ASTRO 302
Lecture 12
AO SYSTEM SCIENCE
1.0 Optimizing an AO system
The Strehl Ratio (obs peak to perfect peak of PSF) is
given by the following sum of wavefront errors:
SR ~ exp(-( sigmaaniso2 + sigmat2 + sigmarec2 + sigmafit2 ))
which can be expanded as:
SR ~ exp(-((theta/thetao )5/3 + (deltaT/tauo)5/3 + (13/N)(1+4n2/N)(lambdaWFS/lambda)2 + 0.54(D/ro)5/3(Ns)-5/6 )))
There are two important cases to look at in detail:
bright
and faint guide stars.
Conclusions:
An AO system optimized for bright guide stars is very different from
one
optimized for faint guide stars.
Above we have a real example
of how the performance of an AO system is effected by the brightness of
the guide star (V=5-16 mag), the readnoise (n=8 or 35 e rms), the
number
of modes corrected (Ns=52 or 80), the integration time (deltaT=0.0036
or
0.01 seconds). This is initial engineering data from the last MMT AO
run.
The observed SRs are close to that expected from theory, but are
somewhat
lower due to 0.02 arcsec rms vibrations in the MMT at ~18 and ~38 Hz.
2.0 Imaging gains with Adaptive Optics
An AO enabled telescope has many advantages:
2.1 Imaging point sources (unresolved objects)
In AO images of point sources (objects that appear unresolved ---like single stars) the flux is is contained within a diffraction-limited core of FWHM= 0.98*lambda/D
So as the size of our telescope
diameter (D) increases:
1) we collect photons over a telescope_area
= pi*(D/2)2 m2 area
2) and we place those photons in
a area of PSF_size = pi*(0.98*lambda/D)2
arcsec2
3) the normalized peak counts of
the central PSF pixel scales as the (1/PSF_size)2 (if SR is constant)
therefore we see that number of photons we have falling onto our central (say 0.020x0.020 arcsec) pixel of our detector will scale as:
#of photons/s = (flux of source) * (telescope collecting area) * (normalized peak counts) * (size of the central pixel)
therefore the flux for a point source can be expressed as:
# of photons/s varies as pi*(D/2)2*(D/0.98lambda)2 or as D4
So an AO equipped 3.0 m telescope will take 16 times longer to detect a faint point source than an AO equipped 6.0m telescope would (assuming the same SR)
Often the SR falls for the larger telescope. A more general expression for 2 telescopes of sizes 1 and 2:
ratio of sensivities(D1/D2) = (D1/D2)4*(SR1/SR2) assuming that both telescopes have the same size pixels (in arcsec on the sky)
example: Say D2 = 3.0 m and D1 = 6.5 m; typically SR2 ~ 60% at 2.2 um and typically SR1~40% at 2.2 at the larger scope (due to poorer fitting error which is typical for a larger scope).
Then we see the 6.5m (even with just 40% strehl) is still 15 times faster than a 3 m scope with 60% strehl.
It is also worth noting that in
the case there is no AO on the 3 m then SR2~0.5% at 2.2 um.
In that case the 6.5m is 1800 times faster than a 3 m without AO
(assuming
as above that both scopes use a 0.02" pixel). Hence we see that most
NIR
imaging of bright point sources is done with AO or HST currently
(especially
in cases where a large field of view is not required).
2.2 Imaging resolved objects
In the case of resolved objects the advantages to AO are less clear.
If the object being imaged has NO structure at or near the diffraction-limit (of the telescope) then there is no improvement in the image as the PSF becomes sharper. This makes sense of course, and in these situations AO correction is of little use.
example: a 2" (arcsec) sized perfectly smooth "galaxy" will be detected equally fast with or without AO.
However, almost all objects, in fact, do have "sub-structure" that is unresolved and therefore benefits from AO correction.
SCIENCE TIP: So if there are point
sources (or substructure) of scientific interest than it is usually
advantageous
to use AO if possible. The bigger the telescope the better!
3.0 At what wavelengths is Astronomical Science currently done with AO?
As the table below shows most AO science is done
between
1-2.5 um currently. (note wavelengths of "mm" in table 1 should read as
microns)
The reason 86.6% of the papers have been focused on science from 1-2.5 microns is for the following reasons:
1) Fitting error:
is given by sigmafit2
=
0.54(D/ro)5/3(Ns)-5/6 then in the case
of bright guide stars:
therefore we need:
Ns > (0.54/sigmafit2 )6/5(D/ro )2 actuators needed (8)
Now if we wish a reasonable maximum SR of 74% then we must keep sigmafit2 to less than 0.3 rad2
Example: In the case of using the K band (2.2 microns) and a D=6.5m telescope (at a good site ro(2.2)=79cm) so (from equation 8):
Ns = 137 actuators at K band (2.2 microns)
Now in the case of visible light ro is much smaller (ro(0.55)=15 cm at a good site) so:
Ns = 3801 actuators at V band (0.55 microns)
Clearly it is much easier to build a 137 element system than a 3801 actuator system! Hence, most AO systems are designed to only deliver decent SR for lambda > 1.0 micron.
An exception to this is the 1000
element system located in Maui. This system was built by the Military
(Air
Force) for imaging low earth orbiting objects. Since many satellites
are
bright they do not mind having a limiting magnitude of V~7 th for their
guide star, since it allows them to work in the visible.
SCIENCE TIP: Strehl Ratios in the visible are very small due to fitting error at almost all telescopes.
2) Thermal background:
Indeed from equation 8 one would
be tempted to use as long a wavelength (lambda) as possible to maximize
the ro (and therefore maximizing the SR). However, there are 2 problems
with going to wavelengths longer than 2.5 microns:
a) the
resolution of the images decreases as (in arcsec; where D is in
microns)
FWHM~0.98(lambda/D)*206264,
(NB: without AO it is fixed at FWHMseeing~0.98(lambda/ro)*206264
) so bigger lambda, lower resolution....
b) the
sky, telescope, and warm optics start to "glow" at wavelengths longer
than
2.2 microns...
It becomes pretty clear from table 3 (above) why there have been very few papers published at L (and none at M band). The reason is there simply too much noise in each image from the thermal background. Indeed, going from K' to L band increases the noise of the image by 64 times, requiring 4163 times more integration time to reach the same detection level on a flat-spectrum source.
However, there are some very cool
targets of great scientific interest (like the cool T~300 K dust disks
around nearby stars, or mature giant gas planets), so if we wish to
image
these objects it might in fact be best to work at M (4.5) or N (10
microns).
The best system for this would be an adaptive secondary like that built
for the MMT.
4.0 A survey of the literature
Popular topics include:
1) looking for faint, cool low mass companions to stars
(like extra-solar planets, brown dwarfs etc.)
2) looking for circumstellar material around young (and
mature) stars (like disks, shells, etc.)
3) looking at binary stars to understand orbits,
masses,
etc.
4) looking at morphology of bodies in the solar system
5) looking at the morphology of galaxies and quasar
hosts
5.0 THE FUTURE
Some fields where the AO systems will continue to do interesting science are:
1) Planetary
science: -asteroidal surfaces, asteroidal Moons, Moons of Giant
planets, clouds of giant planets etc.
2) Stellar
astronomy:
-young
binary stars, stellar clusters, crowded field work etc.
3) Star
Formation:
-young
binaries, circumstellar disks, embedded clusters, nebulae etc.
4) Faint
companions:
-detection of very faint companions to nearby stars, brown dwarf
companions,
white dwarf companions etc.
link here
for
a comparison between a 300 element shack hartmann (on the 10m Keck
telescope)
and a 36 element curvature AO system (on the Gemini 8 telescope). It is
clear that in general higher strehls are better for detecting
companions
at ~0.5" or greater distances -- but inside 0.5" even high strehl
images
become difficult to probe for faint companions. see later in this
lecture
for more details.
5) Extragalactic:-detection
of host galaxies, companion galaxies, morphology, gravitational lens,
interacting
galaxies, the cores of nearby galaxies
etc.
A picture of NGC7469 from the Keck AO system for more
details link here
5.1 PREDICTIONS FOR THE NEAR FUTURE
AO will quickly become the dominant observational technique for the following problems in solar system and galactic astronomy:
A.
60 mas near-IR imaging/spectra of high contrast objects:
Example:
Asteroid surfaces, satellite surfaces, equal magnitude binaries, PAH
structure...
B.
Very faint point source imaging/coronography/spectra near bright point
sources:
Example: Low
mass companions, young exo-planets/brown dwarfs, asteroidal moons,
planetary
moons, extra galactic globular clusters, interacting galaxies...
C.
Imaging/spectra of surfaces that change quickly with time:
Example: all
bodies in the solar system that are resolved, evolved stars, stellar
surfaces,
gravitational lenses...
D.
Imaging/polarimetry/coronography of faint extended structure near
bright
point sources
Example: Circumstellar
disks, debris disks, Ultra compact HII regions, PPNE, Jets/outflows,
QSO
host galaxies...
E.
Imaging/spectra of very crowded star fields/binaries that may be dusty:
Example: Star
formation clusters, Globulars, Galactic Center, starbust clusters,
Giant
HII regions, looking for AGB tip stars and Horizontal Branch stars in
distant
galaxies...
6.0 Artifacts of AO imaging
Although imaging with AO is very powerful there are some tricks to calibrating the PSF
6.1 Calibrating the PSF
It can often be ambiguous what structure is real and what structure is due to the PSF (the image of a point source).
example: In the movie below (hit the "refresh button" to run this movie) we show a series of images of a tight 0.1" binary asteroid. Although it is clear that there are 2 point sources in orbit around each other, each of the individual images have aberrations that distort each image as it is displayed. But it also shows that the PSF is the same for both objects in the field.
It is clear that there is structure in the PSF that
changes
image to image.
The reason for this temporal behavior of the PSF is that ro is changing, the AO correction is changing, and the optical aberrations may also be changing.
Indeed ro may be changing very fast. Typically ro can change by 2x in periods of less than 5 min.
here is some typical seeing data from the VLT
differential seeing monitor at La Sille Chile from last night:
So it is clear that since the PSF is constantly changing it is best to calibrate it. Since often the amount of science we can extract from our AO images is directly related to the degree we can calibrate (and remove) the AO system's PSF artifacts.
6.1.1. Techniques of PSF calibration
1) The most popular approach to calibrating the PSF is to observe a nearby guide star at similar location on the sky, with similar colors and brightness. It is important to observe this PSF star as often as possible (before and after the science target). As well it helps to integrate on the PSF star for the same amount of time as the as the science target was observed.
This can work quite well calibrating the PSF to ~5-10 % accuracy. Often this is all that is required. However, there are cases when the science goals require even better accuracy
6.2 Detection of very faint point sources (extreme AO).
Unfortunately the inner 1.0" of an image is very complex. Each small (~10 nm) sized optical aberration that constructively interferes light in the pupil will produce a very faint "ghost" of the bright guide star. These ghosts are often called "speckles". These speckles are very faint, and due to their chromatic nature, will become very extended at separations greater than ~1.0" from the guide star. Hence speckles can often be ignored for separations greater than ~1.0" from a guide star on an 6-10m telescope (see the Keck image above).
However, if one is interested in detecting very faint objects within 1.0" then it is best to understand the limits placed by "speckle-noise"
Speckle-noise is the noise limit that dominates how close one can image an object next to a guide star. The problem is that the optical aberrations that create "super-speckles" in AO images do NOT disappear and average out over time like speckles produced by the atmospheric aberrations. But once one tries to image a similar PSF star (on a different part of the sky) the flexure of the telescope has changed and the pattern of "super-speckles" is now different (and hence uncalibrated).
See below for example of "super-speckles" in AO
images
of bright guide stars (SR~60%, Ks filter (2.1um), 0.013"/pixels, 60s
exposure)
Above we see how a real companion is easy to detect at a separation of 1.7" with the 8m VLT NACO AO system. However inside 1.0" it becomes much more difficult to detect any faint companions because of the "speckle-noise" floor. The far right hand image shows what an AO PSF looks like for objects 10,000 times fainter (like the real companion). It is hard to detect objects 10,000 times fainter within 0.5" of the guide star.
The bottom curve on the above plot is the theoretical "photon-noise-limited" performance of an AO system. This bottom curve ignores speckle-noise. However, in practice we find speckle noise limits the sensitivity of faint companion detection by >200x for separations <0.5". We also see that since the "super-speckles" are from semi-static optical aberrations, they do not average out over time. At separations of <0.4" a 6 minute image and a 2 hour image are equally sensitive (Close 2000). The only way to go deeper in the inner 0.5" is to use special optical "tricks" like nulling interferometry (the next lecture) or simultaneous differential imaging if there is a sharp spectral feature to exploit (like methane absorption in giant gas planets). Calcite Wollastons are one way of simultaneously making 2 images at once.
This image of the dust around GG Tau was made by use
of a Calcite Wollaston. The wollaston produced simultaneously 2
identical
PSFs with opposite polarization. The difference of the 2 beams removes
the unpolaized light from the central stars to reveal the much fainter
scattered (polarized) light from the dust around the binary (image from
Potter et al. 2003)
6.0 Suppressing Super Speckles
I have developed a few cameras that are specially
designed to supress these
super speckles and let real companions be detected.
By making 4 images at the same time
through 3 different filters, my SDI cameras can
allow the star light to be subtracted from itself
but leave a cool methane rich object alone.
see here
for more about the SDI cameras
here is a real discovery of a very faint
very cool ~900K methane brown dwarf
(SCR 1845 B - Biller et al. 2006)
Note how the SDI device makes idebtical images
of the star's speckles -- but the brown dwarf
changes in brightness in and out of the methane
absorption.
7.0 SKY COVERAGE
A big drawback to AO correction over the whole sky is that you need to have N>n2 to have a low reconstructor error (lecture 6). But we also have to have enough subapertures (Ns~(D/ro)2) to keep the fitting error small. Therefore, there is typically a "limiting-magnitude" (or maximum magnitude) beyond which there is more than a rad2 of wavefront error. This is independent of telescope size (it just depends on ro).
In Francois Roddier's book (Adaptive Optics in Astronomy - which I highly recommend) he has calculated theoretical "maximum magnitudes" (see table below, Roddier's fig 3.10). So the theoretically faintest guide stars possible are around R~17 if you want a SR~30% at K (2.2 um). Note how quickly this rises to a R~13.1 (a 10((17.3-13.1)/2.5) = 47 times brighter guide star) if we need a SR of 30% in the R band (0.65 um). In other words, since ro ~ lambda6/5 you can get the same Strehl on a star 47 times fainter at 2.2 microns compared to 0.65 microns with AO.
There are far more faint stars in the sky than bright ones. The above graph shows your "chance" of finding a field star at a certain distance from any point on the sky as a function of the brightness of the field star.
For example we see there is about a 10% chance of finding a R=15 mag guide star within 20" of our target (at 30o galactic latitude), this increases to 50% within 60".
So the fainter the guide star needed the more likely you are to find one close by.
How close do the stars need to be at K?
If we are willing to have sigmaaniso = 1 rad2
then theta can be as large as thetao. In this case the above
plot shows that if thetao is ~60" at 2.2 microns then
we can see that there is a ~90% chance of finding a R=17.3 mag guide
star
in this large area of sky. So (as is noted in the figure by the "dot"
at
K) it is possible to find nearby guide stars in the K band for good sky
coverage at 30o galactic latitude.
How about the visible (R band)?
In the R band we see thetao is a much
smaller
13.4" (since ro is so much smaller) and the limiting
magnitude
is a much brighter 13.1 mag (since N is smaller -> since Ns is
larger ->
since (D/ro)2 is larger). So in the R band we
need
to find R=13.1 stars within 13.4" of our target! Since R=13.1 is fairly
bright (hence quite rare), we see the sky coverage is much less than
10%
at R band. This is quite different from the >90% at K band!
Conclusion: There is almost no sky coverage for AO at visible wavelengths, but for low Strehls much of the sky can be used at K band.
In theory the best way of increasing sky coverage is to use laser guide stars...
