The Fantastical World of Adaptive Optics

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1 The Fantastical World of Adaptive Optics A multimedia presentation of the physics and technology of adaptive optics James W. Beletic Senior Director, Astronomy & Civil Space

2 400 Years of the Telescope First astronomical use of the telescope ~2 cm diameter aperture Firenze, Italia Galileo Galilei ( ) Ponte Vecchio Uffizi Museo Galileo Palazzo Vecchio 2

3 400 Years of the Telescope We have come a long way.eso 8-meter telescope 3

4 4

5 400 Years of the Telescope telescopes with 6.5-meter aperture or larger 5

6 400 Years of the Telescope telescopes with 6.5-meter aperture or larger Keck two 10-m HET 9.2-m (effective) LBT twin 8.4-m Grantecan 10.4-m Subaru 8.2-m Gemini 8-m MMT 6.5-m Gemini 8-m SALT 10-m (eff.) ESO VLT four 8.2-m Carnegie Magellan two 6.5-m 6

7 The Electromagnetic Spectrum 7

8 400 Years of the Telescope The era of the Extremely Large Telescopes (ELTs) is imminent Existing Large Telescopes 944 m 2 of collecting area GMT 24.5-m 359 m 2 TMT 30-m 707 m 2 E-ELT 42-m 1385 m m 9 8-m 5 10-m 8

telescope aperture r = radius of telescope aperture

9 Why bigger telescopes? See fainter objects Resolve finer detail Light collection area = π r 2 Angular resolution = 1.22 λ / D λ = wavelength of light D = diameter of telescope aperture r = radius of telescope aperture = D / 2 13 milliarcsec is the apparent size of a football in Moscow as seen from Madrid 9

10 Understanding the performance of optical telescopes 10

Interferometric Imaging in Astronomy by Francois

11 Introduction to Fourier Optics by Joseph W. Goodman (3rd edition 2005, first published in 1968) Interferometric Imaging in Astronomy by Francois Roddier (Physics Reports, 1988) (Vol. 170, No. 2, pp ) 11

12 Propagation of Light Only need the electric field to understand telescope optics 12

13 Wave model of image formation Shui Kwok s animation 13

14 Phasor Representation of EM Wave ω = 2πf f = frequency Direction of Propagation Increasing phase Increasing time 180 (π radians) 0 phase Electric Field + 14

15 Huygens-Fresnel Principle of Wave Propagation Christiaan Huygens ( ) Augustin-Jean Fresnel ( ) 15

16 Diffraction-Limited Resolution Image Plane Optical Axis 16

$Diffraction-Limit Phasor Distribution E-field Amplitude D E-field Amplitude$

17 Diffraction-Limit Phasor Distribution E-field Amplitude D E-field Amplitude Intensity (Amplitude 2 ) λ / D 2 λ / D ESI Adaptive Optics James Beletic 17

$Diffraction-Limited Resolution Square Aperture Circular Aperture$ $diffraction limit Sir George Biddell Airy (1801 1892) 1.$

18 Diffraction-Limited Resolution Square Aperture Circular Aperture Intensity Airy Diffraction Pattern Zeroes of function First zero, diffraction limit Sir George Biddell Airy ( ) 1.00 Intensity & Encircled Energy First zero at λ / D First zero at 1.22 λ / D 0.00

19 Strehl Ratio Measure of the quality of imaging system The Strehl ratio is the ratio of the observed peak intensity at the detection plane of a telescope or other imaging system from a point source compared to the theoretical maximum peak intensity of a perfect imaging system working at the diffraction limit. 19

20 Square Aperture - no distortions +2λ OPD -2λ Wavefront (rms = 0 wave) Point Spread Function Power Only DC power -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl = 1.27 relative to circular aperture 20

21 Circular Aperture - no distortions +2λ OPD -2λ Wavefront (rms = 0 wave) Point Spread Function Power Only DC power -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

SPEC Mirror 1 Mirror 2 Mirror 3 Mirror 4 R. curvature (mm) 28800+-100 28762.9 28760.0 28762.6 28759.

82(*) 0.875 0.898 0.893 0.975 CIR @ r 0 =250mm N/A 0.935 0.951 0.935 0.981 Strehl >0.25(*) 0.762 0.

953 (*) λ=500 nm - Very high spatial frequency errors ~3-7 7 nm RMS (wavefront) - Microroughness < 20

22 SPEC Mirror 1 Mirror 2 Mirror 3 Mirror 4 R. curvature (mm) WFE RMS (nm) N/A θ RMS (arc secs) N/A r 0 =500mm >0.82(*) r 0 =250mm N/A Strehl >0.25(*) (*) λ=500 nm - Very high spatial frequency errors ~3-7 7 nm RMS (wavefront) - Microroughness < 20 Å - Correction forces typically ~80 N (spec <120 N) - Matching error measured by direct Hartmann test, negligible (below measurement accuracy) - All radii of curvature within 3.7 mm ESO VLT 8.2-m telescope

23 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV= 0.4 wave, rms = 0.05 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

24 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 0.81 wave, rms = 0.10 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

25 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 1.21 waves, rms = 0.15 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

26 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 1.61 waves, rms = 0.20 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

27 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 2.01 waves, rms = 0.25 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

28 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 2.42 waves, rms = 0.30 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

29 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 2.82 waves, rms = 0.35 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

30 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 3.22 waves, rms = 0.40 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

31 Circular Aperture - white noise +2λ OPD -2λ Wavefront (PV = 3.63 waves, rms = 0.45 wave) Point Spread Function Power Equal power at all spatial frequencies -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

32 Point Spread Function Mirror 4 WFE RMS (nm) 17 Strehl (*) λ=500 nm ESO VLT 8.2-m telescope Strehl =

33 Atmospheric Blurring The bane of ground-based astronomy Long exposure image is called the seeing disk Long exposure image Binary star pair 100 Her, 14 arc sec separation (V mag = 6.0) 10 msec frame time 33

Resolution of Ground-based telescopes If the Theory of making Telescopes could at length be fully brought in Practice, yet there would be

For the Air through which we look upon the Stars, is in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows cast from

Point, composed of those many trembling Points confusedly and insensibly mixed with one another by very short and swift Tremors, and

34 Resolution of Ground-based telescopes If the Theory of making Telescopes could at length be fully brought in Practice, yet there would be certain Bounds beyond which Telescopes could not perform. For the Air through which we look upon the Stars, is in a perpetual Tremor; as may be seen by the tremulous Motion of Shadows cast from high Towers, and by the twinkling of the fix d Stars Isaac Newton ( ) And all these illuminated Points constitute one broad lucid Point, composed of those many trembling Points confusedly and insensibly mixed with one another by very short and swift Tremors, and thereby cause the Star to appear broader than it is The only Remedy is a most serene and quiet Air, such as may perhaps be found on the tops of the highest Mountains above the grosser Clouds. Isaac Newton, Opticks,

35 Atmospheric Seeing ESO Paranal Observatory Seeing statistics for Long exposure image the seeing disk Short exposure image (1/100 sec) Full Width Half Maximum (arc sec) 0.5 µm, zenith 35

36 The Devil behind atmospheric distortions 36

37 Velocity of light Velocity v of light through any medium v = c / n c = speed of light in a vacuum ( m/s) n = index of refraction Index of refraction of air ~

38 Atmospheric distortions are due to temperature fluctuations Refractivity of air N (n 1) 10 6 = 77.6 ( λ 2 ) (P /T) where P = pressure in millibars, T = temp. in K, n = index of refraction. VERY weak dependence on λ Temperature fluctuations cause index fluctuations δn = 77.6 (P / T 2 )δt Pressure is constant, because velocities are highly subsonic -- pressure differences are rapidly smoothed out by sound wave propagation.

39 Important things to remember about the index of refraction (n) formula Wavefront shape (x,y,z) is the same in visible and IR Can measure in visible (lower noise detectors) and compensate for the infrared (easier to correct) 1 C temp change = 1 part in a million change in n Doesn t seem like much, eh? 1 wave distortion in 1 meter! (λ=1 μm) Thermal issues bite all major telescopes who don t pay attention to thermal issues!

40 Adaptive Optics Takes the twinkle out of the stars Short exposure image Long exposure image Image with adaptive optics θ = 1 arc sec θ = λ / D 40

41 Adaptive Optics (AO) The technology of sensing and removing atmospheric distortions Neptune in infra-red light (1.65 microns) Without adaptive optics With Keck AO 2.3 arc sec May 24, 1999 June 27,

42 Galactic Center 42

43 Adaptive Optics in Astronomy Edited by Francois Roddier (1999) Adaptive Optics for Astronomical Telescopes by John W. Hardy (1998) 43

44 Simplified AO system diagram 44

45 45

46 An example of correcting optics 46

47 Not to scale 47

48 48

49 Faint Object Camera Images before and after COSTAR repair 49

50 Demonstration of atmospheric turbulence 50

51 Quantifying Atmospheric Distortions - Power Spectrum - Correlation Length - Correlation time 51

Andrei Kolmogorov (1903-1987) Kolmogorov turbulence cartoon solar

52 Andrei Kolmogorov ( ) Kolmogorov turbulence cartoon solar Outer scale L 0 Inner scale l 0 hν Wind shear convection hν ground 52

53 Kolmogorov turbulence in a nutshell Big whorls have little whorls, which feed on their velocity. Little whorls have smaller whorls, and so on unto viscosity. - L. F. Richardson ( ) Computer simulation of the breakup of a Kelvin-Helmholtz vortex 53

54 Kolmogorov Turbulence Spectrum Energy (log) von Karmann spectrum (Kolmogorov + outer scale) outer scale κ = 2π/λ κ -11/3 inner scale Spatial Frequency (log)

55 Circular Aperture Fractal Noise 55

56 Circular Aperture - no distortions +2λ OPD -2λ Wavefront (rms = 0.0 wave) Point Spread Function Power Only DC power -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

$Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 0.23 wave, rms = 0.$

57 Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 0.23 wave, rms = 0.05 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

$Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 0.$ 15 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD

58 Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 0.69 wave, rms = 0.15 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

$Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 1.$ 35 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD

59 Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 1.60 waves, rms = 0.35 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

$Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 2.$ 50 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD

60 Circular Aperture - fractal noise +2λ OPD -2λ Wavefront (PV = 2.29 waves, rms = 0.50 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

61 Circular Aperture - atmospheric distortion +2λ OPD -2λ Wavefront (PV = 4.57 waves, rms = 1.01 waves) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

62 Circular Aperture - atmospheric distortion +2λ OPD -2λ Wavefront (PV = 5.69 waves, rms = 1.18 waves) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

63 Circular Aperture - atmospheric distortion +2λ OPD -2λ Wavefront (PV = 5.75 waves, rms = 1.10 waves) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

64 Circular Aperture - atmospheric distortion +2λ OPD -2λ Wavefront (PV = 5.05 waves, rms = 1.15 waves) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

65 Circular Aperture - atmospheric distortion +2λ OPD -2λ Wavefront (PV = 4.22 waves, rms = 1.01 waves) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

66 Quantifying Atmospheric Distortions - Power Spectrum - Correlation Length - Correlation time 66

67 Correlation length - r 0 Fractal structure (self-similar at all scales) Structure function (good for describing random functions) D(Δx) = [phase(x) phase(x+δx)] 2 D(Δx) 1 rad r 0 = Correlation length the distance Δx where D(Δx) = 1 rad 2 r 0 = max size telescope that is diffraction-limited r 0 is wavelength dependent larger at longer wavelengths (since 1 radian is bigger for larger λ) But a little tricky, r 0 λ 6/5 r 0 Δx 67

68 Correlation length - r 0 Rule of thumb: 10 cm visible r 0 is 1 arc sec seeing Visible r 0 is usually quoted at 0.55 μm. 0.7 arc sec seeing is 14 cm r 0 at 0.55 μm which provides 74 cm r 0 at 2.2 μm (K-band) Seeing is weakly dependent on wavelength, and gets a little better at longer wavelengths. λ/r 0 λ -1/5 68

69 Correlation time - τ 0 To first order, atmospheric turbulence is frozen (Taylor hypothesis) and it blows past the telescope. τ 0 = correlation time, the time it takes for the distortion to move one r 0 τ 0 r 0 /v τ 0 λ 6/5 Determines how fast the AO system needs to run. τ 0 wind velocity = 30 mph = 13.4 m/sec = 14 cm / v = 15 msec (visible) = 74 cm / v = 80 msec (K) Telescope primary 69

70 Wavefront Sensing 70

71 Misrepresentations & Misinterpretations All drawings are exaggerated, since need to exaggerate to show distortions & angles. Maximum phase deviation across 10-meter wavefront is about 10 μm 1 part in 1 million. Like one dot offset on a straight line of 600 dpi printer in 165 feet (50 meters). From the point of view of light, the atmosphere is totally frozen (30 μsec through atmos). We draw one wavefront, but about wavefronts pass through telescope before atmospheric distortion changes.

72 Shack-Hartmann wavefront sensing Flat wavefront Subaperture focal spots uniformly spaced Distorted wavefront Subaperture focal spots unevenly spaced 72

73 Shack-Hartmann wavefront sensing Divide primary mirror into subapertures of diameter r 0 Number of subapertures ~ (D / r 0 ) 2 where r 0 at the desired observing wavelength is evaluated Example: Keck telescope, D=10m, r 0 ~ 60 cm at λ = 2 μm. (D / r 0 ) 2 ~ 280. Actual # for Keck : ~

74 Curvature wavefront sensing 74

75 Curvature wavefront sensing 75

76 Wavefront sensing Several ways to sense the wavefront. Three basic things must be done: Divide the wavefront into subapertures Optically process the wavefront Detect photons Detecting photons must be done last, but order of the first two steps can be interchanged. Can measure the phase, or 1 st derivative, or 2 nd derivative of the wavefront Defined by optical processing 76

77 Wavefront sensor family tree 1 st Step Divide into subapertures Optical Processing Derivative of measure Shack-Hartmann Point source diffraction Pyramid, Shearing Curvature Shack-Hartmann wavefront sensing stands alone as to how it is implemented. Will it be the dominant wavefront sensing method in 10 years time? 77

78 Deformable Mirrors 78

79 Piezoelectric Transducer (PZT) Mirror or Stack-Array Mirror (SAM) Push-pull principle (piezoelectric effect) Local influence functions Pros: Fast (few khz) resonance frequency No theoretical limit for the number of actuators Cons: Few µm stroke Print-through issues ~$1k/actuator, bulky power supplies (few hundred volts) Generally used with Shack-Hartmann WFS Rectangular or hexagonal geometry 79

80 Most deformable mirrors today have thin glass face-sheets Glass face-sheet Light Cables leading to mirror s power supply (where voltage is applied) Reflective coating PZT or PMN actuators: get longer and shorter as voltage is changed 80

81 Deformable mirrors - many sizes 13 to >900 actuators (degrees of freedom) ~30 cm ~5 cm Xinetics 81

Bimorph (or curvature) Mirror Bent / torsion principle Pros: Global influence functions Stroke of several microns Cheaper than PZT Less print-through than

82 Bimorph (or curvature) Mirror Bent / torsion principle Pros: Global influence functions Stroke of several microns Cheaper than PZT Less print-through than PZT Cons: Slower (few hundred Hz) resonance frequency Limited to a few hundred actuators Generally used with curvature WFS Radial or hexagonal geometry 82

83 Adaptive Optics Works! 83

84 84

85 Neptune without Adaptive Optics 85

86 Neptune with Adaptive Optics 86

87 Imaging the galactic center 87

88 88

89 Andrea Ghez (UCLA) Mass of black hole at center of the Milky Way 4.1±0.6 million solar masses 89

90 Reinhard Genzel Max-Planck-Institut für extraterrestrische Physik Flare at galactic center Last cries of matter falling into the black hole? Test of General Relativity? 90

91 U.S. Air Force 3.5-meter adaptive optics systems AEOS Maui, Hawai i Starfire Optical Range Albuquerque, New Mexico 3.5 meter telescopes Collapsible dome 30 subapertures across pupil 690 controlled subapertures >1 khz update rate 91

92 SeaSat Imaged with Starfire AO System 3.5 meter telescope 30 subapertures across pupil 690 controlled subapertures nm wavelength 3 arc sec 92

93 The Large Binocular Telescope (LBT) Two 8.4-meter mirrors, north of Tucson, Arizona 93

94 The LBT adaptive secondary mirror LBT672a unit: 911mm diameter 1.6mm thick shell, (Mirror lab) 672 actuators Settling time < 1ms 30nm WFE Main advantages: No extra surfaces Position 911mm control diameter of the mirror surface 1.6mm thick shell 672 actuators Settling time < 1ms 30nm WFE 94

95 The LBT AO System installed in 2010 Is now being commissioned 0.16 arc sec separation Triple Star 95

96 Measuring AO performance Strehl ratio Definition of Strehl : Ratio of peak intensity to that of perfect optical system Strehl exp (-σ 2 ) Intensity σ = mean-square wavefront error When AO system performs well, more energy in core When AO system is stressed (poor seeing), halo contains larger fraction of energy (diameter ~ λ/r 0 ) Ratio between core and halo varies during night x 96

97 Circular Aperture - no distortions +2λ OPD -2λ Wavefront (rms = 0.0 wave) Point Spread Function Power Only DC power -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

98 Circular Aperture - atmospheric distortion +2λ OPD -2λ Wavefront (PV = 4.57 waves, rms = 1.01 wave) Point Spread Function Power Power f 11/3-3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

99 Circular Aperture - adaptive optics, 3x3 subapertures +2λ OPD -2λ Wavefront (PV = 2.20 waves, rms = 0.32 wave) Point Spread Function Power Power = power (f c ) freq < f c Power f 11/3 freq > f c f c -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

100 Circular Aperture - adaptive optics, 5x5 subapertures +2λ OPD -2λ Wavefront (PV = 1.60 waves, rms = 0.24 wave) Point Spread Function Power Power = power (f c ) freq < f c Power f 11/3 freq > f c f c -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

101 Circular Aperture - adaptive optics, 7x7 subapertures +2λ OPD -2λ Wavefront (PV = 1.23 waves, rms = 0.19 wave) Point Spread Function Power Power = power (f c ) freq < f c Power f 11/3 freq > f c f c -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

102 Circular Aperture - adaptive optics, 10x10 subapertures +2λ OPD -2λ Wavefront (PV = 0.93 wave, rms = 0.13 wave) Point Spread Function Power Power = power (f c ) freq < f c Power f 11/3 freq > f c f c -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

103 Circular Aperture - adaptive optics, 26x26 subapertures +2λ OPD -2λ Wavefront (PV = 0.43 wave, rms = 0.06 wave) Point Spread Function Power Power = power (f c ) freq < f c Power f 11/3 freq > f c f c -3λ 0 +3λ OPD Histogram Spatial frequency (cycles/m) Power Spectrum of Wavefront Surface -λ 0 +λ OPD Histogram with phase wrapping Strehl =

104 AO Systems work well but not perfectly A 9th magnitude star Imaged H band (1.6 μm) Without AO FWHM 0.34 arc sec Strehl = 0.6% With AO FWHM arc sec Strehl = 34% 104

105 Biggest limit to AO performance is noise of the wavefront measurement 105

106 Most important AO performance plot Strehl Higher order system Lower order system Factor of 2.51 per stellar magnitude = 100 Better WFS detectors Guide star magnitude 106

107 Isoplanatism The core of the globular cluster M15. The brightest stars are about 13 mag, and the faintest visible in each frame are about 16 mag. Frame time is 80 msec, and the frame is 20 x 20 arc sec 107

108 Anisoplanatism - θ 0 An object that is not in same direction as the guide star (used for AO system) has a different distortion. θ 0 = isoplanatic angle, the angle over which the max. Strehl drops by 50% h θ 0 r 0 / h θ 0 depends on distribution of turbulence and conjugate of the deformable mirror. Telescope primary 108

109 Turbulence arises in several places stratosphere tropopause km boundary layer ~ 1 km wind flow around dome Heat sources within dome 109

110 Vertical profile of turbulence Measured from a balloon rising through atmospheric layers 110

111 Anisoplanatism (Palomar AO system) credit: R. Dekany, Caltech Composite J, H, K band image, 30 second exposure in each band Field of view is 40 x40 (at 0.04 arc sec/pixel) On-axis K-band Strehl ~ 40%, falling to 25% at field corner Simulation provided by Francois Rigaut 111

112 Combination of: - Brightness required for guide star - Isoplanatic angle - Distribution of bright stars on the sky Only few % of the sky is accessible with natural guide star AO 112

113 Two choices for addressing limited sky coverage (1) Find science under the lamp post (i.e. live within natural constraints) (2) Make your own guide star! 113

114 Overcoming the limited sky coverage (few %) provided by natural guide stars Laser guide stars 114

sodium atoms in mesosphere (height ~ 95 km) Thought to be deposited

115 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 Total of about 200 kg around entire Earth 115

116 ESO Laser Guide Star System 116

117 Overcoming limitations to the corrected field of view Multi-conjugate adaptive optics (1) Provides wider field of view (2) Increases sky coverage with natural guide stars 117

118 Courtesy: F.Rigaut 118

119 Omega Centauri - Multi-Conjugate Adaptive Optics 119

120 Gemini South 8-meter Multiple Laser Guide Star System 1 st Light in January

121 Highest resolution Earth based image of Jupiter (from ground or space) 121

Credits Many thanks to all who contributed materials and conversations to develop this talk:

Paola Amico European Southern Observatory (ESO), Chile Philippe Dierickx ESO, Germany Enrico

University of Cambridge, England Andrea Ghez UCLA Reinhard Genzel Max-Planck-Institut für

122 Credits Many thanks to all who contributed materials and conversations to develop this talk: Thomas Craven-Bartle Flatfrog Technologies, Sweden Francois Rigaut Gemini Observatory, Chile Paola Amico European Southern Observatory (ESO), Chile Philippe Dierickx ESO, Germany Enrico Marchetti ESO, Germany Claire Max Center for Adaptive Optics, UC Santa Cruz, USA Craig Mackay University of Cambridge, England Andrea Ghez UCLA Reinhard Genzel Max-Planck-Institut für extraterrestrische Physik Simone Esposito Arcetri Observatory Robert Fugate Starfire Optical Range (retired) 122

Wavefront errors due to atmospheric turbulence Claire Max

Wavefront errors due to atmospheric turbulence Claire Max Page 1 Kolmogorov turbulence, cartoon solar Outer scale L 0 Inner scale l 0 h Wind shear convection h ground Page Atmospheric Turbulence generally