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Figure 1. The Mona Lisa (left) is separated into two images; the lower right is dominated by the low spatial frequencies in the image while the upper right contains the high spatial frequencies of the image. Credit: Gerry Harp


Figure 2. Galactic hydrogen in our galaxy as measured by a single ATA dish and displayed in Mercator projection (exemplified by inset). Credit: Gerry Harp


Figure 3. Why a donut? For those in the know, a mathematical operation called the Fourier transform breaks down Lisa's face into a sum of sine waves with different wavelengths or frequencies. These frequencies are often plotted on a rectangular grid, where high frequencies reside near the edges of the rectangle and low frequencies near the center. Excluding the low spatial frequencies leaves a hole at the center of the grid, resulting in a rectangular donut. If you can't visualize a rectangular donut, don't worry; this kind of imagining is best left to professional mathematicians! Credit: Gerry Harp

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Putting the Jelly in the Space Donut

By Gerry Harp
Astrophysicist, SETI Institute
posted: 26 August 2008
05:16 pm ET

The second "A" in ATA stands for array, meaning that this instrument is made of many small dishes

The second "A" in ATA stands for array, meaning that this instrument is made of many small dishes. Although each dish is as big as a house, they are small compared to the complete telescope: ten city blocks on a side. The bigger the telescope, the more detail you see in the images. By breaking up our collecting area into hundreds of small pieces, we capture detail as if we had a telescope the size of a subdivision for the price of a single apartment building.

 

But detail isn't everything. Consider the following example, based on a well-known image by Leonardo da Vinci. Starting with the painting (Fig. 1, left), we deconstruct the Mona Lisa into two parts: one containing all the details of the image, and one containing the coarse structures. The upper right image contains the details, or as we say in radio astronomy, the high spatial frequencies of the image. Most of the beauty of the painting is found here. In case you've never noticed, this image brings out the nature behind Lisa's head, with trees and a flowing creek.

 

But the detail image is gray and blah compared to the original painting. What gives the painting its punch are the low spatial frequencies, represented at bottom right. This image makes you reach for your glasses, and by itself is uninteresting or even ugly. It is only when you add the two right-hand images together that we see the full complexity and brilliance of the original painting.

 

Getting back to the ATA [Allen Telescope Array], when we run the telescope in array mode, we capture all the high spatial frequencies of the night sky, much like the detail image of the Mona Lisa in Figure 1. This is done by comparing radio signals two-by-two for each pair of dishes in the array. With 350 dishes, there are 61,075 distinct antenna pairs (calculation left as an exercise for the reader). But pairwise comparison leaves out a small but critical bit of information in the low spatial frequency component of the image.

 

We can recover the low frequency information by pairing each antenna with itself, which we call single dish mode. Single dish mode does not take advantage of the full size of the array; it is as if there were only one dish. Because one dish is small by the standards of radio astronomy, the image we obtain is blurry and lacks detail.

 

As part of the ATA commissioning, we recently performed single dish observations of the Milky Way galaxy, which is our home. Figure 2 shows a partial map of the hydrogen emission over the entire celestial sphere. The Milky Way has a disk shape, and because of our position inside of the disk, it appears as a broad stripe encircling the Earth. The regions that appear black in the image are directions we have not yet measured. The inset shows a Mercator projection of a world map, which is the same projection used in the observation.

 

Hydrogen gas is not visible to the naked eye, but it represents the majority of the mass in our galaxy (and for that matter, the entire universe). The bulk of the hydrogen is present in galactic disk (horizontal stripe), but smoky wisps of hydrogen are seen both above and below the disk. The disk is narrower toward the center of the galaxy and more diffuse when we look behind, or away from galactic center. Notice the small blemish on the lower left. This is where the sun blocked our view of the galaxy in the background, so it appears as a dark spot.

 

Single-dish observations like these are important for bringing out the full beauty and science in radio images. When combined with highly detailed interferometer observations, they put the punch in the picture, or the jelly in the donut. Expect masterpieces soon.

 

 

 

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