Fundamentals of adaptive optics Ay122a: Astronomical Measurements and Instrumentation, fall term 2017-2018 D. Mawet, Week3, October 11, 2017
Fundamentals of adaptive optics
Ay122a: Astronomical Measurements and Instrumentation, fall term 2017-2018D. Mawet, Week3, October 11, 2017
Palomar trip sign-up
Adaptive optics: motivation
With AO Without AO
AO restores the diffraction limit of telescopes
λ /D
PSFdegradedbytheturbulence Diffrac5on-limitedPSF
λ / r o ~1”@0.5µm
Wavefront error & Strehl ratio
Fried parameter = r0 characteristic size of turbulent cells
φ = typical amplitude of wavefront excursions
Strehl ratio = S = Imeas / Idiff
S = exp(-σ2) with σ = STD(φ)
(Marechal approximation)
φ
Imax!
Imin!
Adaptive Optics 101
Building blocks of adaptive optics systems
Deformable mirror
Wavefront sensor
Science camera
Incoming wavefront
Dichroic beamsplitter
Real-time computer
Closing the loop
Turbulence
Wavefront sensor
Deformable Mirror
Wavefront sensor 101
Why, how, what?
• Purpose: measure the optical disturbances of the turbulence in quasi real time.
• How?
• Measure local slopes/first derivative (piece-wise approximation)
• Shack-Hartmann WFS
• Pyramid WFS
• Measure wavefront curvature => Curvature WFS
• Measure phase directly => Zernike WFS
• The difference between WFS flavors are the way in which phase differences are turned into intensity differences
Main wavefront sensor types
Hartmann test (1900)
Wavefront Screen Reference spots on Detector Slopes = Δy/z
Hartmann screen evolution
Palomar (50s) Lick (60s) Rectangular grid (70s)
Shack upgrade
Shack added the micro-lenses => improved efficiency => increased filling factor => sampling
Example of microlens arrays
Typical SH implementation
Quad cell formula and saturation
b
δx ≅b2(I2 + I1)− (I3 + I4 )(I1 + I2 + I3 + I4 )
#
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&
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δy ≅b2(I3 + I2 )− (I4 + I1)(I1 + I2 + I3 + I4 )
#
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&
'(
saturation
Spot size b acts as a gain factor
b
Slope = 2/b
How to reconstruct wavefront from local tilt?
Δy∝∂φ(x, y)∂y
Deformable mirrors
Deformable mirrors
• Introduction: • DM in a nutshell • Requirements/error budget
• DM types: facesheet vs segmented • DM technologies: 4+1 families • Cost/scaling considerations • Introduction to wavefront reconstruction & Calibration of
DM interaction matrix
Important distinction: adaptive optics vs active optics
Active optics, much slower than adaptive optics (0.1 Hz vs 1kHz)
Deformable mirror in a nutshell
BEFORE AFTER
Incoming Wave with Aberration
Deformable Mirror Corrected Wavefront
Deformable mirror in a nutshell cont’d
Light
CoatingSubstrate
Actuators (e.g. piezo-electric)
Interface to drivers & control electronics
(stroke δi ∝ Vi)
• Dynamic range: stroke (total range) • ± several microns for 8-10 m telescope • ± 15-30 microns for 30-40 m telescope
• Influence function of actuators: • Shape of mirror surface when you push just one actuator • Can optimize your AO system with a particular influence
function, but performance is pretty forgiving (TRUE for ground-base closed loop, not TRUE for space-based high contrast imaging applications)
• Surface quality: • Small-scale bumps can’t be corrected by AO
DM characteristics
Updated 1 March 2012
field of view AO system, the size of the DM cannot be smaller than 200 mm. In most of the cases, a final diameter of 300 to 400 mm reduces the risks on the complete optical design. Considering a 400 mm diameter pupil image, the pitch for the SCAO DM is in the range of 5 mm while it goes to 7 mm for MCAO DMs. For XAO systems the diameter of the pupil image can go down to 200 mm which gives a 1 mm pitch for the DM.
2.4 Actuator mechanical stroke
The mechanical stroke required for a DM is defined not only by the amount of turbulence to compensate for, but also by the request to flatten the DM optical surface itself, to compensate for the telescope residual aberrations and very often for the telescope vibrations.
The mechanical stroke requested by the atmospheric aberrations is given by:
3 O2 √
⁄� (5)
where 1.03 if the DM compensates for the total amount of aberrations and 0.134 in case the DM does not compensate for the tip-tilt. In this equation, O is the wavelength at which is defined; being proportional to O ⁄ the DM stroke is achromatic.
In the ideal case, it is preferred to have the DM also taking care of the tip-tilt compensation but very often the technology does not allow getting enough mechanical stroke for that. The use of an additional tip-tilt mirror is then required.
To specify the DM mechanical stroke, AO engineers shall not consider only the nominal operational seeing. It is well known that the seeing can have quite strong short term evolution (burst of turbulence) and it cannot be accepted to lose an observation because the AO loop crashes due to DM saturation. To improve the robustness of AO systems, the DM stroke is specified for large seeing values considered as a worst case. In the following, a worst case seeing of 2.5 arcsec is used to specify the stroke.
x 8m class telescopes
Using equation (5), the stroke required to compensate for the turbulence excluding tip-tilt is equal to 7 Pm. Adding one extra micron for flattening the DM and another one to compensate for telescope aberrations gives a grand total of 9 Pm. This corresponds to the stroke specified for the DM of NAOS.
x 40m class telescopes
Using equation (5), the stroke required to compensate for the turbulence excluding tip-tilt is equal to 28 Pm.
In the case of a secondary DM, it is necessary to add 5 Pm for flattening the DM, 5 Pm to compensate for telescope aberrations and also a provisional 10 Pm to correct the aberrations coming from the mechanical flexures of the DM itself (2.5 m diameter mirror). For the E-ELT the DM (M4) is also asked to compensate for the residual tip-tilt left uncorrected by the tip-tilt mirror (M5). This additional term amounts to almost 40 Pm in the worst case; summing up quadratically these 40 Pm with the 28 Pm requested for the high order atmospheric aberrations, one ends up with a 50 Pm stroke for time evolving aberrations. Accounting eventually for the correction of static aberrations gives a grand total of 70 Pm.
For MCAO, altitude DMs will have to compensate neither for telescope aberrations, vibrations nor for residual tip-tilt. Only high altitude turbulence has to be corrected for. Assuming two altitude DMs and that 40% of the full atmospheric stroke is provided by the pupil DM, each additional DM needs an 8.5 Pm stroke. Accounting for an extra 1 Pm to flatten each DM, final required stroke is close to 10 Pm.
For XAO, the small pitch does not allow to get large mechanical strokes. The idea is to work in a woofer-tweeter mode where a first DM is used to compensate for large stroke “low” order aberrations while the tweeter exhibits a large number of actuators but only little stroke. For the E-ELT the woofer could be M4. This means that the tweeter has only to correct for the residual high order aberrations. A stroke of 2 to 3 Pm is enough.
2.5 Temporal response
The temporal response of the DSM is driven by the AO loop frequency requirements. Associated to the allocated temporal error, the equations (3) and (4) define the maximum time lag of the AO loop which in turn gives the AO loop frequency keeping in mind that in most of the cases, an AO loop exhibits a two frame time lag. Assuming a simple
Influence function of stacked array
Credit: A. Bouchez Influence function: response to one actuator
Zygo interferometer surface map of a portion of the mirror, with every 4th actuator poked
Influence functions for Xinetics DM
• Push on four actuators, measure deflection with an optical interferometer
Vertical scale exaggerated!
Claire Max, Astro 289C, UCSC
Detailed DM requirements cont’d
• Hysteresis of actuators: • Repeatability • 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) • DM size:
• Not so critical for current telescope diameters • For 30-m telescope need big DMs: at least 30 cm across
DM types and design considerations
Deformable mirror types
Continuous facesheet
Segmented
Liquid crystal
Continuous facesheet DM design considerations
• Facesheet thickness must be large enough to maintain flatness during polishing, but thin enough to deflect when pushed or pulled by actuators
• Thickness also determines “influence function” • Response of mirror shape to “push” by 1 actuator • Thick face sheets ⇒ broad influence function
• Thin face sheets ⇒ more peaked influence function
• Actuators have to be stiff, so they won’t bend sideways
MEMS (MicroElectroMechanical Systems) DM
Electrostatic δ ∝ V2
@Boston MC
@Iris AO
@AlpAO
Electromagnetic δ ∝ V
MEMS actuation mechanisms
MEMS Actuation Mechanisms
http://www.njnano.org/pasi/event/talks/mansfield.pdf
MEMS micro-fabrication
Semiconductor batch processing technology
Examples of MEMS DM
4096-actuator MEMS deformable mirror: - 64x64 - 2 micron of stroke Photo courtesy of Steven Cornelissen, Boston Micromachines
@Boston MC
IrisAO PT489 DM - 163 hex segments, each with 3 actuators (piston+tip+tilt) - made of single crystal silicon - 8 microns of stroke
@Iris AO
@AlpAO
- up to 820 actuators - >10 microns of stroke
Thorlabs Adaptive optics kit
Off to the lab!