Omniscopes：仅需NlogN计算成本的大面积望远镜阵列
Omniscopes: Large Area Telescope Arrays with only N log N Computational Cost
摘要：
我们发现，望远镜阵列的天线布局类别允许廉价的分析硬件（相关器成本缩放为Nlog N，而不是N^2，天线数量为N）是非常大的，不仅包括以前讨论的矩形网格，而且还包括任意层次的网格，在每一级任意旋转和剪切。我们表明，这样的一个2D阵列的n级层次结构的所有相关性可以有效地计算通过快速傅立叶变换，而不是2，但2n维。这可以降低相关器的主要成本，用于需要在广泛分离的角尺度上具有高灵敏度的科学应用，例如21 cm断层扫描（需要短基线来探测宇宙信号，需要长基线来去除点源），有助于未来使用数千或数百万个廉价的偶极天线进行21 cm实验。这种分层网格结合了传统阵列布局的角分辨率优势和矩形快速傅立叶变换望远镜的成本优势。我们还描述了一个算法，如何一个子类的分层阵列可以有效地使用旋转合成产生全球天空地图，最小的噪音和一个良好的特征合成光束。
英文摘要：
We show that the class of antenna layouts for telescope arrays allowing cheap analysis hardware (with correlator cost scaling as N log N rather than N^2 with the number of antennas N) is encouragingly large, including not only previously discussed rectangular grids but also arbitrary hierarchies of such grids, with arbitrary rotations and shears at each level. We show that all correlations for such a 2D array with an n-level hierarchy can be efficiently computed via a Fast Fourier Transform in not 2 but 2n dimensions. This can allow major correlator cost reductions for science applications requiring exquisite sensitivity at widely separated angular scales, for example 21cm tomography (where short baselines are needed to probe the cosmological signal and long baselines are needed for point source removal), helping enable future 21cm experiments with thousands or millions of cheap dipole-like antennas. Such hierarchical grids combine the angular resolution advantage of traditional array layouts with the cost advantage of a rectangular Fast Fourier Transform Telescope. We also describe an algorithm for how a subclass of hierarchical arrays can efficiently use rotation synthesis to produce global sky maps with minimal noise and a well-characterized synthesized beam.
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