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Adaptive Optics I:
principles, wavefront sensors, deformable mirrors
Ay122a: Astronomical Measurements and Instrumentation, fall term 2015-2016
D. Mawet, Week 3, October 14, 2015
Recap from last Monday
Summary of critical values for adaptive optics
•
Fried parameter: r0∝λ6/5
•
Seeing: θ0 = r0/λ∝λ-1/5
•
Coherence time: τ0 = 0.31 r0/V∝λ6/5
•
Greenwood frequency: fG=1/τ0
•
Isoplanatic angle: θ0 = 0.31 r0/h∝λ6/5
Questions
•
If the seeing is 0”.5 at 0.55 microns, what is the seeing at
2.2 microns (K band)?
•
Why is the seeing reported by DIMM/MASS different than
the measured seeing at the focus of the telescope?
•
How do we measure the coherence time?
•
If the seeing is 1”.0 at 0.55 microns, and the wind speed
at h=10 km is 30 m/s, how fast do I need to run an
adaptive optics system to catch up with the atmosphere?
Assignment: write the bubbles
Dome
turbulence
Convection
above primary mirror
Atmosphere
turbulence
Too many optics!
Dust on optics
Polishing defects
Absorption
Misaligned optics
Adaptive Optics 101
Building blocks of adaptive optics systems
Incoming
wavefront
Deformable
mirror
Real-time
computer
Science
camera
Dichroic
beamsplitter
Wavefront
sensor
Closing the loop
Turbulence
Deformable
Mirror
Wavefront
sensor
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
saturation
b
b # (I 2 + I1 ) − (I 3 + I 4 ) &
δx ≅ %
(
2 $ (I1 + I 2 + I 3 + I 4 ) '
b # (I 3 + I 2 ) − (I 4 + I1 ) &
δy ≅ %
(
2 $ (I1 + I 2 + I 3 + I 4 ) '
Spot size b acts as a gain factor
b
Slope = 2/b
How to reconstruct wavefront from local tilt?
∂φ (x, y)
Δy ∝
∂y
Problem of SH-WFS
•
Non-linearity issues at high Strehl
•
Inefficient to sense low-order aberrations such as tip-tilt
σ S−H
π
1 ⎡⎛ 3d ⎞ ⎛ ϑ b d ⎞
=
⎢⎜ ⎟ + ⎜
⎟
2 2 SNR ⎢⎣⎝ 2r0 ⎠ ⎝ λ ⎠
σ S−H
6.3
≅
rad of phase
SNR
2
2
2
1/2
⎤
⎥
⎥⎦
rad
for r0 ≤ d
λ
for r0 = d and ϑ b =
d
Pyramid WFS
Solves SH-WFS
limitations!
Example of Pyramid
WH telescope’s AO system
Curvature WFS
2 images in and out
of focus
I1
I2
Linear relationship
between I1 and I2 and
wavefront curvature
Noise properties of WFS
Guyon 2005
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
Incoming Wave with
Aberration
Deformable Mirror
AFTER
Corrected Wavefront
Deformable mirror in a nutshell cont’d
Actuators (e.g. piezo-electric)
Light
Coating
Substrate
Interface to drivers &
control electronics
(stroke δi Vi)
∝
Effect of wavefront aberrations on image formation
Lens/telescope
FAR
star
PSF
atmosphere
Lens/telescope
FAR
star
Image
OR optical
aberrations
Wavefront error & Strehl ratio
φ
r0 = Fried parameter
(typical scale of wavefront errors, WFE)
Imax!
φ = typical amplitude of WFE
Strehl ratio = S = Imax/Imin
S = exp(-σ2) with σ2 = VAR (φ)
(Marechal approximation)
Imin!
e instruments
define
a Strehl
Ratio
(Sabove
to
associated
AO
module.
This theflavors
R) as
he
purpose of of
this
section
is of
certainly
not
to specification
provide
extensive
error
budgets
for all
the
different
of
the
turbulent
volume
thethe
telescope
(intheir
of SCAO
this
is simply
anisopla
bandwidth
the DM,
error
due
tothe
thecase
measurement
noise,
error
in
can
further
broken
downtoon
into
different
contributors.
ASCAO
verythe
rough
error
tase
to variance
focus on that
theofmain
contributors
impacting
the
DMbudget
specifications.
will
be
made
and
the
turbulent
above
the
telescope
(in
the
ofAssumptions
this
is
simply
thethe
aniso
allbe
the
othervolume
contributors
the
error
(ascase
for example
aliasing
error,
ch
dgiven
following:
which do not reflect
perfectly
the actual status
instruments
at use
sky orthe
under
development
all the
other contributors
to theoferror
budget (as
for on
example
aliasing
error, theb
sourcestoofillustrate
errors, only
twobe
first
areof
ofainterest
be consideredAmongst
as ordersallofthese
magnitude
whatthe
could
theones
design
DM. when specifying a
(1) when specifying
Amongst all these sources of errors, only the two first ones are of interest
The fitting
error
can be expressed
([2],(S[3]):
most of the cases,
science
instruments
define afollowing
Strehl Ratio
R) as specification to their associated AO
he
errorinto
duea to
the fitting
finite
number
DM
actuators,
the error
to thecontributors.
finite
The
error
can of
bethat
expressed
([2], [3]):
⁄ due
nslates
residual
phase
variance
can
be following
further broken
down
into
different
A ver
⁄
thecan
error
due
the measurement
the error in the tomographic
⁄ reconstruction
dget
then
betoexpressed
following:noise,
⁄
ve the telescope (in the case of SCAO this is simply the anisoplanatism error) and eventually
with the pupil diameter and the so-called Fried parameter. is the maximum number
utors to the error budget (as for example the aliasing error, the chromatism error, etc…).
factor
on the shape
the so-called
DM influence
In thisispaper,
a value ofnum
0.3
withwhich
thedepends
pupil diameter
and of the
Friedfunction.
parameter.
the maximum
theones
error
tothe
theshape
finiteofspecifying
number
DM actuators,
the aerror
here
which
depends
the DM of
influence
function. In this paper,
valuedue
of
f errors, only represents
thefactor
two first
aredue
of on
interest
when
a DM.
The temporal error is simply given by ([3]):
ndwidth of the DM, temporal
the error due to the measurement noise,
the error in the tomographic r
ressed followingThe
([2], [3]): error is simply given by ([3]):
the turbulent volume above the telescope (in the case of SCAO this is simply⁄ the anisoplanatism error) a
⁄
⁄
⁄ budget (as for example the aliasing error, the
all the other contributors to the
error
(2)chromatism error,
where is the time lag in the AO loop and represents the atmospheric coherence time ([3]
mongst all these where
sources of
errors,
only
the
twoAO
first
ones
are ofrepresents
interest when
specifying acoherence
DM.
the
atmospheric
time (
is
the
time
lag
in
the
loop
and
and the so-called Fried parameter. is the maximum number of DM actuators and is a
0.314
= coherence time
= Fried
parameter
he
fittingoferror
can
be expressed
following
([2],
[3]):a value of 0.3 is attributed to .
e shape
ther0DM
influence
function.
In this
paper,
0.314
with the mean wind speed weighted by the turbulence
profile along the line of sight of the
⁄
y given by ([3]):
⁄
with the mean wind speed weighted by the turbulence profile along the line of sight of t
Before breaking down ⁄the error budget it is important to specify the expected SR. This
(3)
specific
science
instrument
to
consider
and
no
general
rule
can
be
given;
whyactuato
fo
Before
breaking
down
the
error
budget
it
is
important
to
specify
thethis
expected
Sthe
th the pupil
diameter
and
the
so-called
Fried
parameter.
is
the
maximum
number
ofisDM
R. Th
#
DOF
SPEED
considered
only
as an
educated
guess
used
to
orders
of magnitude
for
the
DM
requirem
specific
science
instrument
to
consider
anddefine
noIn
general
rule
can
be given;
this
is why
the
ctor
which
depends
on
the
shape
of
the
DM
influence
function.
this
paper,
a
value
of
0.3
is
attributed
to
represents
the
atmospheric
coherence
time
([3])
following:
e AO loop
and
N = number
of actuators
τ define
= time
lag
in AO loop
considered only
as an educated guess used to
orders
of magnitude
for the DM requ
For SCAO
systems,
it is
proposed to consider a SR of 50% defined at 2.2 m for a 0.7 arcse
he temporal error
is simply
given by
([3]):
(4)
2
0.314
This
gives
a
residual
phase
variance
of
0.7
rad
which
can
be
broken
down
0.15
rad2arf
For SCAO systems, it is proposed to consider a S of 50% defined at 2.2 into
m for
a 0.7
Adaptive optics error budget
2
⁄
2
R
the
temporal
error and
intothe
0.2
radoffor
The miscellaneous
error
gives a profile
residual
phase
variance
of the
0.7oftwo
rad
which canterms.
be broken
down into 0.15
rad
d weighted byfor
theThis
turbulence
along
line
sight
theremaining
telescope.
for the temporal error and into 0.2 rad2 for the two remaining terms. The miscellaneous er
For
MCAO
theand
same
requirements
are
considered
but
within
a on
2([3])
arcmin
field of vi
represents
the
coherence
time
following:
here
the time
lagimportant
in thesystems,
AOtoloop
error is
budget
it is
specify
the
expected
S
.
This
depends
obviously
each
Ratmospheric
2
2.4 Actuator mechanical stroke
The mechanical stroke required for a DM is defined not only by the amount of turb
the request to flatten the DM optical surface itself, to compensate for the telescope
the telescope vibrations.
Other DM requirements
The mechanical stroke requested by the atmospheric aberrations is given by:
•
•
⁄
3
√
2
where
1.03 if the DM compensates for the total amount of aberrations and
compensate for the tip-tilt. In this equation, is the wavelength at which is defi
DM stroke is achromatic.
Dynamic range: stroke (total range)
• ± several microns for 8-10 m telescope
• ± 15-30 microns for 30-40 m telescope
In the ideal case, it is preferred to have the DM also taking care of the tip-tilt comp
does not allow
getting enough mechanical stroke for that. The use of an additional t
Influence function
of actuators:
To specify the DM mechanical stroke, AO engineers shall not consider only the
• Shape of mirror
when
you
justtermone
actuator
knownsurface
that the seeing
can have
quitepush
strong short
evolution
(burst of turbule
observation because the AO loop crashes due to DM saturation. To improve th
• Can optimizean
your
AO system
withvalues
a particular
stroke
is specified
for large seeing
considered as a influence
worst case. In the follow
used to specify the stroke.
function, but isperformance
is pretty forgiving
8m class telescopes
(TRUE for ground-base
closed loop, not TRUE for space-based high
equation (5), the stroke required to compensate for the turbulence excluding
contrast imagingUsing
applications)
•
extra micron for flattening the DM and another one to compensate for telescope ab
This corresponds to the stroke specified for the DM of NAOS.
Surface quality:
40m class telescopes
• Small-scale bumps can’t be corrected by AO
Using equation (5), the stroke required to compensate for the turbulence excluding
In the case of a secondary DM, it is necessary to add 5 m for flattening the DM
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
purpose of the section 2.1 where only SCAO, MCAO and XAO are considered for the sake of simplici
ns 2.2 to 2.6, the main DM requirements flowing down from the AO error budget are presented and a
arized in the section 2.7. These requirements are defined for 8m and 40 m class telescopes.
Continuous
facesheet
DM
design
considerations
O (rough) error budget
urpose of this section is certainly not to provide extensive error budgets for all the different flavors of AO
focus on the main contributors impacting on the DM specifications. Assumptions will be made and num
en which do not reflect perfectly the actual status of instruments at use on sky or under development but h
considered as orders of magnitude to illustrate what could be the design of a DM.
st of the cases, science instruments define a Strehl Ratio (SR) as specification to their associated AO mod
ates into a residual phase variance that can be further broken down into different contributors. A very ro
t can then be expressed following:
Facesheet thickness must be large enough to maintain flatness during polishing,
but
thin enough
to deflect
pushed
or pulled
by actuators
represents
the error
due towhen
the finite
number
of DM
actuators,
the error due to
• Thickness also determines “influence function”
width of
the DM,
the error due to the measurement noise,
the error in the tomographic recon
turbulent• volume
aboveofthe
telescope
(intothe
case ofbySCAO
this is simply the anisoplanatism error) and e
Response
mirror
shape
“push”
1 actuator
all the other
contributors
to the error
budget
(as for function
example the aliasing error, the chromatism error, etc…
• Thick
face sheets
broad
influence
•
gst all these
sources of errors, only the two first ones are of interest when specifying a DM.
• Thin face sheets
more peaked influence function
tting error can be expressed following ([2], [3]):
• Actuators have to be stiff, so they won’t bend sideways
•
Fitting error k~0.3
⁄
⁄
the pupil diameter and the so-called Fried parameter. is the maximum number of DM actuators a
which depends on the shape of the DM influence function. In this paper, a value of 0.3 is attributed to .
ough) error budget
e of this section is certainly not to provide extensive error budgets for all the different flavors of AO syst
s on the main contributors impacting on the DM specifications. Assumptions will be made and numbers
hich do not reflect perfectly the actual status of instruments at use on sky or under development but have m
dered as orders of magnitude to illustrate what could be the design of a DM.
Segmented DM design considerations
the cases, science instruments define a Strehl Ratio (SR) as specification to their associated AO module.
nto a residual phase variance that can be further broken down into different contributors. A very rough e
then be expressed following:
(1)
represents the error due to the finite number of DM actuators,
the error due to the f
of the DM,
the error due to the measurement noise,
the error in the tomographic reconstruc
piston only
piston + tip/tilt
ulent volume above the telescope (in the case of SCAO this is simply the anisoplanatism error) and eventu
he other contributors to the error budget (as for example the aliasing error, the chromatism error, etc…).
ll these
errors, only can
the twomove
first ones
are of
when
a DM.
• sources
Eachofactuator
just
in interest
piston
(inspecifying
and out),
or
error canplus
be expressed
([2], [3]):
tip-tiltfollowing
(3 degrees
of
•
Fitting error:
in piston
freedom)
⁄
⁄
(2)
pupil diameter
and only:
the so-called
Fried parameter. is the maximum number of DM actuators and
• Piston
k = 1.26
h depends on the shape of the DM influence function. In this paper, a value of 0.3 is attributed to .
• 3 degrees of freedom: k = 0.18
ral error is simply given by ([3]):
⁄
(3)
Deformable mirror technologies
Deformable mirror technology families
Deformation
mechanism
Stacked array
Bimorph
MEMS
type
Electrostrictive/
CFS/Segmented
Piezoelectric
Piezoelectric
CFS
Electro/Magneto
CFS/Segmented
static
Provider
CILAS/Xinetics
CILAS
BMC/IrisAO/
AlpAO/TNO
Voice coil
Magnetic
CFS
Microgate/ADS
LC SLM
Electro optic
LC SLM
Hamamatsu/BNS
Stacked array DMs
ked array DMs are using ferroelectrics actuators made of stacks of individual plates or disks (see Figure 1).
oelectrics material can be either of piezoelectric or electrostrictive form. Lead zirconate titanate Pb(Zr, Ti)O3 (P
lead magnesium niobate Pb(Mg1/3Nb2/3)O3 (PMN) are respectively the most commonly used piezoelectric
rostrictive materials The physics of the piezoelectric or electrostrictive effects is beyond the scope of this paper
not be recalled; the reader is invited to refer to the chapter 4.2 of [5] for more details.
Stacked array DM
Figure 1. Stacked array DM concept. An optical head is assembled on top of an array of ferroelectric actuators. Each
actuator is made of a stack of plates. Electrodes are deposited between each plate. The array of actuators is glued on a
rigid base plate (courtesy CILAS).
carefully
selecting
the
optical
platebyand
rigid
base
plate electronics.
materials,
DM
far above 10 kHz, allowing forare
very
short response
times
verythe
often
limited
thethe
associated
drive
By athermalization
making
this
technology
most
attractive
for
AO
applications
including
ELTs to
igh reliability, large
stroke,
excellent
accuracy,
high
resonant
frequencies
and
flexibility
in
actuator
geometry
carefully selecting the optical plate and the rigidThe
base
plateof
materials,
DM athermalization
can to
bealmost
obtained.
design
stacked array
DMs can be tuned
any need of the customer (very l
3.2 Bimorph
DMsELTs to date.
this technology the most attractive for AO applications
including
hexagonal
makingofthem
suitable
to any AO system
The design of stacked array DMs can be tuned pitches,
to almostrectangular
any need oforthe
customergeometry…)
(very large number
actuators,
small
technology
are on
the
hightransverse
driving
voltages
requiring
bulky
electronics
large bui
pitches, rectangular or hexagonal
geometry…)
making
them
suitable
to
any AO
system.
The main
drawbacks
of racks
this and
ph DMs
Bimorph
DMs
are based
the
piezoelectric
effect.
The bimorph
concept
thousands
creepand
inherent
to the ferroelectric
a long lead time an
technology are the high driving voltages requiring
bulkyactuators,
electronicstheracks
large bundles
of cables inmaterial,
case of multi
stiffness,
highmaterial,
reliability,
large
stroke,
excellent
accuracy,
high resonant
Ms are based on the
transverse
piezoelectric
bimorph
concept
described
inone
Figure
thousands
actuators,
the creep effect.
inherent
the
ferroelectric
a long
lead
time
and2.the cost.
their
highfrequencies
WhenThe
ato control
voltage
isisapplied
to
electrode,
it However,
creates
locally
an electricandf
areaccuracy,
making this
thewhile
most attractive
for AOone
including
ELTs to dat
stiffness, high reliability, large stroke,
excellent
high
resonant
frequencies
and flexibility
inapplications
actuator
geometry
transverse
elongation
in technology
one
wafer
the
second
shows
a corresponding
ontrol voltage is applied
to
one
electrode,
it
creates
locally
an
electric
field
which
in
turn
induces
a
local
are making this technology the most attractive for
applications
3.2 AO
Bimorph
DMs including ELTs to date.
Bimorph DM: transverse PZT effect
bimorph
giving rise contraction.
to a curvature.
a givena set of voltages to the b
elongation in one wafer while the second one
showseffect
a corresponding
ThisApplying
creates locally
Bimorph DMs
shapeset
of of
itsvoltages
optical
Bimorphsurface.
DMs
based on DM
the transverse
piezoelectric the
effect. The bimorph concept is de
fect giving rise to3.2
a curvature.
Applying a given
to
thearebimorph
allows controlling
bimorph
concepttoisone
described
in Figure
2. locally an electric field
optical surface. Bimorph DMs are based on the transverse piezoelectric
When a effect.
controlThe
voltage
is applied
electrode,
it creates
d
transverse
elongation
in one
wafer while
the second
oneinduces
showsaalocal
corresponding con
When a control voltage is applied to one electrode,
it creates
locally
an electric
field which
in turn
effectshows
givinga rise
to a curvature.
ApplyingThis
a given
set locally
of voltages
to the bimo
transverse elongation in one wafer while thebimorph
second one
corresponding
contraction.
creates
a
shape of
its optical
surface.
bimorph effect giving rise to a curvature. Applying
a given
set of
voltages to the bimorph DM allows controlling the
shape of its optical surface.
t
l
Figure 2. Bimorph DM concept. Two disks of polarized piezoelectric material are bonded
2. Bimorph DM concept. Two disks of polarized piezoelectricelectrodes
material are
together;
an On
array
ofand
control
is bonded
placed in
between.
top
bottom of this sandwich, a glass plate is g
ectrodes is placed in between. On top and bottom of this sandwich,
a glass
plate is
glued;
one to
is used
as a reflective
surface,
the other
one
isDM
there
athermalize
DM. A
ground electrode
is bonded
deposited
Figure
2. Bimorph
concept.
Two disks ofthe
polarized
piezoelectric
material are
toge
rface, the other one is there to athermalize the DM. A ground sandwich
electrode isand
deposited
between
the
top/bottom
of
the
the glass
platesinare
(courtesy
CILAS).
electrodes
ismaterial
placed
between.
top andanbottom
ofcontrol
this sandwich, a glass plate is glued
Figure 2. Bimorph DM concept. Two disks of polarized piezoelectric
bondedOn
together;
array of
ndwich and the glass plates
(courtesy CILAS).
surface,
the otheraone
is plate
there is
to glued;
athermalize
DM.
ground electrode is deposited bet
electrodes is placed in between. On top and bottom of
this sandwich,
glass
one isthe
used
as aAreflective
Let’s call the length
of theand
electrode
and (courtesy
the thickness
sandwich
the glass plates
CILAS). of one individual wafer, the
one is there
athermalize
the DM.
A ground
electrode is deposited
between
the top/bottom
the length of the electrodesurface,
and the
theother
thickness
of to
one
individual
wafer,
the transverse
elongation
in each
wafer of the
sandwich and the glass plates
(courtesy
CILAS).
is
given
by
∆Let’s call This
the transverse
piezoelectric
coefficient.
c
the lengthwith
of the electrode
and the thickness
of one individual
wafer,This
the tran
Transverse
elongation
∆
with
the transverse piezoelectric coefficient.
corresponds
to a radius
of curvature
Let’s call the length of the electrode and theisthickness
elongation
in eachcoefficient.
wafer
given byof∆one individual wafer,
with the transverse
the transverse
piezoelectric
This corre
.
The
radius
of
curvature
does
not
depend
on
the
electrode
si
.
The
radius
of
curvature
does
not
depend
on
the
electrode
size,
while
the
stroke
depends
on
the
2
2∆
is
given
by
∆
with
the
transverse
piezoelectric
coefficient.
This
corresponds
to
a
radius
of
curvature
2
. The radius of curvature does not depend on the electrode size,
Radius of curvature
2
2∆
diameter
the considered
following
. This
bending effec
. The radius
of curvature
does
not depend
on area
the electrode
size, while
the stroke
depends
on the
of the considered area 2∆
following
. Thisof
bending
effect
is
competing
with
the local
2
4 PZT
diameter
of
the considered
area following
.
This
bending
effect is
4
4
induced
variation
ofvariation
the wafer
thickness
and
itisand
can
be shown
4.2.5ofof[5])
[5])
diameter
theitconsidered
area
following
.ofThis
bending
effect
competing
with
the
local PZT
riation of the wafer
thicknessofand
can be shown
(section
4.2.5 of
the
diameter
of each
electrode
has (section
induced
the
wafer
thickness
it can
be shown
(section
4.2.5
thattha
th
Stroke
4 [5]) that
to bebimorph
atand
least
four
the
wafer
getdiameter
effect.
bebeattimes
least four
times
thethickness
wafer
toan
getefficient
an efficient
bimorph has
effect.
st four times the wafer
thickness
efficient
effect.
induced
variationtoofget
the an
wafer
thickness
it to
can
shown
(section
4.2.5
of [5])thickness
thattothe
of eachbimorph
electrode
to be at least four times the wafer thickness to get an efficient bimorph effect.
It is worth
that the spectrum
of a the
bimorph
deformation
decreases asas
matc
It is worth
noting
thatnoting
thematching
spectrum
of awell
bimorph
deformation
decreases
m
noting that the spectrum of a bimorph deformation
decreases
as
pretty
one
of
the
⁄
bimorph
DMs
excellent
candidates
AO app
atmospheric
It⁄ is worth noting that the spectrum
of a bimorph
deformation
decreases
as ), making
matching
pretty
well
the onecandidates
of the forfor
⁄ (
), making
bimorph
DMs
excellent
AO
aberrations
( applications.
), making bimorph DMs⁄ atmospheric
excellent
candidates
for aberrations
AO
c aberrations (
), making bimorph
DMs
excellent
candidates
for
AO
applications.
atmospheric aberrations (
Credit:array
A. Tokovinin
Bimorph DMs manufacturing process is much simpler than stacked
ones. There is
Ms manufacturing process is much simpler than
stackedDMs
arraymanufacturing
ones. There is process
no need is
to much
manufacture
Bimorph
simplerrows
thanofstacked array ones. There
Bimorph mirrors are well matched to curvature
sensing AO systems
•
•
Electrode pattern shaped to match sub-apertures in
curvature sensor
Mirror shape W(x,y) obeys Poisson Equation
(
)
∇ ∇ W + AV = 0
2
2
where A = 8d31 / t
2
d31 is the transverse piezo constant
t is the thickness
V (x,y) is the voltage distribution
allow for wireless high degrees of freedom DMs.
sections.
Piezoelectric (PZT)
e of stacks of individual plates or disks (see Figure 1). The
• PZT:form.
LeadLead
Zirconate
Titanate
trostrictive
zirconate
titanate Pb(Zr, Ti)O3 (PZT)
re respectively the most commonly used piezoelectric and
electrostrictive
effects
isfor
beyond
the scope of this paper and
• Piezo from
Greek
Pressure
ter 4.2 of
[5] for more
details.
• Material
gets longer
or shorter when you apply V
•
Stack of PZT ceramic disks with integral electrodes
•
Displacement linear in voltage
•
Typically 150 Volts
•
10-20% hysteresis
(actuator doesn’t go back to exactly where it started)
Δx ~ 10 microns
These different kinds of DMs are described in the following se
3.1 Stacked array DMs
Electrostrictive
(PMN)
Stacked array
DMs are using ferroelectrics actuators made o
ferroelectrics material can be either of piezoelectric or electro
• PMN: Lead
and lead
magnesium
niobate Pb(Mg1/3Nb2/3)O3 (PMN) are
Magnesium
Niobite
electrostrictive materials The physics of the piezoelectric or e
will
notlonger
be recalled;
thetoreader
is invited
tofield
refer to the chapter
• Material
gets
in response
an applied
electric
•
Quadratic response (non-linear)
•
Can “push” and “pull” if a bias is applied
•
Hysteresis can be lower than PZT in some temperature ranges
•
Both displacement and hysteresis depend on temperature (PMN is
more temperature sensitive than PZT)
Electrostrictive (PMN) vs piezoelectric (PZT)
Hysteresis PMN<PZT (f(T))
Infamous “S-curve”
Stacked arrays, example
Xinetics/Keck
146mm clear aperture
349 actuators on 7 mm spacing
Kinetics @ Keck
Stacked arrays, example cont’d
Credit: A. Bouchez
Xinetics, 64x64
Palm-3000 DM
Prior to face sheet bonding
Insane cabling
challenges!
Influence function of stacked array
Credit: A. Bouchez
Influence function:
response to one actuator
Zygo interferometer
Influence functions
for Xinetics DM
surface map of a portion of
the mirror,
with deflection
every 4th
• Push on four actuators,
measure
actuator poked
with an optical interferometer
Vertical scale exaggerated!
Stacked arrays, example cont’d
CILAS, 41x41 SPHERE DM
Example of bimorph DM (good match to curvature WFS)
Credit: CILAS
Electrode Pattern
Wiring on back
•
ESO’s Multi Application Curvature Adaptive Optics (MACAO) system uses
a 60-element bimorph DM and a 60-element curvature wavefront sensor
•
Very successful: used on 2 instruments (CRIRES & SINFONI) and for the
VLTI
MEMS (MicroElectroMechanical Systems) DM
@Boston MC
@AlpAO
Electrostatic δ ∝ V2
@Iris AO
Electromagnetic δ ∝ V
MEMS actuation mechanisms
MEMS Actuation Mechanisms
MEMS micro-fabrication
Semiconductor batch
processing technology
Examples of MEMS DM
@Boston MC
@Iris AO
4096-actuator MEMS
deformable mirror:
- 64x64
- 2 micron of stroke
Photo courtesy of Steven
Cornelissen, Boston
Micromachines
-
IrisAO PT489 DM
- 163 hex segments,
each with 3 actuators
(piston+tip+tilt)
- made of single
crystal silicon
- 8 microns of stroke
up to 820 actuators
>10 microns of stroke
@AlpAO
Voice coil deformable secondary mirrors (DSM)
•
•
•
•
(c) Micro gate
Pioneered by U. Arizona
and Arcetri Observatory in
Italy
Developed further by
Microgate (Italy)
Installed on:
• U. Arizona’s MMT
• Large binocular telescope
(Mt. Graham, AZ)
• Magellan telescope, Chile
Future: VLT AOF
Voice coil actuator
(c) Micro gate
F = kBLIN (Lorentz force)
k = constant
B = magnetic flux density
I = current
N = number of conductors
Thin shell and magnet array
VLT AOF thin shell (<2mm thick!)
LBT DSM magnets
Adaptive secondary DMs have
inherently high stroke: no need
for separate tip-tilt mirror!
LBT DSM performance
SR > 80% at H
DSM are crucial to ELT
(c) Micro gate
GMT M2
EELT M4
(c) Micro gate
Pros and cons of DSM
•
•
Pros:
•
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
•
High stroke
Cons:
•
Harder to build: heavier, larger actuators, convex.
•
Harder to handle (break more easily)
•
Difficult to control mirror’s edges (no outer “ring” of actuators outside
the pupil)
Liquid crystal spatial light modulators
ween
el
e acts as
o higher
Nematic liquid crystal
orientation
changes OPD
veloped
the
or by
e
with
electric
field
right. In
se
due to
esults
ng
Measured zero-order diffraction efficiency
~ 90%
(c) BNS
Measured zero-order diffraction efficiency
~ 61%
SLM CONSTRUCTION
Several parameters help define SLM characteristics. Pixel pitch is defined as the center-to-center spacing between adjacent pixels.
Liquid
crystal
spatial light modulators cont’d
describe our reflective
SLM products.
Interpixel gap describes the edge-to-edge spacing between adjacent pixels. Figure 4 below illustrates basic specifications used to
Transparent Electrode
Image Pixels
Cover Glass
Liquid Crystal
VLSI Die
Pin Grid Array Package
Pixels are square and arranged in an XY pattern.
Cross section of a BNS LCoS SLM.
(c) BNS
Polarized light enters the device from the top, passes through the cover glass, transparent electrode and liquid crystal layer, is
reflected off the shiny pixel electrodes, and returns on the same path. Drive signals travel through the pins on the bottom of the pin-
Very high density (512x512)
an electric field between that electrode and the transparent electrode on the cover glass. This field produces a change in the optical
but
slow controlled,
and polarization
sensitive
properties of
the LCchromatic,
layer. Because each pixeltoo
is independently
a phase pattern may be generated
by loading different
grid array package, through the bond wires and into the silicon die circuitry. The voltage induced on each electrode (pixel) produces
voltages onto each pixel.
The problem of dead actuators
Light leaks
=>
contrast killing effect
Summary, cost and scaling considerations
Cost scaling & evolution
•
•
Conventional DMs
• About $1000 per degree of freedom – So $1M for 1000
actuators
• Adaptive secondaries cost even more.
• Replace existing secondary mirrors
• VLT DSM in range $12-14M
MEMS (infrastructure of integrated circuit world) – Less
costly, especially in quantity
• Currently ~ $100 per degree of freedom
• So $100,000 for 1000 actuators
• Potential to cost 10’s of $ per degree of freedom
Cost vs performance
Cost-Performance
Sources
•
A. Tokovinin’s CTIO webpage:
•
http://www.ctio.noao.edu/~atokovin/tutorial/intro.html
•
Claire Max Ay289: http://www.ucolick.org/~max/289/
•
Principles of Adaptive Optics (3rd edition): R.K. Tyson
•
Observational Astrophysics (2nd edition): P. Lena
•
Fundamentals of Atmospheric and Adaptive Optics: P. Hickson (2008)
•
Overview of Deformable Mirror Technologies for Adaptive Optics and
Astronomy, P.-Y. Madec 2012, SPIE 8447-05