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We show that the class of antenna layouts for telescope arrays allowing cheapanalysis hardware (with correlator cost scaling as N log N rather than N^2 withthe number of antennas N) is encouragingly large, including not only previouslydiscussed rectangular grids but also arbitrary hierarchies of such grids, witharbitrary rotations and shears at each level. We show that all correlations forsuch a 2D array with an n-level hierarchy can be efficiently computed via aFast Fourier Transform in not 2 but 2n dimensions. This can allow majorcorrelator cost reductions for science applications requiring exquisitesensitivity at widely separated angular scales, for example 21cm tomography(where short baselines are needed to probe the cosmological signal and longbaselines are needed for point source removal), helping enable future 21cmexperiments with thousands or millions of cheap dipole-like antennas. Suchhierarchical grids combine the angular resolution advantage of traditionalarray layouts with the cost advantage of a rectangular Fast Fourier TransformTelescope. We also describe an algorithm for how a subclass of hierarchicalarrays can efficiently use rotation synthesis to produce global sky maps withminimal noise and a well-characterized synthesized beam.

Omniscopes: Large Area Telescope Arrays with only N log N Computational Cost