Preprint
UCRL-JC-144864
Adaptive Optics Control
Strategies for Extremely
Large Telescopes
D.
T.
Gavel
This article was submitted to:
SPlE
(The International Soceity for Optical Engineering)
San Diego, CA.,
July
31
-
August
5,
2001
July 26,
2001
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Adaptive Optics Control Strategies for Extremely
Large
Telescopes
Donald
T.
Gavel
Lawrence Livermore National Laboratory, Livermore,
CA
ABSTRACT
Adaptive optics for the 30-100 meter class telescopes now being considered will require an extension
in
almost
every area of A0 system component technology. In this paper, we present scaling laws and strawman error budgets
for A0 systems on extremely large telescopes (ELTs) and discuss the implications for component technology and
computational architecture. In the component technology area, we discuss the advanced efforts being pursued at the
NSF
Center for Adaptive Optics (CfAO) in the development of large number of degrees of freedom deformable
mirrors, wavefront sensors, and guidestar lasers. It
is
important to note that the scaling of present wavefront
reconstructor algorithms will become computationally intractable for ELTs and will require the development of new
algorithms and advanced numerical mathematics techniques. We present the computational issues and discuss the
characteristics of new algorithmic approaches that show promise in scaling to ELT A0 systems.
1.
INTRODUCTION
Serious discussion is now taking place concerning the construction of 30,
50,
even
100
meter optical telescopes. Certainly
such monumental projects will require the most advanced technologies in structures and optical fabrication. Designing
adaptive optics systems for telescope apertures of this size presents its own set
of
challenges. Some of these challenges are
matters of cost and
scale
of
components, i.e how do we build deformable mirrors, wavefront sensors, etc. with numbers
of
elements that scale with aperture area without incurring enormous costs
or
making the system physically too large.
Additional challenges are in maintaining reliability and observing efficiency
in
the face of the greatly increased system
complexity.
We can start the discussion with
a
broad-brush overview
of
the
A0
system concepts for extremely large telescopes (ELTs)
and, from well-known scaling laws, determine the requirements for basic system components. We then consider the state of
the
art
in these component areas and
ask
if rates of technology development will meet the ELT timelines.
2.
A0
CONCEPTS
FOR
ELT’S
A
preliminary design
of
a
30-meter telescope
is
being pursued in a collaborative effort by the University
of
California and
California Institute of Technology. The concept is
a
segmented mirror primary
/
monolithic secondary in a Ritchey-Chretien
design, essentially
a
scaled-up version of the Keck IO-meter except that the segments are smaller to save on fabrication costs.
Adaptive optics systems can be tailored to the wavelength band, instrument, and observing program. Here are four baseline
systems:
1.
Low-emissivity, low-order adaptive and active optics for imaging in the
5
-
20+
micron band.
2.
Low-order, high sky coverage, single natural guide star system for infrared astronomy in the
2
-
5
micron band
3.
Tomographic AO: multiple deformable mirrors at atmospheric conjugate layers, multiple guide stars for high sky
coverage infrared Astronomy to
1
micron. This
is
good for extragalactic astronomy and probing dust obscured star
forming regions.
“Extreme” AO:
a
high Strehl, narrow field adaptive optics system targeted toward probing the space close to bright stars
in the near
IR
-
this would be used in the direct detection
of
extra solar planetary systems, dust disks, etc.
We’ll focus
our
attention in this paper mostly on systems 3 and
4,
since they present the most interesting technological
challenges.
Other large telescope projects may follow along similar baseline A0 paths. At this stage in the development
of
the A0
knowledge base however, we can start to hypothesize interesting “deployments” of A0 systems that depart from the
traditional.
For
example, one can envision building
A0
systems into each instrument package. If the components can be
made small enough, the entire A0 system could be put in
an
camera IR dewar, which reduces the thermal emissivity
4.
significantly. Infrared wavefront sensors are a distinct possibility
in
the near future
as
IR
sensor arrays become faster and
lower noise. There are
two
benefits to sensing in the
IR:
first natural stars tend to be brighter at near-infrared wavelengths,
thus increasing the sky coverage, and second, there is some benefit in the wavefront error budget
as
Hartmann spots become
dieaction-limited (see section
3).
We can also imagine incorporating the understanding
of
atmospheric physics and the understanding of the dynamics of the
A0
system into process of doing
A0
astronomy. There
is
an important ongoing effort to understand the nature and stability
of the
A0
point spread function. Data from on-site seeing instrumentation and telemetry from the
A0
system itself will be
combined to produce estimates
of
the point-spread function simultaneous with each observation. Perhaps with advances in
the modeling, we will have the ability to
predict
seeing in advance, and
so
schedule
A0
observations accordingly.
k30
m
WF
error
Atmospheric
fitting
nmF
=lU,W
64
WF
3ensor
noise
mv
=
10
m
3.
ERROR
BUDGETS AND SCALING
LAWS
D=lW
m
WF
mar
Atmosphaic
fitting
nlxl~
=90,000
64
WF
mmr
noise
mv
=
10
69
Simple strawman error budgets
for
ELT
A0
systems can be worked out for the sake of illustrating the component
requirements. In order to produce reasonable Strehl images, say
S=0.5,
the total wavefront error must be kept to under about
u7.5
rms.
We use the Marechal approximation
S
-
exp(-ot}
(o
given in radians) to relate wavefront error to Strehl. This is
about
130
nm at
1p
wavelength. Some of this error budget of course must be given over to the uncorrectable
or
unmeasureable parts of the optical train (non-common path errors). More of it must be given to wavefront aberrations caused
by the telescope optics, for example, segment phasing, tilt, and placement, which, although partially corrected by adaptive
optics, introduce spatial
or
temporal frequency components that are not completely corrected. Finally we are left with what
the atmosphere gives us.
For
this there are well-known scaling laws. Table
1
gives representative error budgets for 30-meter
and 100-meter apertures. They include three terms: DM fitting error, i.e the limit due to finite spatial frequency
of
the
wavefront sensor/corrector, measurement error, which is the limit due
to
noise in the guidestar detection process, and servo
error which is the limit due to finite temporal frequency tracking of the wavefront by the closed loop
A0
system. We neglect
for now the complicating additional terms such
as
cone-effect with the laser guidestars, anisoplanatism, and the like, since
they depend in
a
more complex manner on the particulars of the observation, imaging field, and multi-conjugate
A0
geometry. Suffice it to say that the cone effect error would dominate in single laser guidestar
A0
system on a 30 meter
telescope. The multi-guidestar tomographic reconstruction is required to bring the cone-effect term down to size, but at the
expense of introducing other small terms that depend in complicated manner on the field angle, brightness and position of
auxiliary natural guidestars.
Sen0
bandwidth
fa
=
335
Hz
73
114
nm
Servo
banWidth
fa
=
335
HZ
73
RSS
119
nm
Table
1.
Representative error budgets for
A0
systems on ELTs with
an
8’th magnitude on-axis natural guidestar
Scaling laws
for
the
rms
wavefront error contribution
of
each of these terms
is
Atmosphere
fitting
-
(d/r~)~‘~
WF
sensor
noise
-
In(D0F)
be’”
fsiM
dP
rg(’-p)
Servo
bandwidth
-
f
-516
s
Where d is the
DM
actuator spacing,
ro
is Fried’s seeing parameter
(-50
cm at
1
micron at a good astronomical site),
DOF
is
the number of degrees of freedom on the DM, b
is
the brightness
of
the guidestar
(-10
),
and
fs
is the wavefront
measurement sampling rate.
p
is
an exponent in the wavefront measurement error term which depends on
ro
at the
wavelength of the wavefront sensing. For d
>>
ro,
where the guidestar size
is
dominated by seeing, p
=
0.
In this regime, an
increase in subaperture size increases the number of photons but simultaneously degrades the spatial sampling of the
wavefront (areas of the aperture effected by individual slope measurement errors are larger).
For
d
<<
ro
where the guidestar
size is dominated by difiaction, the exponent approaches p
=
-1.
In this regime the diffraction-limited guidestar spot gets
smaller with subaperture size, improving the centroiding. Present day
A0
systems use visible light and subapertures are
rn
J2.5
typically larger than
To,
a regime where there is no first order benefit to increasing subaperture size. Future A0 systems may
likely use infrared wavefront sensors and larger subaperture sizes would provide a benefit to the error budget that trades
against the atmospheric fitting term.
We can now write down the “technology scaling laws” that relate difficult cost
or
difficulty factors to telescope size.
Certainly, to keep the atmospheric fitting error fixed, the number
of
deformable mirror degrees of freedom must increase with
telescope diameter squared, and along with it the size of the wavefront sensor array
DOF
-
D*
Secondly, to keep
up
the wavefront sensor read rate, the pixel readout speed must increase correspondingly
Finally, if we use the standard least-squares reconstructor algorithm, where we need to calculate commands for each of the
degrees of freedom given each of the wavefront sensor slopes with a
fill
matrix-muliply, the computation rate scales with
FLOPS
-
f,
D4
4.
COMPONENT TECHNOLOGIES
4.1
Deformable mirrors
The largest “conventional” deformable mirror (one using piezo-transducers) had on the order of 2000 actuators. Buttable
monolithic arrays of transducers are under development by Xinetics, inc. that may exceed this number, but still scale
in
cost
on the order of
$lk
per actuator
as
has been the case
for
a number
of
years with these types of mirrors. Two -900-actuator
mirrors are in use today (on the AMOS 3-m telescope on Haleakela and the 3-m at Starfire optical range). The Keck A0
systems use 349 actuator mirrors,
as
does the Mt Palomar 5-m telescope
A0
system and the Mt Wilson 2.5-m.
MEMs
(micro glectro-mechanical device) technology is a promising wave of the future, both in terms
of
cost per actuator and
scalability to very large numbers of degrees of freedom. There small size is also attractive from the standpoint
of
overall A0
system size, but too small presents a problem of A0 system field of view. This is because the beam demagnification from
ELT aperture (30-100 m) to MEMs (-lOmm, say) would lead to and extreme magnification of field angle. Limiting
incidence angles on the MEM to 45 degrees say would only result
in
an arcminute field on the 30 m and
20
arcsec on the 100
m.
The push
is
to make
100
and
200
mm size MEM devices
for
astronomy. A number of such devices technologies are
under development
in
a collaboration lead by the Center for Adaptive Optics.
A
144 degree-of-freedom,
3
x 3 mm device
produced by Boston Micromachines has recently been tested
in
our
laboratory.
A
1000 actuator device is due to be delivered
later this year. The cost of these devices is roughly $20 per degree of freedom.
The requirement for multi-conjugate adaptive optics (MCAO) on the 30-meter telescope is 10,000 degrees of freedom.
Extreme AO, with 10 cm subapertures on the 30-meter, will need upwards of
100,000
degrees of freedom. This would be
possible on a 200 mm MEMs device with 0.6
mm
actuator spacing, which is‘a reasonable extrapolation for this technology
over the next 10 years
or
so.
A 100-meter telescope needs this size device for routine MCAO (scaled to 30 cm subapertures).
4.2
Wave front sensors
Wavefront sensors present another dimension of challenge for astronomical adaptive optics. In recent years the push has
been toward larger, faster, and lower noise CCD arrays for visible light wavefront sensing. The 80 x 80 CCD-39 by Marconi
Applied Technologies (formerly
EEV)
has 3 electrons read noise and is a choice for the Gemini MCAO system.
MITLincoln Labs has developed 3 electron 64 x 64 (used at Keck and Lick) and 128 x 128 (used at Starfire Optical Range)
CCDs that read
as
fast
as
1500 frames per second.
At this point, lower noise may not necessarily be the goal; the photon noise from the guidestar will dominate assuming on the
order of 100 detected photo-events per subaperture per frame will be necessary for reasonable atmospheric correction. The
big issue (for big telescopes) is size and readout speed. The 128
x
128 CCDs with 2 x
2
pixels per subaperture, and no pixel
guard band, can accommodate
up
to 4000 subapertures. 30-meter MCAO will need
10,000,
so
this requires at least a
200
x
200
array. Furthermore this array must read out at the standard, say
500
Hz, frame rate
for
correction in the IR. Depending
on the parallel output-port architecture, this may not require increased pixel read rate over existing devices.