Adaptive Optics Nicholas Devaney GTC project, Instituto de Astrofisica de Canarias

1. Adaptive OpticsNicholas DevaneyGTC project, Instituto de Astrofisica de Canarias 1. Principles 2. Multi-conjugate 3. Performance & challenges

2. Outline • Background (reminder) • Concept of Adaptive Optics • Gain in Image quality • Components • Designing a system • Limitations

3. Effect of turbulence on Images • The spatial resolution of ground based telescopes is limited to that of an equivalent diffraction-limited telescope of diameter r0 - the Fried parameter • The Fried parameter is determined by the integrated strength of turbulence along the line of sight. It therefore depends on zenith angle (). (airmass=1/cos().) • Since it is defined in terms of phase (1 rad of rms wavefront error), it also depends on wavelength

4. AO Concept N.B. Measure and correct phase errors only

5. Modal Correction • Can write phase error as an expansion of Zernike polynomials (for example) • Zernikes are used mostly because everyone uses them ! The first correspond to familiar Seidel aberrations (tip, tilt, defocus,Astigmatism+defocus, Coma+tilt etc.) • Useful to consider what happens as we correct n=1,2,3.... Zernikes; n is the order of correction.

6. Modal Correction • When j terms are perfectly corrected, the residual variance is given by • The  coefficients have been calculated by Noll (JOSA 66, 207-211, 1975) • In order to determine how image quality improves as a function of the degree of compensation, first consider how the phase structure function changes...

7. Modal Compensation • Recall that for uncompensated turbulence the structure function is given by • Cagigal & Fernandez define a Generalised Fried parameter,0, such that for r < lc • The Generalised Fried parameter is related to the residual variance by

8. Structure function with modal compensation

9. Modal Compensation • The partially corrected PSF has two components, a coherent core and a halo, with • The width of the halo depends on the generalised Fried parameter as follows: and the central peak Intensity is given by

10. Modal Correction of PSF

11. Signal-to-Noise in AO corrected Images • Detecting faint stars against background depends on the signal-to-noise ratio (snr). This is defined as the ratio of the mean signal to the standard deviation. A detection usually requires SNR > 5. • The main sources of noise in Astronomical images are • Background noise : Sky and thermal (IR) • Detector noise • Photon noise

12. AO advantage in point source detection Consider observing with a telescope of diameter D meters. The number of background photons detected in in t second with a pixel of side a radians is given by NB is the sky radiance in photons m-2 s-1 Sr-1  is the overall quantum efficiency For a point source of Irradiance HS photons m-2 s-1, the number of photons detected in time t is Let b=the fraction of this signal within the pixel of side a, so the Signal=bPS. From Poisson statistics:

13. AO advantage in point source detection So the snr is given by For faint sources, with no AO assume pixel size matched to seeing; a=2/r0 With AO, change pixel size to match diffraction-limit; a=2/D and the fraction of the point source flux in this pixel is given by the Strehl Ratio, S

14. AO advantage in point source detection The Gain in SNR from AO is given by Example: D=10m, r0=1m, S=0.6 G=6 D=100m, r0=1m, S=0.4 G=40 In stellar magnitudes the gain is given by The integration time to reach a given magnitude with the same snr These results are optimistic since AO usually reduces throughput and increases the background

15. Wavefront Sensing • The vast majority of AO systems employ a wavefront sensor to measure wavefront phase errors (an alternative approach is ‘dithering’). • These are generally based on classical techniques of optical testing. Do not necessarily give quantitative measure of phase since usually works closed-loop i.e. Only need to detect null condition. • Most phase measurements are based either on Interferometry or on Propagation

16. Phase Estimation Aberrated wavefront R Perfect lens

17. Phase Estimation using Interferometry • Interference of two waves u1(r) and u2(r) • Point Diffraction Interferometer (PDI) pinhole Semi-transparent

18. Mach-Zehnder Interferometer Pinhole Detector 1 Detector 2 Ref: J.R.P. Angel, Nature vol. 368 p203 (1994)

19. Lateral Shear Interferometer For small shear d • Can vary sensitivity by adjusting d • Does not need coherent reference

20. Wavefront sensing using propagation Most wavefront sensing techniques rely on converting wavefront gradients into measurable intensity variations. If we write the complex amplitude as then the change in Irradiance along the propagation path is given by the first term is irradiance variation due to local tilt of the wavefront. The second term is due to wavefront curvature. The intensity changes are enhanced by placing a mask at one plane and measuring the resulting intensity distribution at another plane

21. Shack-Hartmann wavefront sensor M F C x r f z

22. Telescope  ’ microlens array Collimator Shack-Hartmann design • Also need sytem to select guide star in field: • -pair of steering mirrors • -single mirror at reimaged pupil • -pick-off system • May need to include an Atmospheric Dispersion Corrector • More optics if want to use with both natural and laser guide stars (z ~ f2/H) b ’ f

23. Shack-Hartmann sensor gain Output Input tilt

24. Curvature Sensing Recall Transport of Intensity equation If in addition then we have

25. l F P1 P2 f Curvature Sensing

26. Curvature Sensing l P1 f

27. Real curvature sensor.... Vibrating Membrane Mirror Bimorph DM Lenslet array Optical fibers Avalanche photodiodes (APDs) Computer

28. Pyramid Wavefront Sensor P F f

29. Pyramid Wavefront Sensor P F f

30. I2 I1 R b1 b2 I4 I3 Pyramid wavefront sensor modulation

31. M D P F Canonical wavefront sensor M Periodic pattern of bars Ronchi test Crossed cylinder lenses Shack-Hartmann F Knife edge Schlieren 1/4 wave retarding spot Zernike phase contrast Grating Shearing Interferometer Variable curvature mirror Curvature sensor Pyramid Pyramid sensor

32. 80-90% QE over 450-750nm stable geometry (up to 128x128 pixels available for AO) SNR for faint sources limited by readout noise for AO 5e rms at 1 MHz Multiple ports Need cooling 85% QE at 0.5 m No read-out noise Can be electronically gated One device = one pixel (but faster than charge transfer) Need active quenching Need cooling Detectors employed in WFS CCDs APDs

33. Deformable mirror requirements • Number of actuators • Actuator spacing (pupil size) • Actuator stroke (usually tip-tilt removed) on D=10m, r0=10cm at 0.5 m; 3 =1.35m • Actuator influence function, interactuator coupling • Actuator Hysterisis • Temporal response (>1kHz) • Input voltage range • Surface quality (figure, smootness, reflectivity) • Probability of failure

34. Actuator types • Piezoelectric (PZT) • stack N elements to give range • operates over wide temperature range • hysterisis 10-20% • Electrostrictive (PMN) • low hysterisis at room temperature • long term stability • hysterisis is temperature dependent • Magnetostrictive (Terfenol-D) • 20% hysterisis • operates over large temperature range • long term stability

35. DM types • Segmented • piston only or piston-tip-tilt • Thin plate deformable mirrors • Bimorph mirrors • Deformable secondary mirrors • Membrane mirrors • Liquid crystal mirrors

36. DM types Discrete actuator faceplate Bimorph electrode Bimorph electrode size > 4x thickness Difficult to make high order baseplate

37. Adaptive Secondary Mirrors • Making the secondary mirror of the • telescope adaptive minimises emissivity • and maximises throughput • Systems being developed for MMT and LBT • Mirror resonant frequency lower • Maintenance difficult • Calibration tricky http://caao.as.arizona.edu/caao/

40. Performance Limitations • The performance of real AO systems is limited by severaL sources of error. These can be studied by detailed numerical simulation or using approximate formulae. • Consider errors in wavefront tip-tilt (expressed in radians of tilt) seperately from remaining error, expressed in radians. • The corresponding Strehl ratios are given by • where is the correction wavelength, D is the telescope diameter. The final Strehl ratio is given by the product of these:

41. Sources of error • Noise in the wavefront sensor measurement • Finite number of actuators in the deformable mirror • Delay between measuring and correcting wavefront errors • Angular offset between guide source and object of interest • Uncorrectable optical errors (in the telescope & AO system) • Scintillation • .....

42. Noise in wavefront sensing • A general expression for the phase measurement error due to photon noise is where nph is the number of photons in the measurement,  is the angular size of the guide source image, d is the subaperture and  is the measurement wavelength. The constant  depends on the details of the phase measurement. For faint sources the read noise dominates over the photon noise.

43. Noise in wavefront sensing • Bandwidth error • The wavefront sensor has to integrate photons for a finite amount of time before a measurement can be made. In order to ensure stability, the closed-loop bandwidth should not exceed 1/6 - 1/10 of the sampling frequency. • Greenwwod defined an effective turbulence bandwidth. For a single turbulent layer moving at v ms-1 the wavefront error due to a finite servo bandwidth fsis

44. Optimal bandwidth

45. Note on calculating photons Sometimes see very optimistic estimates of throughput.... Usually will not use a standard filter in WFS

46. Deformable mirror fitting error • Error due to the finite number of actuators in the deformable mirror. For an actuator pitch (i.e. Separation) of d, the error is given by: where  depends on the type of deformable mirror and the actuator geometry.

47. Finite Subaperture size • Finite subaperture size leads to aliasing of high-frequency wavefront errors into low-frequency errors. • Usually, the subaperture size is made equal to the deformable mirror actuator spacing. There is then a trade-off between snr in the wavefront sensing and fitting+aliasing errors

48. Optimal Subaperture Size note: can simultaneousely optimise subaperture d and exposure time

49. Putting it all together • Bright star Error Budget or equivalently dominated by fitting and bandwidth error

50. Error budget for GTCAO