Adaptive optics and wavefront correctors

1. Adaptive optics and wavefront correctors

2. stratosphere tropopause 10-12 km wind flow over dome Boundary layer ~ 1 km Heat sources w/in dome Atmosphere from 0 to 20 km… Measured from a balloon rising through various atmospheric layers

3. And what about spatial telescopes ? • It is definitively a solution for some applications But extremely difficult and expensive to make large telescopes… • Telescope under study for first light around 2015-2020: • USA : TMT diameter of 30 meter • Europe : E-ELT diameter 42 meter • 42 meter in space ???????? No !!!! • Ground based telescopes necessary to get more • photons & a better angular resolution with higher • diameter … large telescope WITH adaptive optics • Space telescope will remain necessary anyway because • of atmosphere absorption at certain wavelengths

4. How does adaptive optics help? Light from both guide star and astronomical object is reflected from deformable mirror; distortions are removed Measure details of blurring from “guide star” near the object you want to observe Calculate (on a computer) the shape to apply to deformable mirror to correct blurring

5. Adaptive optics system DM fitting error Feedback loop: next cycle corrects the (small) errors of the last cycle Non-common path errors Phase lag, noise propagation Measurement error

6. Classical Adaptive optics Deformable miror control astro. imaging Wave front sensor

7. Close loop / open loop AO WaveFront Sensor Real Time Computer WFS RTC Main advantage of close loop : the WFS is working around 0, measuring small perturbations => It is working in its linearity domain wavefront DM CAM Open loop Deformable mirror Imaging camera CAM DM wavefront WFS Close loop RTC

8. Adaptive optics increases peak intensity & width of a point source Lick Observatory No AO With AO Intensity How is the Point Spread Function after adaptive Optics ? With AO No AO

9. When AO system performs well, more energy in core When AO system is stressed (poor seeing), halo contains larger fraction of energy (diameter ~ r0) Ratio between core and halo varies during night Definition of “Strehl”: Ratio of peak intensity to that of “perfect” optical system Intensity x AO produces point spread functions with a “core” and “halo”

10. Correction quality ? • Strehl ratio : I[0,0] is the intensity of the Point Spread Function at the center of the image (Strehl, K., 1902, Zeit. Instrumenkde, 22, 213) Post AO Ideal case

11. Correction quality ? Other parameter might be more interesting, depending upon the objective: • Full width half maximum (FWHM)  resolution • Ensquared/encircled energy  spectroscopy • Indirect criterium: - detection/signal to noise ratio - quality of image reconstruction

12. Adaptive optics system elements • Deformable mirror to correct the wavefront • Wavefront sensor to measure the distortion that has to be corrected • Real time computer / control algorithm to calculate the instructions to the DM from the WFS measurements Each of them brings specific limitations / error terms

13. Residual phase variance 2 OA residu = 2miror + 2wfs + 2temp. + 2atm. res. + 2anisoplanatism { 2ph & ron + 2aliasing + 2scintill. Classical Adaptive optics Now, we are going to study each of these elements…

14. DM caracteristics • Number of actuators and spatial arrangement • Dynamic range: stroke (total up and down range) • Typical “stroke” for astronomy  several microns. For vision science up to 10 microns • Spectral range • Temporal frequency response: faster than coherence time t0 • Influence function of actuators: • Shape of mirror surface when you push just one actuator • Surface quality: Small-scale bumps can’t be corrected by AO • Hysteresis of actuators: • Want actuators to go back to same position when you apply the same voltage • Power dissipation: • Don’t want too much resistive loss in actuators, because heat is bad (“seeing”, distorts mirror) • Lower voltage is better (easier to use, less power dissipation)

15. Influence function of deformable mirror One actuator Two actuators correlation coeff Between two actuators Influence function and interactuator distance gives correlation coefficient

16. Types of deformable mirrors: large • Segmented • Made of separate segments with small gaps • Each segment has 1 - 3 actuators and can correct: • Piston only (in and out), or • Piston plus tip-tilt (three degrees of freedom) • “Continuous face-sheet” • Thin glass sheet with actuators glued to the back • Zonal (square actuator pattern), or • Modal (sections of annulae, as in curvature sensing) • Bimorph • 2 piezoelectric wafers bonded together with array of electrodes between them. Front surface acts as mirror.

17. Types of deformable mirrors: small • Liquid crystal spatial light modulators • Technology similar to LCDs for computer screens • Applied voltage orients long thin molecules, changes index of refraction • Allows large number of pixels DM (typically LCD : 512x512 pixels) • Only problem… response time slow… • MOEMS (micro-Opto-electro-mechanical systems) • Fabricated using microfabrication methods of the integrated circuit industry • Many mirror configurations possible • Potential to be very inexpensive • Very large number of actuators possible • No problem of response time

18. Continuous face-sheet deformable mirrors Glass face-sheet • DMs generates a wavefront fitting error due to its limited degree of freedom • sfitting2 = aF ( d / r0 )5/3 rad2 • Characteristics: actuator separation, temporal response, influence function, surface quality, hysteresis Light Cables leading to mirror’s power supply (where voltage is applied) PZT or PMN actuators: get longer and shorter as voltage is changed Anti-reflection coating

19. Continuous face-sheet DM’s: Xinetics product line • Range from 13 to > 900 actuators (degrees of freedom) About 12” Xinetics

20. Influence functions for Xinetics DM • Push on four actuators, measure deflection with an optical interferometer

21. Bimorph mirrors Bimorph mirror made from 2 piezoelectric wafers with an electrode pattern between the two wafers to control deformation Front and back surfaces are electrically grounded. When V is applied, one wafer contracts as the other expands, inducing curvature

22. 600µm MOEMS Micro deformable mirror in poly-Silicium (continuous membrane) Influence function of the deformable mirror

23. Fitting error sfitting2 = aF ( d / r0 )5/3 rad2 • Physical interpretation: If we assume the DM does a perfect correction of all modes with spatial frequencies < 1 / r0 and does NO correction of any other modes, then aF = 0.26 • Equivalent to assuming that a DM is a “high-pass filter”: • Removes all disturbances with low spatial frequencies, does nothing to correct modes with spatial frequencies higher than 1/r0

24. Fitting error and number of actuators sfitting2 = aF ( d / r0 )5/3 rad2 DM DesignaF Actuators / segment Piston only, 1.26 1 square segments Piston+tilt, 0.18 3 Square segments Continuous DM 0.28 1

25. Consequences: different types of DMs need different actuator counts, for same conditions • To equalize fitting error for different types of DM, number of actuators must be in ratio • So a piston-only segmented DM needs ( 1.26 / 0.28 )6/5 = 6.2 times more actuators than a continuous face-sheet DM • Segmented mirror with piston and tilt requires 1.8 times more actuators than continuous face-sheet mirror to achieve same fitting error: N1 = 3N2 ( 0.18 / 0.28 )6/5 = 1.8 N2

26. Adaptive secondary mirrors • Make the secondary mirror into the “deformable mirror” • Curved surface ( ~ hyperboloid)  tricky • Advantages: • No additional mirror surfaces • Lower emissivity. Ideal for thermal infrared. • Higher reflectivity. More photons hit science camera. • Common to all imaging paths except prime focus • Disadvantages: • Harder to build: heavier, larger actuators, convex. • Difficult to control mirror’s edges (no outer “ring” of actuators outside the pupil)

27. MMT-Upgrade: adaptive secondary • Magnets glued to back of thin mirror, under each actuator. • On end of each actuator is coil through which current is driven to provide bending force. • Within each copper finger is small bias magnet, which couples to the corresponding magnet on the mirror.

28. Adaptive secondary for the MMT U. Arizona + Arcetri Observatory > 300 actuators