The bad news for severe weather geeks like me is that not every night can have a thunderstorm. So we need to find things to look at in the sky when there's no clouds or lightning to capture our attention.
Truth be told, I was an astronomy geek long before I became a weather geek, but my interest in astronomical observing tended to be visual. I had spent vast amounts of my youth connecting various cameras to my supply of telescopes, but the results tended towards blurry images and long waits at the photo developers to see what I'd done wrong a week earlier.
But last Christmas, my son talked me into buying a T-adapter to connect his Nikon DSLR to one of my telescopes. And since then, we've been hooked on astrophotography. And it turns out that taking good pictures of celestial objects is easier than one might think, once a few basic principles of "what is signal?" and "what is noise?" are understood. And once we understood these, our photography efforts improved greatly, as the following image shows.
That image is of M31, the Andromeda Galaxy. It was taken with a box-stock bottom-of-the-line Canon digital camera (the 1000D), through a small telescope (an AstroTech AT66) that really isn't much more in terms of its optics than half of a pair of really good binoculars. The mount used to guide the telescope can be described as "hopelessly inadequate for the job", yet the picture's quality speaks for itself. So how did we get such a fine image from such simple equipment?
As SST/TA's resident Nassim Nicholas Taleb fan, I tend to think of this question in terms of Taleb's dichotomy of mediocristan and extremistan. Mediocristan is the world of statistical variation we are used to, where distributions of such parameters as height and IQ live. Variations in this world are captured reasonably well by Gaussian (i.e., bell-shaped) probability curves, with symmetrical statistical distributions about some easy-to-determine mean (average) value.
Extremistan is where we find those low-probability/high impact entities that Taleb calls Black Swans. This parcel of intellectual real estate is characterized by wildly different characteristics from the norm, so that terms like "average" don't help much in understanding overall tendencies, and where much of the domain of interest is as interesting as watching paint dry, so that only rarely are truly spectacular results found.
Here's a good example of how these astronomical prizes are found: this image is taken in the direction of the heart of our galaxy, and two especially interesting objects pop up there, the Lagoon Nebula in the south (down) and the Trifid nebula to the north (up). Note that there's lots of celestial real estate that's full of stars, but that the bright nebula are rarer in this view, even though this direction for our observation is about as rich an area as we'll find at this end of the universe.
And it turns out that this is a pretty good approximation for looking at the night sky. If you get out under a good dark sky far from any city lights, and examine the heavens with a substantial pair of binoculars, you'll soon find that most of the sky is populated with just a bunch of relatively nondescript stars, but some of it has some more interesting features, e.g., where the Milky Way traces the shape of our own galaxy. And if you use more powerful optical aid, then you'll soon learn that just pointing a big telescope at random generally leads to small fields of view that have some stars in them, but nothing all that interesting.
The key word in that last sentence is "generally". Because if you know where to look, then amazing things can be found, e.g., galaxies, nebula, clusters and such. These sights are rarer, and their signals do not lie in mediocristan, but live squarely in extremistan, because they run the gamut from small clusters of like-minded stars, to the remnants left over from supernova explosions, to stellar nurseries where new suns are being born, to clusters of galaxies that defy comprehension in their sheer scale.
But the problem is noise... because whether you're looking at these extremistanistic signals or taking pictures of them with expensive imaging equipment, there's noise found in the optical train, either in your own eye (which is notoriously noisy in the dark) or in your camera. And this noise makes detection of the beautiful signals difficult or impossible.
Luckily for the astronomy geek, the laws of statistics can be used to fix this problem, so that we can use low-cost optical and camera equipment to gain high-value images of celestial objects. The key is appreciating that noise lives in mediocristan, and in particular, it has a statistical distribution that has mean zero, and that is essentially Gaussian. What this means to us is that if we take a whole bunch of images of the same object, and then average them, the signal persists while the noise dissipates.
And then we get better results than we deserve.
Here's an example, taken at 4 am last week, just as the winter constellation of Orion was rising right before sunrise. This first image is a 30-second exposure at high gain from my Canon XS camera taken through an old-school Celestron Schmidt-Cassegrain telescope, and we can see that something interesting is going on here, but exactly what is not yet obvious.
The compound stellar system known as Trapezium is visible near the center of the nebula, and there are hints of interesting color appearing in the frame, but we really can't see much of anything in particular. But if we crank up the gain in the image, more hints appear of structure and color, but unfortunately, they appear along with an awful lot of noise, as the next image shows.
This is an improvement in terms of seeing the bigger picture of this nebula, but we can do better by taking more exposures, and then adding them up and dividing by the number of exposures, so that the signal persists, but the noise tends towards its average value of zero. Then we can easily see the structure of the Great Nebula in Orion emerge in the next image of this sequence:
So the key here is to stack up a sequence of not-so-interesting noisy images, so that we can extract a single relatively noise-free picture by taking advantage of the fact that what we seek is found in Extremistan, and what we wish to disappear lives in Mediocristan. Thanks to that simple fact, we can readily keep what we want and lose what we don't.
And this statistical magic is not confined to big bright objects like the Orion Nebula. Here's the same result applied to a dim object that barely registers in any individual frame. This example here is NGC 891 (NGC = New Galactic Catalogue), an edge-on spiral galaxy at the edge of the constellation Andromeda. The individual images barely register anything beyond a fairly-barren star field, even with a 30-second exposure at high gain through a good-sized telescope:
As always in astronomy, success lies in knowing just where to look, and in the center of this individual frame is a ghostly little needle-shaped apparition better known as NGC891. If we crank up the gain in this image, we begin to see the shape of this galaxy, but we also see a whole lot of noise:
And if we stack a bunch of these images (in this case, 20 of them, for a total of 10 minutes of exposure), then we begin to get somewhere, and the shape of an entire galaxy emerges for our consideration:
This technique of getting better images than we deserve can be utilized on just about anything found up there, and planets are especially good targets for this imaging method. In this case, we don't try to save up a lot of photons via a small set of long exposures, because solar system objects are pretty bright. Instead, we take a ton of short exposures by making a movie of the object, and then working our averaging technique over hundreds or thousands of very-short-duration frames.
Here's an image of Jupiter taken last week. Not much to see here beyond a Jovian disk suffering from a lot of noise and distortion introduced by the earth's atmosphere...
But if we stack up about 500 of the clearest frames from a movie of Jupiter taken through the telescope's optical train, a much clearer picture of this fascinating planet emerges:
You gotta love that Great Red Spot, now that you can see it!
Armed with this technique, almost any modern telescope can be connected to the simplest digital single-lens-reflex camera, and the result is remarkable given the simplicity of the equipment involved. And while it helps to have a good equatorial mount for tracking the stars, even the simplest clock-driven alt-azimuth mounts found on entry-level telescopes can be effectively utilized for astrophotography by taking account of the field rotation that occurs with time, so that the averaging process just requires a tad more alignment work in order to gain the best images.
So thanks to good optics and modern digital camera technology, you too can be an astrophotographer. All it takes is knowing where in Extremistan the interesting objects are to be found, and then using the Mediocristan residence of the camera noise to improve the signal while getting rid of the noise.
--Cieran
Please visit the web site for my novel "The Butcher's Cleaver." It is now for sale on-line at Barnes & Noble, Amazon and iUniverse.com pl
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