2.0 Optimizing an AO system

From lecture 6 we learned that:

Since:

SR ~ exp(-( sigma_aniso² + sigma_t² + sigma_rec² + sigma_fit² ))

therefore, from equations 3,4,5 and 7 (of lecture 6)

SR ~ exp(-((theta/theta_o )^5/3 + (deltaT/tau_o)^5/3 + (13/N)(1+4n²/N)(lambda_WFS/lambda)²  +  0.54(D/r_o)^5/3(Ns)^-5/6   )))

There are two important cases to look at in detail: bright and faint guide stars.
 

2.1 Bright Guide Stars

We see that for BRIGHT guide stars (N>>n) we can optimize the SR by:
minimizing the fitting error which dominates the residual error
this cam be done by:
  1) building a fast AO system with many actuators (deltaT < 0.001 sec, Ns>1000)

Io is a good example of a bright guide "star" (V~7). The sharpest image is from NASA's Galileo spacecraft. The image to the left of that is a Keck AO image (Ns=320) at 2.2 microns. The image below that is at L band (3.5 microns). Note how the hot volcanoes are "glowing" in the L band image. the bottom right image is without AO. Click here to see a movie of Io in orbit.
 
 
 
 
 
 

2.2 Faint Guide Stars

But in the case of faint guide stars (when N~n) we have to  worry most about the reconstructor error, so to maximize the SR we need to:
minimizing the reconstructor error which dominates when (N~n)
this can be done by:
  1) building an AO system with fewer subapertures (so each subaperture gets as many photons as possible)
  2) integrating as long as possible on the WFS CCD (so N>n², at the risk of somewhat increasing phase lag errors)
  3) minimizing the WFS CCD readnoise (n<3 e rms per readout)

above is a picture of a very faint guide star (V~21,I~17). This star is almost a brown dwarf. Here we used the Gemini/Hokupa'a curvature AO system. With only Ns=36 on a D=8.2m telescope, and with n=0 (since Avalanche PhotoDiodes are used instead of CCDs) very faint guide stars can be used. However, the final SR is quite low (<5%) but this H band image (1.65 microns) still detects a possible companion (which is likely a background star) that is 10,000 times fainter. This detection would not have been possible from the ground without a "faint guide star optimized" AO system.

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.
 

3.0 Imaging gains with Adaptive Optics

   An AO enabled telescope has many advantages:

3.1 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 1/(PSF_size) (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*(pi*(0.98*lambda/D)² )^-1  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).
 
 

3.2 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!
 
 
 
 

4.0 SCIENCE WITH AO

4.1 Young stars, binary stars:

A very rich area of research in adaptive optics is that of binary stars and young stars.

These fields are excellent for AO since they require both infrared observations (to see through the dust around young stars) and high resolution.

Here is a circumstellar disk of dust surrounding a young binary star. Planets may be forming in such disks.
 
 
 

A typical example of how the MMTAdaptive Optics (AO) system can make very sharp images of some young massive OB stars in the Orion trapezium cluster. With AO "OFF" this object appears to be just 2 stars. With AO turned "ON" it is clearly a tight group of 4 visual stars (2 of these are in a tight 0.1" binary, one is the bright guide star, and the other is a rarely seen very faint companion slightly to the right (and 100x fainter) than the bright star). For more technical details about the MMT AO system click here.

Click to see a MOVIE (AVI format, 2.2 MB) of the Adaptive Optics system "closing the loop, opening the loop, then closing the loop" on this target (Theta Ori 1 B). With AO this object appears to be just 2 stars, but with AO turned on it is revealed that the lower "star" is really a 0.1" binary. (Movie Credit: Guido Brusa, CAAO, Steward Observatory)
 

Such images are in the infrared but sharper than the images Hubble can make from outside the atmosphere at the same wavelengths. Typically images made by large AO equipped telescopes will be ~0.050" (20x sharper than a 1" image - which is the best one can hope for usually without AO).
 

4.1.1 Images of star clusters

  Clearly a big field for AO science is in clusters of stars.

   Here is a movie of how faint stars become visible (at the center of our galaxy) when AO correction is applied (Keck AO movie)
 

   Here is an image of a young cluster of stars made from J, H, K' images taken at the CFHT telescope (of the young star MWC1080) see Brandner and Close et al. 2000
 
 
 
 
 
 
 
 
 
 
 
 
 
 

4.2 The surface of the Sun

Another fascinating use of AO is to image the surface of the Sun. These images from the National Solar Observatory in New Mexico are a big improvement over non-AO images (as this movie proves). However, solar astronomers can combine AO and some image processing to pull up the sharpest features (see movie) to make even more impressive insights into the Sun's surface.

Also sun spot movies from the Swedish Solar telescope AO system are also amazing.
 
 
 
 
 
 
 
 
 
 
 
 

4.3 Planetary Astronomy

Studies of other planets in our solar system is also a ripe field of study for AO.
 

Here is a picture of Neptune without AO and with AO at the Keck Telescope
 

For example the planet Neptune has complex methane clouds that can be seen revolving as the planet turns (movie  from the University of Hawaii AO group Hokupa'a images).

An image of Uranus showing the darks rings in the NIR (Keck AO image)
 

Also recent images of Saturn's moon Titan which has a dense methane atmosphere show how this atmosphere can act like a lens as 2 background stars pass behind it (movie from the Mt Palomar PALAO system).
 
 

Also AO has been the only way to detect moons around main-belt asteroids --see Merline et al. Close et al.

However, adaptive optics are not just for the professionals on the largest telescopes. Even backyard telescopes can gain a lot from simple AO systems that cost only a few thousand dollars. Stellar Products builds a simple AO system that stabilizes and corrects the most common wavefront errors. Here is a movie of Jupiter taken in a backyard with a 9 inch telescope using such an AO system.

Click here to see a movie of the large asteroid Vesta (4) in orbit in the narrowband Feldspar line in the J band (1.2 microns). Keck AO movie.
 
 
 
 
 
 
 
 
 

4.4 Planets Around Other Stars

The search for planets outside of our solar system is one of the great new fields in astronomy. In 1995 the first planet around another star (51 Peg) was inferred from radial velocity measurements of the primary. Today there are over 80 such stars that appear to have Jupiter like mass planets in orbit. However, there has not been a single direct detection of light from these planets.
 
 

Above we have an image of a brown dwarf around a nearby star (Mike Liu, IfA, Hokupa'a/Gemini image of 15 Sge)

It would be incredibly exciting to actually image a planet around another star. My prediction is that AO will do just this in the next year.

Already we can detect brown dwarfs around stars (see image above).
 

Brown Dwarfs are somewhere between 75-13 Jupiter masses. They are not massive enough to considered hydrogen burning stars, but they are likely too massive to be considered planets.

We can now (with AO) detect low mass stars and brown dwarfs as companions to stars. Very soon it should be possible to directly detect gas giants around nearby stars. However, it will be much tougher to directly detect Earth-like planets around other stars. This will require great effort, but it might be possible with a future 30 m telescope and very fancy AO correction from the ground... (see R. Angel's upcoming lecture)
 

Above we show some of the first very low mass stars and brown dwarf companions found with Hokupa'a/Gemini AO (see Close, Siegler, Freed, & Biller 2003).
 

4.4.1 AO IMAGING OF LOW MASS STARS:

We have now found that of 39 low mass stars observed 9 have low mass companions. All of these companions could never have been found without AO from the ground. Hence it appears that brown dwarfs form into binaries about 10-15% of the time, but they tend to have smaller separations (typically ~4AU). There are no know cases of low mass binaries with separations greater than 16 AU.
 

The distribution of low mass binaries is 10 times closer than that of more massive binaries
 
 
 

If it is possible to lock on low mass (lower luminosity targets) it becomes easier to detect very faint companions
 
 
 
 

There are even hints of lower mass (planetary mass objects) in some of these images of low mass stars.
 
 
 
 

5.0 WHAT CAN WE LEARN FROM CURRENT AO SYSTEMS?

1) Currently AO has become a commonplace technique at many telescopes.

2) Almost all large D>4m telescopes have facility AO systems either running or close to operational.

3) Since diffraction-limited scopes gain as D⁴ power on point sources there is a clear advantage to AO on large telescopes.

4) AO is now quite a common technique practiced by experts and general IR astronomers.
 
 
 
 
 
 
 
 
 
 

5.1 PAST REFEREED SCIENCE PUBLICATIONS IN AO

below we show a histogram of all science papers published in for purely scientific goals:

We see that AO has rapidly increased in productivity. As new generations of observers are trained in AO and as new (larger) facility AO systems come on-line the number of exciting results steadily increases.
 
 
 
 
 
 
 
 
 

Here we see how different AO systems have had different amounts of success in publishing refereed astronomical papers. Some very simple conclusions can be drawn: the systems that are most sensitive to faint guide stars (PUEO, UHAO) have the most publications.  The Adonis system was the only AO system in the south which made it very productive. Laser guide star systems have not yet solved the "faint-guide star problem".
 

5.2 Other Keys to sucessful AO systems:

location, location, location: The site of the telescope. Most of these papers are produced at the best sites where r_o is largest (Mauna Kea and Chile)

Another key to success is the ability to work from 1-2.5 microns and have a simple User Interface for the operator/astronomer.

Another big advantage is being able to utilize faint guide stars. Currently Curvature AO Systems (CS) can reach fainter limiting magnitudes (R~16-17 at an 8m) compared to Shack Hartmann systems (SH).

Another key is to have access to the southern sky. Only Adonis could operate in the south.

We also find Laser Guide Stars (LGS) are not yet ready for "prime time" despite the enormous amount of work that gone into them. Only 1 published paper (from Alfa) has utilized a laser for pure science. The potential is great however, and so hopefully we soon see LGS science papers as commonplace.
 
 
 
 
 
 

6.0 Imaging the human eye with AO

Images of a human retina (with out AO and with AO) (CfAO image)

Images of the retina at different wavelengths (CfAO image)
 

click here to see some interesting AO work on the human eye at the University of Rochester
 
 
 
 
 
 

6.0 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 sigma_fit² = 0.54(D/r_o)^5/3(Ns)^-5/6 then in the case of bright guide stars:

      therefore we need:

Ns > (0.54/sigma_fit² )^6/5(D/r_o )²       actuators needed            (8)

EXAMPLE:      Now if we wish a reasonable maximum SR of 74% then we must keep sigma_fit² to less than 0.3 rad²

In the case of using the K band (2.2 microns) and a D=6.5m telescope (at a good site r_o(2.2)=79cm) so (from equation 8):

      Ns = 137 actuators at K band (2.2 microns)

Now in the case of visible light r_o is much smaller (r_o(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 FWHM~0.98(lambda/D), 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.
 

7.0 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
 
 

8.0 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.
    5) Extragalactic:-detection of host galaxies, companion galaxies, morphology, gravitational lens, interacting galaxies, the cores of nearby galaxies
etc.
 
 
 
 

8.1 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...