Adaptive Optics Overview Phil Hinz What (Good) is Adaptive Optics?

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1 Adaptive Optics Overview Phil Hinz What (Good) is Adaptive Optics? System Overview MMT AO system Atmospheric Turbulence Image Structure References: Adaptive Optics for Astronomical Telescopes John Hardy Useful Relations Nuts and Bolts of AO Wavefront Sensors and Correctors Wavefront Reconstruction Image quality Natural and Artificial Guide Stars AO Modes SPIE field guide for Adaptive Optics

2 Background It has been long known that the atmosphere limits the resolution achievable by optical telescopes. For example, Newton wrote that... the Air through which we look upon the Stars, is in a perpetual Tremor... all these illuminated Points [from different portions of the telescope] constitute one broad lucid Point, composed of these 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, and without any trembling of the whole. Long telescopes may cause Objects to appear brighter and larger than short ones can do, but they cannot be so formed to take away the confusion of Rays which arises from the Tremors of the Atmosphere. 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.

3 Images with Increasing Aperture

4 What is Adaptive Optics? Real time (<100 ms update rate) correction of wavefront aberrations induced by atmospheric refraction. Useful for diffraction-limited imaging mainly in the 1-10 micron wavelength range but effort is ongoing to use at shorter wavelengths as well. Requires a relatively bright (V<15) reference star although artificial beacons are in use. Field size is governed by the height of the turbulence.

5 Usefulness of Adaptive Optics The use of adaptive optics is expanding as the capabilities increase, but typical observations include: faint companion detection studies of protoplanetary disks around young stars close binaries quasar host characterization spectroscopy at high spectral resolution photometry and spectroscopy in crowded regions AO is available on all large ground-based telescopes.

6 AO system Overview

7 AO system components

8 The MMT AO System 1. This loop 2. is performed at 550 Hz 3. Measure aberrations due to the atmosphere with WFS Camera Calculate secondary shape needed to correct measured aberration Apply this shape to the deformable secondary Adaptive Secondary Mirror WFS Camera Reconstructor Computer

9 Atmospheric Turbulence Temperature variations in the atmosphere result in index of refraction variations. This, in turn causes corrugations in wavefronts propagating through the atmosphere. Large scale temperature variations create flow of air which will interact at boundary layers to create turbulence. Large scale eddies cascade into smaller scale turbulence. The resulting index variations have typical power spectra (strength versus spatial scale) which are characteristic of the turbulent process.

10 Kolmogorov Turbulence Resulting phase variations are characterized by a structure function: 5/ 3 r 2 x1, x 2 = x 1 x 2 2 =D r =6.88 r0 In radians2 The structure function is only valid for scales above the inner scale (where viscosity damps out the turbulence) and below the outer scale which is the characteristic input size of a cell of temperature variation. Rule of thumb: RMS phase variations are 1 micron per m of separation.

11 Turbulence from a boundary layer Bigger whirls have little whirls, Which feed on their velocity; Little whirls have smaller whirls, and so on to viscosity.

12 2 Cn profiles The strength of the turbulence is measured as an index of refraction variation (termed Cn2). The turbulent layers are not limited to the ground, but extend well up into the troposphere. Cn2

13 Coherence Length The integral of Cn2 over the height of the atmosphere provide the characteristic scale for phase aberrations in the structure function. r 0, z =0.19 6/ 5 cos z 3/5 C 2n dh

14 The Fried (Coherence) Length Defined as the size scale for which the rms phase error is 1 radian. (~15 cm at visible wavelengths). 6 /5 r 0 =r 0,550 0 Wavelength dependent: Can be estimated from the seeing: r = 0 FWHM seeing Think of the Fried length as the largest coherent patch on a wavefront.

15 Coherence Time A rough approximation (not accurate) is that the turbulent wavefront is blown across the aperture at the average wind speed of the atmosphere. A typical wind speed is 10 m/s. So we expect coherence times of In the visible this is 5 ms. t 0 =0.3 r0 v Rule of Thumb: The correction speed should be ~10x the coherence time.

16 Don't we also need to consider the Wavefront Amplitudes? Amplitude variations occur if the angle the light is bent is sufficient to cause it to interfere with the next cell over. r0 h We can write theta as = r0 so amplitude effects are small if r 20 h r0 h

17 Isoplanatic Patch The average height of the turbulence limits the field of view over which the correction is valid The characteristic scale for this is the isoplanatic patch, given by: 0=0.31 r 0 / h where h is the average height of the turbulence, typically 5 km.

18 Image Structure The point spread function of an adaptive optics system is complicated by the fact that the light is only partially corrected. A portion of the total energy, S, is gathered into an Airy pattern. The remaining energy, 1-S, is spread into a halo with a characteristic size of the seeing disk.

19 Strehl Ratio The Strehl Ratio is defined as the peak brightness of an actual image relative to an unaberrated image. This can be related to the rms wavefront error by the approximation: S =e 2 where sigma is expressed in radians. This equation is appropriate for wavefront errors < 2 radians or a Strehl of > 0.1.

20 Strehl versus wavelength The wavefront error, in units of length, is essentially wavelength independent. If we express this in radians of phase error the quantity is inversely proportional to wavelength. We can scale the expected Strehl using the relation: 0 = 0

21 Contribution to Strehl Potential sources of wavefront error include time delay, fitting error, isoplanatic error, photon noise error If we assume the wavefront error terms are independent we can write: 2= i2

22 Errors and System Design Systems typically trade-off time delay errors and read noise errors (due to low fluxes) Flux can be increased by using large subapertures at the expense of fitting errors. For any system, the main two choices are: How many subapertures do you need? How fast do the corrections need to happen? The answer depends on wavelength and the brightness of the guide star.

23 Error relations Fitting Error Photon error d fit =a r0 ph = 5/ 6 d= subaperture size 4 N ph = N ph Time Delay error t delay =5.5 t0 Isoplanatic error iso = 0 5/ V d2t 5/6 t= integration time

24 Strehl versus seeing Sigma (nm)

25 Predicted Strehl versus Guide Star K band H band J band 1x1 2x2 3x3

26 Peak intensity relative to diffraction limit How good a Strehl do you need? PSF, λ=2.2 µm, D/r0 = DOF 50 DOF DOF 12 DOF 2 DOF 0.01 uncorrected Radius (arcsec)

27 Sky Coverage Galactic Galactic latitude

28 Ways of describing the wavefront You can think of characterizing the wavefront in two qualitatively different ways: Zonal description of phase Modal description of phase Zonal wavefront description are more straightforward but random errors are not smoothed out. Modal wavefronts describe the wavefront as an amplitude for functions of r, and theta: Zernike modes.

29 Zernike Modes

30 Wavefront Sensors The phase of a wavefront of light is not directly observable. Laboratory optics measurements address this by interfering the light with a reference source. The source needs to be coherent to do this You typically carry out this measurement by measuring the interference at four different phase shifts between the beams. This is a problem for astronomy where the source is not necessarily coherent and the wavefront is changing quickly.

31 Astronomical Wavefront Sensors The solution is to measure image position variations which correspond to the angle of arrival of a photon. This gives you a delta phase over a delta distance.

32 A Shack Hartmann Wavefront Sensor

33 Aspects of Shack Hartmann Design Simple, most prevalent design Not optimal design for wavefront measurement. Number of subapertures is fixed by optics. Shack-Hartmann based systems MMT AO Keck AO VLT NAOS Gemini Altair

34 Curvature Systems We can also derive phase information by looking at the intensity to either side of the pupil plane. The intensity difference is directly proportional to the phase error in that zone.

35 Curvature System Phase error Image on One-side of pupil Intensity difference image Image on other side of pupil Actuator positions

36 Aspects of Curvature Sensors Curvature systems have historically used APDs to optimize the signal to noise. This enhances the faint guide star limit compared to CCDs due to the low read noise. The zonal correction (no reconstructor) makes implementation easier. Curvature Based Systems CFHT Hokupa'a on Gemini Subaru Telescope

37 Wavefront Reconstruction For wavefront sensors which measure slope we need an intermediate step to calculate the wavefront

38 Wavefront Reconstruction The process of a wavefront reconstruction is a matrix operation where we have a vector of slopes of length S=2*subapertures, A vector of nodes on the corrector corresponding to N actuators An I=NxS matrix relating the influence of each actuator on the slopes.

39 Reconstruction Example In general we have the Relation: S=I N Assume we have a 2x2 Shack-Hartmann with a 3x3 actuator grid arranged as below a c b d If we push up actuator n1 we expect to see a slope, ax, and ay. We have thus characterized A and C in the interaction matrix. The inverse matrix of I can be used to calculate actuators positions from slopes. This is called the reconstructor matrix.

40 Wavefront Correctors Deformable Mirrors Voice Coil Actuators (adaptive secondaries) PZT actuators (Xinetics) MEMs (Boston MicroMachine) LCD optics

41 The MMT adaptive secondary 640mm x 2mm Thin Glass Shell Reference Body Voice Coil Actuator Cooling Lines Control Electronics

42 Laser Beacons Two flavors: Rayleigh Backscatter (MMT) Sodium Resonance (Keck)

43 Laser Beacon issues Laser Beacon Wavefront sensors are not sensitive to the tip-tilt variations of the image 90 km Consequently you need a tip-tilt natural guide star to derive this value. There is an additional error term due to focus anisoplanatism. 20 km Can be overcome with a constellation of beacons and multiple wavefront sensors.

44 Error Summary

45 AO Modes Single Conjugate AO: Diffraction-limited, field size determined by isoplanatic patch. Ground-Layer AO: Use of multiple guide stars to improve seeing across a wide (5') FOV. Multi-Conjugate AO (MCAO): Use of multiple DM's and multiple guide stars to create wide-field diffraction-limited images.

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47 Auxiliary Material

48 MMTAO Science Cameras ARIES: µm imager Clio: 3-5 µm imager MIRAC-BLINC: 6-25 µm imager and nuller Jupiter at 4.8 µm Protoplanetary Nebula at 9.8 and 11.7µm IC 2149 at 2.1 µm Don McCarthy Craig Kulesa Suresh Sivinandam Ari Heinze Phil Hinz Bill Hoffman Phil Hinz

49 ARIES (1-2.5 um imager) um HAWAII imager commissioned 1-5 um spectrometer is currently being completed. Two magnifications provide for 20 and 40 FOV (0.019, and /pix). IC 2149 at 2.1 microns. (courtesy Patrick A. Young, Donald W. McCarthy, and the ARIES-MMTAO team.) Measured H band sensitivity: H=19.6, 10σ, for t = 10 s integration.

50 Mid-Infrared Array Camera (MIRAC) The Bracewell Infrared Nulling Cryostat (BLINC) 256x um imager Nulling channel using two subapertures Imaging scale is /pixel. N band sensitivity is ~0.1 Jy in 10 s Chopping is carried out with an internal mirror.

51 Clio Design Diffraction-limited imaging from H through M-bands large well-depth, high throughput InSb array optimized for 3-5 µm imaging (Indigo Systems Inc.) Cooled optics (77K), baffling, and cold stops to minimize instrument thermal background Coronographic option built in (have ability to add field and pupil stops and PSF shaping wave plates) SPIE Clio - Page 3 1 arcsec fake 10 Jupiter mass planet at 20 AU around nearby star

52 Quad cell signals If we want to maximize the signal to noise, we use the minimum number of pixels to sense the centroid. A quad cell gives us this ability where I 2 I 1 I 3 I 4 x= I 1 I 2 I 3 I 4 but there is a loss of information in the scale of the offset.