TMT Blog

Future Mariners: Astrometry with TMT Part 2

In Part 1 of this article, I described astrometry and why it's such an important part of astronomy. Now, we're going to look at how TMT will perform astrometry to a new degree of precision.

 

TMT's Astrometry Challenge

TMT will have to satisfy an exacting astrometry requirement. In assessing astronomical separation, TMT will have to achieve the equivalent of measuring the distance between two boulders about as far apart as the Grand Canyon is wide—but the boulders are on the Moon, and the measurement is being taken from Earth. The measurement can't be off by more than a couple of centimeters.

Astrometry is really hard to do to this level precision. To make it happen, we're going to need to get rid of extraneous information that enters, or is built into, the telescope, and invites inaccuracy—things like whirling caused by the Earth's rotation, blurring caused by our atmosphere, and distortion caused by imperfections in our instruments.

Earth’s Rotation

Much of modern astronomy focuses on very faint objects, and we need to stare at those objects for as long as possible to gather enough light from them to make images for study. Obviously, we can't make the Earth stand still during these long exposure times. When we observe with a ground-based telescope, such as TMT, the Earth’s rotation makes the stars look as if they are drifting in the direction opposite the rotation.  We’ve probably all seem images like the following, taken at night with a long exposure. This particular image shows a telescope I first visited when starting my work on the Atacama Large Millimeter/Submillimeter Array, in Chile:

Of course, the stars and galaxies out there actually are moving across the sky, but they're so far away that their motion is much smaller than the effect of the Earth’s rotation. So, the Earth’s rotation creates the impression of additional motion, and it’s that additional motion that we want to eliminate. To compensate, we move our telescope at the same speed as the Earth’s rotation, but in the opposite direction. Photographers and cinematographers use something like this technique when taking pictures of a moving object.  If they want the moving object to be in focus, they track it with the camera.  The background blurs, but the object is in focus. 

TMT will have such precision pointing that it will be able constantly track an object across the sky while factoring out even very tiny rotation effects on short timescales. Our telescope structure is designed to point better than 0.6 arcsec, equivalent to tracking a soccer ball from about 1.4 km (about a mile) away. This means we'll be able to measure the position and movement of only the object we're studying, rather than a mix of that object and our own planet. 

Earth's Atmosphere

When making precise astronomical observations, we need superb image quality. If you're familiar with this blog, you will have noticed that astronomers don't like to settle for mediocre-quality images. We always try to find ways to make our images as clear and accurate as possible, so we can learn the most from the objects we are studying.

One challenge when working from the Earth’s surface, even at the top of a mountain, is that we have to look through the atmosphere. The atmosphere is turbulent, and turbulence blurs images. We therefore have to correct for turbulence in order to get the best possible image quality. I've written a two-part article in this blog on adaptive optics. For more on the basics of adaptive optics and how adaptive optics will be implemented on TMT, take a look at that article.  But even the best adaptive optics system can't neutralize all of the optical effects of turbulence. We're still left with some residual turbulence, which slightly distorts the position of the image at which we're looking. As a result, the same object will appear at very slightly different locations on-sky during different exposures.

Imagine we make an image, centered on our crosshairs, and get the following apparent location of a star, after we have compensated for the effect of the Earth’s rotation:

 

 

 

 

 

 

 

 

Then we take another exposure, which gives us this apparent location of the same star, again after compensating for the Earth’s rotation:

 

 

 

 

 

 

 

 

The perceived location is now different because of the residual turbulence in our atmosphere, even after adoptive optics correction. So, even beyond adaptive optics, we still need ways of dealing with the residual effects of turbulence. We do that by taking lots of images of an object, and then averaging out the information on where that star appears to be located. In the example above, the same object appeared in slightly different locations on sky during different exposures.  If we take, and collect together, many exposures of the same object, here’s the kind of thing we might get:

Statistically, most of the apparent positions will fall around a certain spot, which we can then consider to be our most probable location of the star, further minimizing the effects of turbulence on our astrometric accuracy.

Optical Distortion in our Telescope and Camera

Physical imperfections in our observatory mirrors, lenses, and their supporting structures prevent us from directing light precisely where we want it to go; we call this optical distortion. Distortion can dull the sharpness of an image, which in turn can cause errors or imprecision in where an astronomical object appears to be in the sky.  Because of distortion, we might not just get blurring. We might actually see an object in the wrong place compared to where it really is. So we need to reduce distortion as much as possible.

Unfortunately, we can’t always bring distortion down to the required level.  We're stuck with whatever tiny imperfections may be present in the materials that make up our mirrors and lenses, and the mechanical tolerances in the way each item is mounted. Nonetheless, we can use an elegant workaround. We don’t always need to reduce the distortion to the required level; we only need to know what the distortion is to the required level of precision.

To do this, we use “field stars” to help us figure out—and factor out—the distortion. A field star is one we can see in the same exposure with our astronomical object of interest. Thanks to earlier astrometry efforts, we already know the actual, exact positions of many astronomical objects, and those positions have been carefully cataloged. (More about star catalogs in a moment.) This means we can usually look up the exact, actual positions of at least some of the field stars in our image, and use the information we find to calibrate out distortion.

If this approach sounds familiar, perhaps you recall a similar tactic used in adaptive optics. In the article on adaptive optics, I explained how we use "guide stars" to help us understand and compensate for the effects of something we wouldn't otherwise be able to measure: atmospheric turbulence. In astrometry, field stars are used to deduce something else that can't be measured directly: the distortion being caused by flaws in our optical equipment. So, in both adaptive optics and astrometry (and in many other areas of science and technology), we use extrapolation to help us build our knowledge.

Here’s an example of how we can use field-star-extrapolation to factor out something called pincushion distortion. Imagine a cushion, with equally spaced horizontal and perpendicular lines on it. We start with the cushion flattened out. It looks like this:

 

 

 

 

 

 

 

You can see how the distance between adjacent lines remains constant.  The "cushion" looks like a flat grid of squares. Now fluff the cushion, and the grid looks like this:

You can see how the distances between the lines are now different—the pattern of perpendicular lines is distorted.  In optics, this is pincushion distortion, where previously straight lines along the edge of a lens now bend in toward the center.

 

 

 

 

We want to determine the location of an astronomical object of interest, say a particular galaxy (NGC 1300 in this case).  We take a photo through our telescope and camera. Unfortunately, we have some pincushion distortion in our optics. But fortunately, in the same image with that galaxy, are a number of other stars, which we can make use of as so-called field stars.

Because we have a distorted image, we reverse-engineer it, taking into account where we should be seeing the field stars whose precise locations we already know from our catalog. We correct the apparent positions of those field stars, and apply the correction to the rest of the image. This allows us to figure out what the location of the galaxy actually is:

Using our workaround, although we couldn't flatten out the cushion (that is, remove the distortion from the telescope's lenses, mirrors, etc.), we could nevertheless work the distortion out of the image, using field stars and math to extrapolate the galaxy's true position.

Astronomers have now mapped and cataloged the locations of field stars in as many different directions as possible, to increase the likelihood that there will be field stars of known location close enough to astronomical research objects to compensate for the effects of optical distortion. As you can imagine, it is much more efficient simply to look up information on the sky surrounding our astronomical object of interest than it would be to repeat all the research on that section of sky.

How Do We Know the True Position of the Field Star?

From the last section, you might wonder how people determined the exact positions of field stars to begin with, so that they could be conveniently cataloged for use by later observers. The answer is little by little, piece by piece—just as with the cartographers of old we talked about in Part 1 of this article.

The first astrometrists (a word I just made up) did their work millennia ago. Ancient civilizations created maps of the night sky with constellations. Just as with ancient maps of the Earth, these maps were approximate. But they contained the brightest stars and defined the positions of these stars and separations between them, and thus were the result of an astrometric process. In time, and over many generations, astronomers produced better and better maps of the objects in the sky.  One of the most notable efforts was that of Tycho Brahe who, in the 16^th century, recorded the most accurate and complete catalog of naked-eye sky maps at that point in our history. Interestingly, he chose not to make use of the telescopes that were available at the time because their optics were of such low quality, but his work was nonetheless so valuable that his data were used by Johannes Kepler to derive the laws of planetary motion.

As telescopes improved, more and more stars could be observed in between those previously known. Star by star, object by object, people were able to measure and catalog the things they discovered in the (apparently) empty gaps in between the known stars.  As this process has gone on, fainter and fainter field stars have been made available for astrometrists. That is the legacy on which we’ll build when we do astrometric observations with TMT: using the existing measurements from previous observations as references (field stars) for the even fainter objects we will be able to observe.

There’s a particular type of object that we often use to populate our reference sky. As you know, many objects astronomers study are so far away that their light takes hundreds of millions of years to get here, and those objects appear incredibly small and not very bright in the sky. But far away doesn’t always mean dim. Some objects, such as quasars, are far away, but nonetheless very bright in the sky. Objects that are both bright and far away are particularly useful as points of reference for two reasons. One: bright objects are easier to see. And two: faraway objects move across the sky so minutely that after we subtract out the rotation of the Earth, we can regard them as essentially fixed in place, which means we have one less variable to worry about. Our modern coordinate frameworks for astrometry strive for as much precision and accuracy as possible, and quasars therefore give us reliable markers on the sky, to complement our coordinate system.

TMT's Astrometry Ambition

TMT is expected to make path-breaking discoveries in a number of scientific areas, including astrometry. Just to give one example, we’ll use TMT to observe, with extreme precision (recall the astrometry requirement I touched on before), the motions of stars around the centers of galaxies. We expect this to help us find and map the exact locations and masses of additional supermassive black holes.

To make these exciting new discoveries, TMT will employ the approaches I've just described, and there has been recent progress on many fronts. Here are three that I want to highlight for the moment.

TMT’s Adaptive Optics System

For our adaptive optics system, we have started the final design review process for our dedicated Narrow Field InfraRed Adaptive Optics System (NFIRAOS). Moreover, our Infra-red Imaging Spectrograph (IRIS) has kicked off its own final design phase. More on these in future dedicated blog entries.

TMT’s Primary Mirror Segments

TMT's large primary mirror—the thing that most sets it apart from existing observatories—means we’ll be able to collect lots of light from even very faint objects. Imagine trying to put together a puzzle by candlelight, and then suddenly having not just another candle, but an entire chandelier to illuminate the puzzle pieces.  The more light we can collect, the easier it will be for us to see what goes where. The large size of TMT’s primary mirror also means it will be easier to zoom in on objects in the night sky that appear very small. It's as if, doing our puzzle, we could study each individual piece more clearly, and more easily see where it fits into the larger collection of pieces already joined together.

Much has happened since I last reported on our primary mirror optics program. Our colleagues in Japan have sent lots of glass to the United States: here’s a panoramic image of our storage facility in California. Each wooden crate contains one circular blank piece of glass, which will be polished, then cut from a circular shape to a hexagonal shape, to make a mirror segment. You can see we don’t have much floor space left, so we're leasing additional floor space for the next shipment of glass that will arrive later this year. In parallel, our USA optics contractor is ramping up to start polishing this glass next year.

Our Japanese colleagues have sent practice pieces of full-size glass to the teams in China and India that also will polish segments for TMT’s primary mirror. I reported recently on the work in Nanjing, and here’s a new photo of their polishing setup, which is all coming together nicely:

Finally, here are some updated photos of the Indian optics facility in Bangalore.

New Star Catalogs

Science is a collaborative effort, and when we use TMT for astrometry, we'll have access to the most recent and accurate star catalogs available to the broader astronomical community. These catalogs contain the latest and most comprehensive information about where field stars truly are in the sky. One of the most important catalogs comes from The European Space Agency, which has launched the second of its dedicated astrometry missions, the Gaia Space Telescope:

Here’s Gaia’s latest map, with data on the positions and motions of some 1.7 billion stars, and which will be enormously valuable in locating field stars for other observatories such as TMT:

In Closing

Mariners and cartographers of old had to figure out where things were on Earth.  These individuals started with vague outlines and vast areas left blank, or filled with fanciful imaginings. But each successive generation learned more, developed more sophisticated techniques for observing, measuring, and depicting the world around them, and built on what earlier explorers had learned. And eventually, people were able to map the entire globe to a high degree of precision and even pinpoint locations on Earth from space. 

In astrometry, our techniques for mapping the heavens are essentially an inspired and creative extension of same techniques explorers have long used on Earth, but without the advantage of sailing to the places we're trying to map. Still, just like the explorers of old, astronomers today are piecing together the puzzle that eventually becomes the map of the cosmos, bit by bit, building on what's been learned before.  TMT is a key part of this grand exploration and promises to expand our knowledge of the Universe in ways we might not even be able envision today.

References

Matthias Schöck, Tuan Do, Brent Ellerbroek, Luc Gilles, Glen Herriot, Leo Meyer, Ryuji Suzuki, Lianqi Wang, Sylvana Yelda, “Thirty Meter Telescope Astrometry Error Budget”, Proceedings of the SPIE, Volume 9148, id. 91482L 13 pp. (2014). DOI: 

10.1117/12.2057089

Acknowledgement

Many thanks to my colleague Matthias Schöck, TMT System Scientist, for helping with this blog entry.