density profile: Real data: Kumar et al. 2007

15. Image of sodium light taken from telescope very close to main telescope Rayleigh scattered light from low altitudes Light from Na layer at ~ 100 km Max. altitude of Rayleigh ~ 35 km

16. 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 D 2 transition is short: 16 nsec Can’t just pour on more laser power, because sodium D 2 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

17. 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?

18. Can see vertical distribution of Na atoms by looking at laser return from side view Propagation direction ~ 105 km ~ 95 km

19. Time variation of Na density profiles over periods of 4 - 5 hours Night 1: single peakedNight 2: double peaked At La Palma, Canary Islands

20. Next: discuss line profile of D 2 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.

21. Doppler Broadening dominates line shape 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.

22. Shape of Doppler-broadened sodium: Na D 2 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? ~ 2.5 GHz -3 -2 012 2 0 4 6 8 10 12 Answer: ~ 250 velocity groups within the Doppler profile

23. Result of previous calculation: If sodium layer is illuminated with a single frequency laser tuned to the peak of the D 2 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 N sat = a few x 10 16 photons/sec.

24. CW lasers produce more return/watt than pulsed lasers because of lower peak power Keck requirement: 0.3 ph/ms/cm 2 3 3 Lower peak power  less saturation

25. 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.

26. LASER TECHNOLOGY

27. 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

28. 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.

29. 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.

30. 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.

31. 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

32. Lasers used for sodium guide stars 589 nm sodium D 2 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)

33. 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

34. 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 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

35. 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

36. Keck laser guide star

37. 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

38. PARSEC dye laser at the VLT, Chile Under the Nasmyth platform More compact than Lick and Keck lasers (I think...)

39. 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 –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

40. 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

41. 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

42. Future lasers: all-fiber laser (Pennington, LLNL and ESO) Example of a fiber laser

43. 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

44. WORKING WITH LGS

45. Laser guide star AO needs to use a faint tip-tilt star to stabilize laser spot on sky from A. Tokovinin

46. 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

47. Sky coverage is determined by distribution of (faint) tip-tilt stars Keck: >18th magnitude 1 0 271 degrees of freedom 5 W cw laser Galactic latitude = 90° Galactic latitude = 30° From Keck AO book

48. LGS Hartmann spots are elongated Sodium layer Laser projector Telescope Image of beam as it lights up sodium layer = elongated spot

49. Elongation in the shape of the LGS Hartmann spots Off-axis laser projector Keck pupil Representative elongated Hartmann spots

50. Keck: Subapertures farthest from laser launch telescope show laser spot elongation Image: Peter Wizinowich, Keck

51. LGS spot elongation due to off-axis projection hurts system performance Ten meter telescope From Keck AO book

52. For ELT’s new CCD geometry for WFS being developed to deal with spot elongation CW LaserPulsed Laser Sean Adkins, Keck

53. 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

54. Pixel Island Concept

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

56. Cone effect, continued Characterized by parameter d 0 Hardy Sect. 7.3.3 (cone effect = focal anisoplanatism)   FA 2 = ( D / d 0 ) 5/3

57. Dependence of d 0 on beacon altitude 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

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  tilt 2 = (  /  tilt ) 5/3 –New: focus anisoplanatism  FA 2 = ( D / d 0 ) 5/3 –Laser spot larger than NGS  meas 2 ~ (  b / SNR ) 2

59. 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