Introduction to Adaptive Optics. Tim Morris

Transcription

1 Introduction to Adaptive Optics Tim Morris

2 Contents Definitions and introduction Atmospheric turbulence Components of an AO system Wavefront Sensing Wavefront Correction Turbulence Conjugation Laser Beacons AO Modelling

3 Adaptive Optics (AO) Real-time correction of wavefront distortion The diffraction limit of an 10m telescope in in the visible is approximately 0.01 FWHM At the very best astronomical sites in the world, you ll very rarely see images much better than 0.4 FWHM. Why?!? Atmospheric turbulence distorts stellar wavefronts Turbulence results in blurred images Two solutions: Put your telescope in space Limited to a small mirror Expensive Correct for the atmospheric distortion ADAPTIVE OPTICS!

4 Know Your Enemy (me) Enemies AO Conference The Atmosphere

5 What does turbulence look like?

6 The Atmosphere Kolmogorov model of turbulence Kinetic energy in large scale turbulence cascades to smaller scales Inertial interval Inner scale l 0 2mm. Outer scale L 0 10 to 100 m Turbulence distributed within discrete layers The strength of these layers is described by a refractive index structure function: 2 D ( r n( r) n( ) n D () r n C r 2 2 / 3 n Strength of turbulence can be described by a single parameter, r 0, Fried s parameter Fried s parameter is the diameter of a circular aperture over which the wavefront phase variance equals 1 rad 2 J. Vernin, Universite de Nice. Cerro Pachon for Gemini IGPO

7 Isoplanatic angle, temporal variation Angle over which wavefront distortions are essentially the same: / sec Cn ( h) h dh It is possible to perform a similar turbulence weighted integral of transverse wind speed in order to derive an effective wind speed and approximate timescale of seeing τ 0 is the characteristic timescale of turbulence Note the importance of C n2 (h) in both cases

8 Atmospheric Seeing - Summary Dependence on Wavelength 6 6 r =0.55 m =1.6 m r 0 10cm =2.2 m 0 10ms 36ms 53ms

9 2 Image quality Image quality is determined by the wavefront variance across the telescope pupil The above equation gives the phase variance over a telescope of diameter D T A phase variance of less than ~ 0.2 gives diffraction limited performance There are 3 regimes D T < r 0 Diffraction dominates D T ~ r 0-4r 0 Wavefront tilt (image motion) dominates D T >> r 0 Speckle (multiple tilts across the telescope aperture) dominates 5 3 D T radians r 0 4m telescope: D/ r 0 (500nm)=20 D/ r 0 (2.2 m)=3.5 2

10 Strehl ratio Uncorrected 0.49 FWHM Corrected 0.20 FWHM MARTINI WHT, K-band There are two components of the PSF for 2 < 2 radians 2 So width of the image is not a useful parameter, use height of PSF: Strehl ratio: For small 2 : R ~ exp (- 2 ) Note that 2 should be expressed in radians 2 R = Peak intensity in a (un)corrected image Peak intensity in a diffraction limited image

11 AO Performance RMS error terms in AO add in quadrature Easiest to perform as nanometers RMS wavefront error Many sources of error Temporal DM sampling Anisoplanatism WFS noise Once added in quadrature, the RMS wavefront error can be converted to a Strehl Ratio

12 Wavefronts Zernike polynomials are normally used to describe the actual shape of an incoming wavefront Any wavefront can be described as a superposition of zernike polynomials

13 Atmospheric Wavefront Variance after Removal of Zernike Polynomials j n m Zernike Polynomial Name Resid. Var. (rad 2 ) Constant (D/r 0 ) 5/ Tilt (D/r 0 ) 5/3 2 cos Tilt (D/r 0 ) 5/3 2 sin Defocus (D/r 0 ) 5/ Astigmatism (D/r 0) 5/3 6 sin Astigmatism (D/r 0) 5/3 6 cos sin Coma (D/r 0 ) 5/ cos Coma (D/r 0 ) 5/ sin (D/r 0 ) 5/ (D/r 0 ) 5/3 8 cos3

14 Components of an AO System

15 High order AO architecture Wavefront controller Typically a deformable mirror (DM) May not be optically conjugate to an image of the primary Wavefront sensor (WFS) Shack Hartmann (WFS) or Curvature Sensor (CS) Beamsplitter Dichroic, multi-dichroic, intensity, spatial or combination Controller Typically multi-processor or multi-dsp Interfaces Can be complex and include removal of noncommon path errors to science instrumentation (hence an interface to science data path) Laser beacons Multi-conjugate AO: many beacons, DMs

16 Astronomical Adaptive Optics Correcting the fluctuating aberrations caused by atmospheric turbulence above ground-based optical and near-infrared telescopes. Science target Laser * * Natural Guide Star Adaptive Mirror control signals Control System wavefront information dichroic beamsplitter Visible light Wavefront Sensor atmospheric turbulence IR light Telescope Corrected Science focus Corrected Image Uncorrected Uncorrected Corrected 4/12/2010 image wavefront wavefront 16

17 Wavefront Sensing

18 Wavefront Sensing Types of Adaptive Optics Wavefront Sensor (WFS) Shack-Hartmann WFS Curvature Sensor Interferometers Others Performance comparison of Shack- Hartmann (SH) and Curvature Sensor (CS)

19 Shack-Hartmann Wavefront Sensor (WFS) Microlens Array Detector Each xy offset measures the local wavefront slope across the corresponding lenslet. Wavefront

20 Curvature Wavefront Sensor Input Wavefront Focal Plane Sensing Planes

21 Wavefront Sensors and Detectors The curvature sensor minimises the number of pixels required to remove a given wavefront variance the use of noiseless fibre-coupled avalanche photo-diodes is therefore feasible Shack-Hartmann requires more pixels so a CCD is normally employed low read-noise multi-port specialised devices

22 Comparison of SH and CS (~0.5 seeing) (Pete Doel, University of Durham)

23 Comparison of SH and CS (~1 seeing) (Pete Doel, University of Durham)

24 Wavefront Control

25 Wavefront Control Deformable Mirror (DM) types: Continuous Bimorph Segmented Hysteresis System order

26 Types of Adaptive Mirror (J.C.Dainty, Imperial College)

27 Deformable Mirror One type of Deformable Mirror (DM): Flexible continuous phase sheet Minimum physical actuator separation ~ 1mm Fitting error: 2 f =k (r s /r 0 ) 5/3 rad 2 reflective surface Actuators: typically PZT or PMN throw: 2-20 microns r s = projected actuator separation on sky k = fitting coefficient for DM type. (continuous face sheet: )

28 Continuous Face-sheet Deformable Mirror

29 Bimorph Mirror (J.C.Dainty, Imperial College)

30 Bimorph Deformable Mirror

31 228 degree of freedom adaptive mirror The ELECTRA Segmented Adaptive Mirror (76 tip-tilt-piston segments) built by ThermoTrex, San Diego

32 R e l a t i v e C e n t r a l I n t e n s i t y Wavelength microns Wavefront Fitting Error Comparison 1 Comparative AO Technology Limits for WHT r0 = 0.155,t0 = 1000,t= 1,d0 = Segmented 10, 0% Segmented 0% 0.4 Segmented 0.2 % hysteresis Continuous face sheet 8,0.4 Bimorph n= 7 Bimorph n= tip - tilt

33 Actuator Hysteresis PMN (electrostrictive) Low (<2%) hysteresis at 20 o C; High (~40%) at 0 o C Low drive voltage (<100V) soft PZT ~15% but temp. stable low drive voltage hard PZT ~2%, stable high drive voltage (1000V)

34 Hysteresis Effect of high hysteresis: Continuous mirror: 2-3 times more WFS samples required Segmented mirror: makes piston control hard Solutions: low hysteresis actuators linearise with motion sensor (e.g., strain gauge) linearise with figure sensor Example: ELECTRA: has strain gauges (with temperature compensation) which reduce hysteresis from ~15% to <0.1%

35 Sky Coverage The big problem with AO

36 You can t observe off-axis! Angle over which wavefront distortions are essentially the same: / 3 Cn h h dh sec ( ) This is a very small angle ~5 in the visible It means that if you look at an object that s a large angular distance away from your guide star, you get poor correction!

37 Guide Star Availability. All sky. Model: D. Simons, Gemini prob >=1 stars R mag radius (arcsec)

38 Guide Star Availability. (Galactic Latitude > 30 degrees) Model: D. Simons, Gemini 0.8 prob >=1 stars R mag radius (arcsec)

39 NGS sky coverage model for ING by Remko Stuik, Leiden Observatory

40 Remember the Enemy? The Atmosphere

41 Enemy + Physicist leads to

42 Complicated plan to defeat enemy Adaptive Optics is no different Part of plan that requires a really big laser

43 Laser Guide Stars Creating an artificial wavefront reference Really Big Laser Physicist GLAS LGS AO system commissioning 2007

44 Laser Guide Star Purpose of a laser guide star (LGS) is to increase the sky coverage by creating a bright wavefront reference anywhere in the sky to replace the natural guide star Two types of LGS: Rayleigh (Green or UV) uses Rayleigh backscatter beacon height up to ~20km requires time-gating to set beacon height Sodium D (Orange) uses excitation of mesospheric sodium atoms beacon height 80-90km no time-gating required tuned to sodium D line at 589nm

45 Comparison of Rayleigh backscatter and sodium-resonance backscatter. (Courtesy of MIT Lincoln Lab.)

46 Rayleigh and Sodium Guide Stars at La Palma (IC Applied Optics Group + Tom Gregory, ING)

47 Durham s Rayleigh Laser Guide Star

48 Other LGS Systems Keck Subaru (Keck)

49 Other LGS Systems VLT WHT US Military

50 LGS sky coverage model for ING by Remko Stuik, Leiden Observatory

51 LGS sky coverage model for ING by Remko Stuik, Leiden Observatory

52 Laser Beacon Limitations Tilt reciprocity no tip-tilt signal from laser beacons must use a natural guide star focus is complicated for sodium beacons low frequency atmospheric focus may be masked by changes in effective beacon height Focus Anisoplanatism (cone effect) Sodium layer saturation Safety/site issues

53 Tilt Reciprocity (J.C.Dainty, Imperial College)

54 Multiple Tip/Tilt NGS s? Consider a turbulence profile with focus aberrations at two ranges (blue) LGS measurements (yellow) cannot determine range of the aberration Tip/tilt information lost Equal focus measurement from each LGS, regardless of aberration range Tip/tilt NGS measurements can determine range from the differential tilt between stars Three tip/tilt NGS s needed for all three quadratic modes Alternate approaches: Rayleigh LGS s, or a solution to the LGS tilt indeterminacy problem f r)=a(cr+d) 2 =ac 2 r 2 +2acdr+ad 2 ~ ac 2 r 2 After tilt removal f r)=ar 2

55 Angular and Focal Anisoplanatism

56 Strehl Ratio Focal Anisoplanatism Effect of Na beacon Focal Anisoplanatism (Cone Effect) 0.8 d 0 =3m d 0 =5m d 0 =8m Wavelength (microns)

57 Schemes for the use of multiple laser beacons (J.C.Dainty, Imperial College)

58 Turbulence Conjugation (if normal AO is just a bit too easy)

59 Multiple Conjugate AO Putting a second DM in a plane conjugated to a higher layer of turbulence allows off-axis correction Requires multiple guide stars

60 Multi-Conjugate AO No AO (MCAO) Multiple LGS, Multiple DM: Wide corrected FOV Conventional AO MCAO Courtesy of GEMINI

61 Strehl Uniformity vs. FOV 0 degree zenith angle, 50% Cerro Pachon Turbulence Profile 5 LGS, 16 by 16 subapertures, 3 DM s No WFS noise or servo lag Courtesy of GEMINI

62 MCAO Control Loop Architecture Differential Focus Adjustment LGS Tracking (option) Boresight Adjustment Integrator LGS WFS s Integrator Primary NGS WFS (Option) Wave Front Tomography Average DMFS 3 Blend BTO Tip/ Tilt Loops DM 3 Boresight Adjustments Auxiliary NGS WFS s Integrator OIWFS (Option) DMFS 2 Blend Blend DM 2 DM 1 Low-order Offload to TCS Tip/Tilt Focus+Astig. Cubic and Above Piston and Waffle Blend TTM Tip/Tilt Offload SM Courtesy of GEMINI

63 AO Modelling (or AO on a budget)

64 AO Modelling Computer Modelling Required for performance prediction, instrumentation choices, instrumentation and AO systems engineering, detailed design. 8m Monte Carlo models using processor Beowulf clusters are available, examples: ESO/RTN (LeLouarn et al) Durham (Wilson et al) Ellerbroek/Rigaut: Memory requirements scale as D 4 CPU requirements scale as D 6 D > L 0 poses new challenges for optimisation of WFS sample rate and control law (both in performance model and implementation)

65 Durham 12-processor cluster simulations (Richard Wilson) DCAO I-band simulation (the full Monte Carlo): D Tel diam (m) WFS order Tmx (s) Tloop (s) 4 8x x x (MOVIE) 16 32x Tmx is the time taken to produce the poke/control matrix, which as expected goes as something like D 4. Assuming that the wavefront reconstruction calculation does not take over as the slowest component (ie. we use sparse matrix techniques), then we can project the timings to higher orders assuming that Tloop goes as D 2 and Tmx as D 4 : Projecting from the 24x24 case gives: 32 64x (12 hours) x (190 hours) [ELT] 256x (3045 hours) loops required for 10 seconds of seeing Need a factor of ~100 speedup. Assuming better parallelisation, this could be accomplished with order of magnitude larger cluster of up-to-date CPUs, and hardware acceleration.

66 Durham 12- processor cluster simulations (Richard Wilson) 24 x 24 WFS r 0 =20cm at V Science at 1μ. C n2 is just 2 layers (0km, 5km) 500Hz simulated sample rate Top left: 24x24 WFS Top right: phase map at science pupil Bottom left + right: science PSF at 2 field points: 30 arcsec apart.

67 Does it actually work on-sky?

68 AO Scientific Potential Actual AO image tip/tilt simulation of Galactic Center image (K) at CFHT 0.1 slit Doug Simons Gemini

69 NGC Starburst galaxy PUEO image: fov 10x10, resolution~0.13

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71 Io imaged with Keck AO

72 The GLAS LGS AO System INGRID J-band image of M15, 20s exposure, 20 diameter FOV, Open loop FWHM ~0.45, Closed loop ~0.2 (Moffat fit to PSF)

73 What does this mean to an astronomer?

74 Observing with an AO System Position of target in the sky? Nearer zenith is better (less atmosphere to correct) Is there a suitable guide star near your target? What wavelength do you want to observe in? Longer is better for AO as turbulence is weaker What field of view do you require? Current facility-class AO systems are not multiconjugate What performance can you expect? Highly dependent on weather How long does it take to set-up the AO system? Will a variable PSF across the field affect your results? What is the throughput to the Science CCD with the AO system? Extra surfaces in the optical path lower efficiency

75 End