Adaptive Optics: Beating the Sky. Reduce the Background. We have talked about how to try to study the very faintest objects in the night sky. Obvious stratagies included building the largest telescopes we can; using the most sensitive detectors we can design; and observing as many targets at once as we can. That may seem to be an exhaustive list, but there is one more thing we can do -- namely, we can try to make the target stand out more brightly against the background glow so that it is more efficiently studied. In fact, there are two ways to accomplish this; we will consider them in turn. We can reduce the glow, or we can 'sharpen the image.' If you stand one hundred metres away from me and light a match, I may not even notice the flare of light if it is bright daylight whereas I would certainly see in in the depths of night. The light from the match is inconsequentially bright compared to the enormous numbers of other photons reaching my eyes, either directly from the sun or after they are reflected from other objects in my field of view. Indeed this is exactly why we cannot see stars in the daytime sky! Light from the sun is scatttered to some extent by the molecules in the atmosphere, which is why the sky looks bright. (This process is more efficient for short-wavelength blue light than for longer-wavelength red light. This explains why the sky is blue: see page 305 of your text.) No matter what direction we look in, if it is daytime our eyes are receiving a lot of scattered sunlight, and the faint stars are lost against this uniform background. The contrast is simply too low. Even at night there is a problem: the atmosphere itself glows faintly, partly because of the deposition of energy from incoming cosmic rays and energetic particles from the sun (the solar wind). This general glow is much intensified when there are solar flares which add to the solar wind, after which we see enhanced emissions called the ``Aurora Borealis'' or ``Northern Lights.'' Another contributor to the glow of the atmosphere, of course, is scattered city lights. When you drive at night, you can see the glow of a big city from a long way off! How can we improve on this? The first step is to work at night, so that the scattered sunlight is not a problem. In addition, we can place observatories high up on mountains, or even go into space (as with the orbiting Hubble Space Telescope) so that the atmospheric glow is minimized or eliminated. Even then, however, there is a broad background of diffuse faint light. You may think that astronomers see stars and galaxies as bright points against a completely black background, but this is not right. There are billions of stars and galaxies in the far reaches of the universe, objects which are so numerous in total that there is effectively a whole continuous background of them off in the distance. In other words, we detect light even from the dark regions between the obvious stars. Every object is seen in contrast against at least some background light, an effect which sets an ultimate limit.

Make the Sharpest Images Possible.

If the light from a star is smeared out into a big fuzzy blob, it will not show up very well against an already bright background. But it the light of the star could be focussed into the tiniest, crispest image possible, you would notice it more readily: it would then be a dazzling pinpoint of light easily picked up against the background. So the ultimate goal is to make telescopes produce the very best images they can. There are two factors which limit the quality of images available at the focus of the telescope. The first is the optical quality of the mirrors and lenses themselves. Let me first remind you that the wave nature of light itself presents certain fundamental limitations, at least in principle. But in general, the very largest optical telescopes are limited more by other factors than by these theoretical limitations. Indeed, it is very difficult to make a big modern telescope like the 8-metre Gemini telescope on Mauna Kea so perfect in shape that it will produce an image as good as theory should allow. (The very best mirror ever made is that in the Hubble Space Telescope, and it is considerably smaller.) As a result, the slight imperfections in the mirrors and lenses do indeed contribute somewhat to the less-than-ideal image. But a more important constraint, at least until recent years, has been the limitation imposed by the turbulence in the Earth's atmosphere. You will get some idea of the importance of this if you visualise looking across the desert on a hot day. People and objects in the distance look blurry because of the turbulence caused by the hot air rising from the sun-baked sand and rock. Light coming in from above the atmosphere can be thought of as a series of `wavefronts' (just like a water wave at sea) which enter the telescope and bounce off the curved mirror. The mirror is intended to be of such a shape that the wave is focussed to a single location, and ideally we should get a single sharp image limited in size only by the theoretical constraints imposed by the wave nature of light. This would be the case if there were no atmosphere above us, and the mirrors were absolutely perfect in shape.The actual situation is somewhat different. The air above the telescope is full of little turbulent eddies, just like the eddies and ripples you see in a stream of water, and the incoming wavefronts get deflected and distorted by these effects. This would seem inevitably to smear out a star image into something much broader, thereby reducing the contrast and making the faintest stars unreachable from our telescope. And so it was thought for many years. Recently, however, developments spearheaded by astronomers working at the CFHT have shown that there are ways in which this can be corrected, ways which make ground-based telescopes much more powerful than ever before. How do they work?

Controlling the Sheep.

An obvious partial solution is to go up high on a mountain, which we do, so that we are above as much of the atmosphere as possible. For a complete solution, we can go to space, as with the Hubble Space Telescope which has been placed into orbit around the Earth. But space programs are expensive, and there is a stringent weight and size limit to the telescope you can launch. So let us try to solve the problem from the ground. Each little turbulent cell of air above the telescope makes a bit of the light change direction ever so slightly, and what should have been a single sharp image is actually a broad illuminated patch made up of a whole host of slightly mis-registered smaller blobs of light. (A big telescope is so large that will be quite a lot of these turbulent cells of air high above the mirror, up where the atmosphere is most turbulent, so the image is inevitably broken up into a bunch of blobs.) In a stretch of imagination, the ripples and irregularities introduced to the wavefront of light as it passes through the atmosphere remind me of something like a flock of sheep crossing a field. As they meander along, various individual sheep make random excursions away from the flock and may in fact wander away on their own. Sheep owners counter this with the use of sheep dogs, whose role is very simple: they notice a single sheep starting to separate from the pack and run around the outside of the pack to confront the offending sheep -- they crouch in front of it and `stare' it back into the pack. Can we do something analogous to the separate small blobs of light which constitute our nice crisp star image? Think about the important elements required. We would need: some way of recognizing that a `piece of the image' (a small blob of light, a single sheep) is starting to drift away from the pack (the image formed by the superposed light of all the blobs); we would need to have the ability to force that piece of the image back into place (as the dog does to a sheep); and we would need to be able to do this quickly, so that the star image stays tiny all the time. If the dog takes five minutes to respond to the sheep's random motion, it will be too late. Even if all the sheep tend to stay together on average, which is certainly the case for the starlight (no particular bit of it goes wandering off `into the neighbouring farm' as a sheep might), the uncontrolled flock will be generally straggly rather than a tightly bunched group. So, we need a way of detecting incipient problems, plus a way of correcting them, all at some fairly high speed. Let us consider these elements in turn - but not necessarily in this order.

Our Sheepdog: A Rubber Mirror.

The first thing we seek is a method for forcing an errant blob of light back into the pack. This would be readily accomplished if only we could deform a small part of the main mirror of the telescope, to force the particular blob of light back onto the right path - but only for an instant, because the random wanderings and distortions in the wavefront are constantly changing. In other words, we need a flexible, deformable mirror, and the ability to change and control its shape very quickly and precisely. This is simply not possible with the huge primary mirrors found in modern telescopes. The mirror in the CFHT, for example, is 3.4 metres in diameter, and several tens of centimeters thick; it is made of glass, and quite rigid. Its front surface, the shiny surface from which the light reflects, simply cannot be made to change shape in the required way, or quickly enough to solve the problem. But there is a way. When I discussed the advantages that reflecting telescopes had over refracting telescopes, one of the points I made was that we could insert, as needed, a whole series of other smaller mirrors to change the direction of the light and bring it, say, to some different focal position. (Think back to the coudé focus, for instance: see page 178 of your text.) This realization affords us the solution we need: at some later stage in the beam of light from the telescope, we can insert a small, purpose-built deformable mirror to do the necessary image compensation. Such a mirror is not literally made of rubber, of course, but it is quite flexible -- and small! In the Adaptive Optics Bonnette (AOB) at the CFHT, for example, the deformable mirror measures only a few centimeters across and has 27 separate actuators. (That is, there are twenty-seven little sections of it which can be separately pushed or pulled to redirect the light the correct way.) In this way, we can ensure that each little blob of light gets correctly sent to the perfect focus, so that the star images are ideal. But how will we know which way to deform the mirror? If we push a bit of the mirror the wrong way, we will simply worsen the effects (as if the sheepdog were to chase an individual sheep away from the pack rather than back into it). We need some sort of feedback.

Feedback.

Real life abounds with examples of what a scientist, engineer, or mathematician would call feedback. You often hear the expression `positive feedback' used to mean nothing more than a positive response (like praise) for some action. In its technical sense, however, it really applies to situations in which the response is used to initiate or regulate further actions. For instance, if student evaluations tell me that I am not communicating the course material very well because I am using too many technical terms and too much mathematics, I can respond in one of two ways: I can take this into account in subsequent lectures, and try to use language which is more accessible to the majority of the students; or else I can get indignantly annoyed, and say to myself ``What a bunch of wimps! If they think the course is too technical so far, just wait until I get into the really tough stuff!'' You can see that the outcomes are of diametrically opposed kinds, which we could call positive and negative. Which is which? Well, the first response - my attempt to accommodate the needs of the students - could be called positive because it is what the students wanted in reply to the criticism; but it could also be called negative because it leads to a reduction in the unwanted behaviour. This is really a matter of semantics in human behaviour, although it can be more precisely defined in scientific contexts. (You can also see how unstable or runaway feedback loops might arise! For instance, if I follow the second option, I will presumably generate even more criticism, and consequently become even more stubborn and offensive, perhaps without limit, until the whole class riots in protest. This has not yet happened in Physics 015.)

Astronomical Feedback: Studying the Image.

In the rather far-fetched analogy I presented, the sheepdog has an easy job: a quick glance at the pack tells the dog which individual sheep are starting to drift away from the group, and it can go after those offenders. But, as we will see, the astronomical problem is not quite so straightforward. Let us be very precise about our objectives here. We want to see how the image of the star looks at some instant, and use that information to decide whether and how to adjust the deformable mirror so as to improve the image. In short, we need a feedback loop. How can we arrange this? I don't want to go into this in detail, but let me sketch a general approach which captures some of the spirit of the exercise even if it is not correct in all details. The first consideration is that we could choose to work entirely by trial and error. In other words, we could briefly examine the star image, push one of the actuators to slightly deform the mirror, and see how the image changes. If it gets a little worse, pull the actuator back and move it the other way. In this fashion, push and pull the actuator back and forth until the image is as good as you can make it - all in just a tiny fraction of a second! And then do this for each actuator in turn, in a quick continuous cycle, hundreds of times a second. The real difficulty is to figure out a way of actually examining the instantaneous image of the star, so that we can judge whether our fiddling around improves it or not. Don't forget that our astronomical targets are typically very faint, and we need a very long exposure to get a decent picture at all. And here is the difficulty! We do not have the freedom to look at the image as it is accumulating in our CCD any more than a photographer can peer at the film in the back of the camera to see how the exposure is coming along. Looking at the image means reading out the data, which ends the exposure. It is true that we can read the data out of the CCD whenever we wish. We could, for instance, have a whole series of fantastically short exposures - perhaps a million of them, each a thousandth of a second long (which adds up to about sixteen minutes of total exposure). But each time we read out the data we introduce what is called `electronic read noise,' a kind of interference which degrades the quality of the image, and reading a CCD out quickly makes this problem even worse. Adding up a million brief exposures would never be as good as a long single one (not to mention the difficulty in handling all the data). For that reason, we would prefer to leave the light to accumulate until the very end of the exposure (perhaps twenty minutes later). But then how can we hope to gauge the quality of the image during the exposure? There are two possibilities: When we take astronomical images, we are typically using only part of the light emitted by the star. For instance, we might want to see how bright it is in the blue part of the spectrum. In that case, we don't care how much red light it gives out (and so we use a coloured filter to allow only the blue light to reach our instrument). But rather than ignore or waste the unwanted red light, perhaps we could split it off into some different direction and see how good an image the red light produces (and study how it changes when we deform our rubber mirror). Presumably when the image formed by the red light is as good as we can get it, as gauged by a device called a 'wavefront sensor,' the image formed by the blue light will also be quite good, since both kinds of light pass through the same turbulent atmosphere before reaching the telescope. And we don't mind reading out the image formed by the red light very frequently because we don't want the red image for any scientific purpose anyway. But suppose our object is rather faint (as is often the case). There simply may not be enough photons reaching the wavefront sensor to permit the computers to work out how to improve the image. In this case, you need to hope that your target (a star, or a remote galaxy) has a second, brighter star close to it in the sky -- I mean very close to it, almost right beside it in fact. If it does, that brighter star can be used as a reference. In essence, you fiddle around with the deformable mirror until the image of the reference star is as good as you can make it (and make continuing corrections all through the duration of the long exposure). Since the reference star and the target are close together in the sky, the light from both of them passes through the same atmosphere (mostly), so this works pretty well.

Turn on the Lasers!

There is still a problem. What if your target is faint, and has no bright star near it, nothing to act as a reference? How will you carry out your Adaptive Optics? Amazingly, one answer might be to attach lasers to telescopes, and to create (in a sense) artificial reference stars, using the telescope itself like a searchlight. The idea is this: We fire the laser through the telescope in the upward direction, opposite to the direction from which light ordinarily arrives. The beam of laser light reaches high up into the sky, high enough to stimulate what is called the `sodium layer', a part of the atmosphere about 50-60 km above the ground. This stimulated area emits light which goes off in all directions, including back down towards the telescope. (The sodium atoms in the atmosphere fluoresce in a way reminiscent of what happens in neon lamps.) From the ground, the patch of emission looks like a small spot - an artificial star - and its sharpness and quality depends on how turbulent the air was that it passed through. In other words, it is an ideal reference star for Adaptive Optics. You can see that this solves the problem: no target in the sky is beyond our reach, because we can always make a reference star if nature did not provide one. The techology has been tested, but there are problems: safety: the lasers we use are not particularly strong (not like the industrial lasers used to cut metal) but they would, for instance, temporarily blind airline pilots. It is not a good idea merely to shine lasers into the sky arbitrarily. public relations: many observatories rely on public ordinances which require home owners to keep their lights shielded. It would be very difficult to enforce such ordinances if the mountaintop looks like a laser show! interference: Mauna Kea, like many other observatories, is the home to many telescopes. If one of them is shining lasers into the sky, the performance of the others will be compromised whenever they happen to look in a direction which crosses the laser beam (the scattered light will ruin the observations). In short, the technology is promising, but widespread use may be a long way off.

The Results.

One of the fundamental reasons for wanting such excellent image quality is to improve the contrast of stars against the background glow so that even fainter things can be seen. (It is also interesting, of course, to see finer detail on already bright objects, like the moons of Jupiter.) The CFHT has been a world leader in the area of adaptive optics, and much of the technology and understanding developed there has guided what is being done with the new 8-metre telescopes. On page 185 of the text, you can see an example of the sort of improvement which is attainable, as demonstrated with the CFHT itself. Using the AOB at the CFHT, we have been able to get very 'deep' images of the very centre of our own Milky Way galaxy, images which show many dozens of faint stars which could simply not be seen otherwise. The results can be spectacular! In class, I showed the results of a decade-long study of the changing positions of the stars near the center of the Milky Way galaxy. The motions reveal that the stars are moving in complex orbits, clearly controlled by the gravity of something very massive (about two million times as massive as the sun). But the central object is emitting no light whatever. It must be a black hole! Please note that this exciting discovery would simply not have been possible without adaptive optics. The turbulence in the Earth's atmosphere would have smeared out the images so much that the details of the motions simply would not have been observable. In the last analysis, it is no exaggeration to say that ground-based telescopes can now do many things that we once thought could only ever be done from space, using telescopes completely unaffected by the troublesome atmosphere of the Earth. With adaptive optics, we can 'beat the atmosphere' and get images just as sharp as those provided by the Hubble Space Telescope -- and better, in fact, since we have larger mirrors which have better theoretical resolution to start with and which collect many more photons. But the HST still has an essential role to play in that it can observe light which cannot reach the ground, light such as the ultraviolet wavelengths which are absorbed high in the Earth's ozone layer. We will learn more about such in due course. Previous chapter:Next chapter


0: Physics 015: The Course Notes, Fall 2004 1: Opening Remarks: Setting the Scene. 2: The Science of Astronomy: 3: The Importance of Scale: A First Conservation Law. 4: The Dominance of Gravity. 5: Looking Up: 6: The Seasons: 7: The Spin of the Earth: Another Conservation Law. 8: The Earth: Shape, Size, and State of Rotation. 9: The Moon: Shape, Size, Nature. 10: The Relative Distances and Sizes of the Sun and Moon: 11: Further Considerations: Planets and Stars. 12: The Moving Earth: 13: Stellar Parallax: The Astronomical Chicken 14: Greek Cosmology: 15: Stonehenge: 16: The Pyramids: 17: Copernicus Suggests a Heliocentric Cosmology: 18: Tycho Brahe, the Master Observer: 19: Kepler the Mystic. 20: Galileo Provides the Proof: 21: Light: Introductory Remarks. 22: Light as a Wave: 23: Light as Particles. 24: Full Spectrum of Light: 25: Interpreting the Emitted Light: 26: Kirchhoff's Laws and Stellar Spectra. 27: Understanding Kirchhoff's Laws. 28: The Doppler Effect: 29: Astronomical Telescopes: 30: The Great Observatories: 31: Making the Most of Optical Astronomy: 32: Adaptive Optics: Beating the Sky. 33: Radio Astronomy: 34: Observing at Other Wavelengths: 35: Isaac Newton's Physics: 36: Newtonian Gravity Explains It All: 37: Weight: 38: The Success of Newtonian Gravity: 39: The Ultimate Failure of Newtonian Gravity: 40: Tsunamis and Tides: 41: The Organization of the Solar System: 42: Solar System Formation: 43: The Age of the Solar System: 44: Planetary Structure: The Earth. 45: Solar System Leftovers: 46: The Vulnerability of the Earth: 47: Venus: 48: Mars: 49: The Search for Martian Life: 50: Physics 015 - Parallel Readings.


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