Adaptive optics and wavefront correctors

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

And what about spatial telescopes ? It is definitively a solution for some applications 3 But extremely difficult and expensive to make large telescopes… Telescope under study for first light around : 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? 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 Light from both guide star and astronomical object is reflected from deformable mirror; distortions are removed

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

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

Close loop / open loop AO 7 RTC WFS DM CAM WaveFront SensorReal Time Computer Deformable mirrorImaging camera WFS CAM RTC DM wavefront O p e n l o o p C l o s e l o o p Main advantage of close loop : the WFS is working around 0, measuring small perturbations => It is working in its linearity domain

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

9 AO produces point spread functions with a “core” and “halo” When AO system performs well, more energy in core When AO system is stressed (poor seeing), halo contains larger fraction of energy (diameter ~ r 0 ) Ratio between core and halo varies during night Intensity x Definition of “Strehl”: Ratio of peak intensity to that of “perfect” optical system

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 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 Correction quality ?

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 12 Each of them brings specific limitations / error terms

13  2 ph & ron +  2 aliasing +  2 scintill. =  2 miror +  2 wfs +  2 temp. +  2 atm. res. +  2 anisoplanatism { Residual phase variance  2 OA residu 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  0 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)

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

16 Types of deformable mirrors: large Segmented –Made of separate segments with small gaps –Each segment has 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 Anti-reflection coating Glass face-sheet PZT or PMN actuators: get longer and shorter as voltage is changed Cables leading to mirror’s power supply (where voltage is applied) Light DMs generates a wavefront fitting error due to its limited degree of freedom DMs generates a wavefront fitting error due to its limited degree of freedom  fitting 2 = a F ( d / r 0 ) 5/3 rad 2 Characteristics: actuator separation, temporal response, influence function, surface quality, hysteresisCharacteristics: actuator separation, temporal response, influence function, surface quality, hysteresis

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

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

23 Fitting error  fitting 2 = a F ( d / r 0 ) 5/3 rad 2 Physical interpretation: If we assume the DM does a perfect correction of all modes with spatial frequencies < 1 / r 0 and does NO correction of any other modes, then a F = 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/r 0

24 Fitting error and number of actuators  fitting 2 = a F ( d / r 0 ) 5/3 rad 2 DM Design a F Actuators / segment Piston only, square segments Piston+tilt, Square segments Continuous DM

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: N 1 = 3N 2 ( 0.18 / 0.28 ) 6/5 = 1.8 N 2

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