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Astronomers want bigger and better telescopes. That’s understandable. But in the world of radio telescopes, there’s a problem looming: Greater sensitivity requires a bigger surface area, and the cost for a steerable single-dish telescope grows with area faster than linearly. So really big dishes are just too expensive to build.

That’s why astronomers are interested in the much cheaper approach of connecting many smaller dishes together to form an interferometer. Such an array of dishes can be as large as you like. The problem here is that in an interferometer, the signals from each dish have to be correlated with all the others, and the computational cost of this rises quadratically–i.e., the cost is proportional to the square of the number of dishes.

That soon becomes prohibitive, so astronomers have looked at two cost-cutting measures, say Max Tegmark at MIT in Cambridge and Matias Zaldarriaga at the Institute for Advanced Study in Princeton, N.J.

The first is to divide the array into groups, each considered a single element. This cuts the correlation cost from N^2 to (N/M)^2, at the price of reducing the sky area covered by a factor M. So the savings comes from ignoring part of the sky and not having to compute it.

The second is to arrange the antennae into a rectangular grid that can be correlated using fast Fourier transforms. This reduces the computational cost from N^2 to N.log2 (N) at the price of lower resolution.

That’s not such a bad trade-off. The question that Tegmark and Zaldarriaga ask is what shapes of array can benefit from this N.log2 (N) computational cost improvement.

Their answer is a surprisingly large class of arrays. It turns out that not only rectangular arrays but arbitrary combinations of grids should benefit.

That should make it possible to build arrays of dishes of almost any size and still benefit from the N.log2 (N) computational cost. Tegmark and Zaldarriaga say,

“This opens up the possibility of getting the best of both worlds, combining affordable signal processing with baseline coverage tailored to specific scientific needs.”

Such huge arrays would be omnidirectional and omnichromatic so Tegmark and Zaldarriaga coin the term omniscopes to describe them.

Ref: arxiv.org/abs/0909.0001: Omniscopes: Large Area Telescope Arrays with only N log N Computational Cost

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