Download Adaptive Optics I

Outline
Adaptive Optics
Adaptive Optics and OIR
Interferometry
!
■
■
■
!
!
■
■
Astro 6525 Fall 2015
November 17 2015
■
■
Turbulence
Adaptive Optics
Wavefront Sensing
Control Systems
Error Terms and Limitations
Laser Guide Stars
GLAO/MCAO/MOAO
2
Optical vs Radio Telescopes
Fraunhofer Diffraction
■
■
■
■
S is a diffraction aperture
The illumination is spatially coherent (c.f. spatially incoherent
vC-Z theorem)
The math is (more or less) the same.
Result is the complex amplitude of the far field diffraction is the
2D fourier transform of the aperture
U (x, y) /
ZZ
A(⌘, ⇠)e
ik(x⇠+y⌘)
⌘
y
P1
⇠
h⌫
⇠ 1K
k
h⌫
⇠ 30, 000K
k
d⇠d⌘
O
S
R1
x
R
O0
d
R2
P2
4
Turbulence
Turbulence
“Before I die, I hope someone would explain
quantum mechanics to me. After I die, I
hope God will explain turbulence to me.”!
Greater whorls have lesser whorls,!
which feed on their velocity.!
And lesser whorls have smaller whorls,!
and so on to viscosity.!
L.F. Richardson
!
W. Heisenberg
5
6
Animation Credit: Stanford Center for Turbulence Research
The Kolmogorov turbulence model,
derived from dimensional analysis
Kolmogorov turbulence, cartoon
solar
Outer scale L0
Inner scale l 0
hν
• v = velocity, ε = energy dissipation rate per unit mass,
ν = viscosity, l0 = inner scale, l = local spatial scale
• Energy/mass = v2/2 ∝ v2
Wind shear
convection
• Energy dissipation rate per unit mass
ε ~ v2/τ = v2 / ( l / v) = v3 / l
v ~ ( ε l )1/3
Energy v2 ~ ε 2/3 l 2/3
hν
ground
Page 26
Page 20
7
8
Turbulence
Kolmogorov Power Spectrum
• 1-D power spectrum of velocity fluctuations: k = 2π / l
5NDISTURBED7IND&LOW
Turbulence
Φ(k) Δk ∝ v2 ∝ ε 2/3 k −2/3 or, dividing by k,
Φ(k) ∝ k −5/3 (one dimension)
• 3-D power spectrum: use fact that Φ3D(k) = - (dΦ/dk)/2πk
Observatory
on First
Mountain Ridge
Φ3D(k) ∝ k −11/3 (3 dimensions)
• For rigorous calculation: see V. I. Tatarski, 1961, “Wave
Propagation in a Turbulent Medium”, McGraw-Hill, NY
Page 30
Ocean
Optical turbulence profiling using Stereo–SCIDAR
Figure 5.1: Schematic of turbulence generation in the wake of obstacles. Most worldclass observatories are located on the first mountain ridge near the coast (or on
mountains on islands), with prevailing winds from the ocean.
9
9
Michelson Summer School Proceedings
10
Turbulence in a Stratified Atmosphere
SCIDAR
Figure 8. Example turbulence profile from the JKT, La Palma, 15th September 2013. The upper plot shows the profile of the optical
turbulence as a function of time. The lower plot is the same but with the layer wind velocities overlaid. The length of the arrows denote
the relative wind speed and the direction corresponds to the turbulent layer direction as defined by the cardinal directions shown in the
top right of the lower plot. The conjugate altitude of the analysis plane was set to 0 m.
Shepherd et al 2013 (arXiv: 1312.3465)
12
(a)
(b)
(c)
(d)
(e)
Figure 9. Spatio–temporal cross–covariance functions for the data taken at a conjugate altitude of -2 km (intensity scale inverted for
clarity). The plots show cross–covariance functions generated with temporal delays equal to 1 frame (∼10 ms) from -2 frames (a) to
+2 frames (e). The case of no temporal delay is shown in (c). By examining the position of these peaks in subsequent frames the wind
velocity (magnitude and direction) can be calculated.
Physics of Turbulence
Physics of Turbulence
7ARM#OLD!IR
!DIABATIC!TMOSPHERE
-ECHANICAL
4URBULENCE
-ECHANICAL
4URBULENCE
/PTICAL
4URBULENCE
.O/PTICAL
4URBULENCE
13
14
Physics of Turbulence
Meterologist’s Altitude
References:!
Quirrenbach, Michelson Summer School “Principles of Long Baseline Interferometry” http://olbin.jpl.nasa.gov/iss1999/
coursenotes.html
AFGL Tech Report: Dewan et. al. “A Model for Cn2 (Optical Turbulence) Profiles Using Radiosonde Data”; !
Tatarski “The effects of the turbulent atmosphere on wave propagation”;!
Sasiela “Electromagnetic Wave Propagation in Turbulence: Evaluation and Application of Mellin Transforms”
15
16
Meterologist’s Latitude
17
B. Geerts & E. Linacre
Marechal Approximation (Ruze)
Think Fourier Components…
S⇡e
2
Fringe Herding
σ2 << 1
σ2 >> 1
Marechal Approximation
Mauna Kea, H band (1.6 µm)
Adaptive Optics
Marechal Approximation
Mauna Kea, V band (0.5 µm)
Adaptive Optics
Adaptive Optics
Adaptive Optics
Lick adaptive optics system at
3m Shane Telescope
DM
Wavefront
sensor
Real Data
Off-axis
parabola
mirror
Strehl Gain
Lick AO System
IRCAL infrared camera
Deformable Mirrors (Wavefront Corrector)
Elements of an adaptive optics system
■
■
Most common is PZT stack + facesheet
Also:
■ MEMS
■ Segmented
■ Membrane
■ Bimorph
■ Ferrofluid
Iris AO, Inc.
■ Liquid Crystal
Rigid
High-Quality
Mirror
Segment
Bondsites
Actuator
Platform
Electrodes
Temperature
Insensitive
Bimorph
Flexure
Figure 2. Schematic diagram of a deformable mirror (DM) segment. Segments are tiled into an array to form the
DM. The rigid mirror segment is bonded to the actuator platform. This hybrid structure enables many different
coatings and maintains excellent optical quality over large temperature ranges. A factory calibrated piston/tip/tilt
controller places voltages on the electrodes based on the desired piston/tip/tilt positions or Zernike representation.
31
32
DM Specification Details
Stroke: 5 m, 8 m
Piston/tip/tilt positioning with calibrated
controller enables linear position control
Driver: Factory calibrated Smart Driver II
drive electronics
Update Rate: 3kHz (6-8 kHz April 2010)
Segment Size and Gap: 700 m vertex to
vertex (350 µm on a side)
Segment Pitch: 606.2 µm center-to-center
segment pitch
Response Time [20%-80%]: < 150 µs
Fill Factor: > 98% (6 m gaps between
segments)
Closed-Loop Resolution: > 12 bit
Coupling Coefficient: 0% because of
segmentation
Segment Surface Quality: < 30 nm rms
max, < 20 nm rms typical
How to reconstruct wavefront from
measurements of local “tilt”
Wavefront Sensing
■
■
Designs outside the scope of these specifications are possible (e.g. more
Except for heterodyne, don’t measure phase directly
Many solutions, most come from optical metrology
heritage
■ Slope sensors
■
■
■
■
■
Standard Optical Coatings: Gold,
protected aluminum
Optional Optical Coatings: Dielectric,
protected silver
Wavelength of Operation: Visible - IR
White-light Operation: Yes
Hysteresis: < 0.1%
Actuator Drive Voltage: < 200V
Actuator Drive Current: < 1A
Operating Temperature Range: 5°C f
70°C
o -40°C f 85°C by request
Mirror-Segment-Warp Temperature
Dependence: <1 nm PV/°C
Laser Power Handling: ~100 W/cm2 with
protected-Aluminum @ 532 nm
segments, faster response times, different coatings) but will require
Iris AO, Inc.
custom fabrication runs. Please contact Iris AO to discuss.
2680 Bancroft Way, Berkeley, CA 94704, Phone: (510) 849-2375, Fax: (510) 217-9646, http://www.irisao.com
Rev A.8
Page 2 of 4
January 2010
Shack-Hartmann
Pyramid
Curvature
...
Interferometers
■
■
■
Shearing interferometer
Point diffraction interferometer
...
33
34
Shack-Hartmann wavefront sensor concept measure subaperture tilts
Curvature wavefront sensing
■
f
F. Roddier, Applied Optics, 27, 1223- 1225, 1998
More intense
CCD
35
Less intense
CCD
Normal
derivative at
boundary
Laplacian (curvature)
36
Control System
■
Control Matrix
Adaptive Optics in general operates as a closed loop control
■
■
■
■
■
■
37
Control Matrix example: Waffle
■
Wavefront sensor measurements:
W
M
Deformable Mirror Commands
Control Matrix
M = CW
Interaction Matrix
W = AM
!
Control Matrix vs Interaction Matrix
!
A 1 W = (A 1 A)M = M
!
C=A 1
!
Note: matrix inversion is usually approximate,
and has singular values
Simulations of Waffle
Fried sensor/actuator geometry
39
40
Control system stability
41
42