Omniscopes: Large area telescope arrays with only N logN computational cost
We show that the class of antenna layouts for telescope arrays allowing cheap analysis hardware (with correlator cost scaling as Nlog N rather than N[superscript 2] with the number of antennas N) is encouragingly large, including not only previously discussed rectangular grids but also arbitrary hie...
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| Format: | Article |
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American Physical Society (APS)
2018
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| Online Access: | http://hdl.handle.net/1721.1/116597 https://orcid.org/0000-0001-7670-7190 |
| _version_ | 1826212369442799616 |
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| author | Zaldarriaga, Matias Tegmark, Max Erik |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Zaldarriaga, Matias Tegmark, Max Erik |
| author_sort | Zaldarriaga, Matias |
| collection | MIT |
| description | We show that the class of antenna layouts for telescope arrays allowing cheap analysis hardware (with correlator cost scaling as Nlog N rather than N[superscript 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 two but 2n dimensions. This can allow major correlator cost reductions for science applications requiring exquisite sensitivity at widely separated angular scales, for example, 21 cm tomography (where short baselines are needed to probe the cosmological signal and long baselines are needed for point source removal), helping enable future 21 cm experiments with thousands or millions of cheap dipolelike 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. |
| first_indexed | 2024-09-23T15:20:17Z |
| format | Article |
| id | mit-1721.1/116597 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T15:20:17Z |
| publishDate | 2018 |
| publisher | American Physical Society (APS) |
| record_format | dspace |
| spelling | mit-1721.1/1165972022-09-29T14:21:04Z Omniscopes: Large area telescope arrays with only N logN computational cost Zaldarriaga, Matias Tegmark, Max Erik Massachusetts Institute of Technology. Department of Physics Tegmark, Max Erik We show that the class of antenna layouts for telescope arrays allowing cheap analysis hardware (with correlator cost scaling as Nlog N rather than N[superscript 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 two but 2n dimensions. This can allow major correlator cost reductions for science applications requiring exquisite sensitivity at widely separated angular scales, for example, 21 cm tomography (where short baselines are needed to probe the cosmological signal and long baselines are needed for point source removal), helping enable future 21 cm experiments with thousands or millions of cheap dipolelike 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. United States. National Aeronautics and Space Administration (Grant NAG5-11099) United States. National Aeronautics and Space Administration (Grant NNG 05G40G) National Science Foundation (U.S.) (Grant AST-0607597) National Science Foundation (U.S.) (Grant AST-0708534) National Science Foundation (U.S.) (Grant AST-0908848) National Science Foundation (U.S.) (Grant PHY0855425) David & Lucile Packard Foundation 2018-06-26T13:34:22Z 2018-06-26T13:34:22Z 2010-11 2009-09 2018-06-15T18:25:38Z Article http://purl.org/eprint/type/JournalArticle 1550-7998 1550-2368 http://hdl.handle.net/1721.1/116597 Tegmark, Max, and Matias Zaldarriaga. “Omniscopes: Large Area Telescope Arrays with Only N Log N Computational Cost.” Physical Review D, vol. 82, no. 10, Nov. 2010. https://orcid.org/0000-0001-7670-7190 http://dx.doi.org/10.1103/PhysRevD.82.103501 Physical Review D Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Physical Society (APS) American Physical Society |
| spellingShingle | Zaldarriaga, Matias Tegmark, Max Erik Omniscopes: Large area telescope arrays with only N logN computational cost |
| title | Omniscopes: Large area telescope arrays with only N logN computational cost |
| title_full | Omniscopes: Large area telescope arrays with only N logN computational cost |
| title_fullStr | Omniscopes: Large area telescope arrays with only N logN computational cost |
| title_full_unstemmed | Omniscopes: Large area telescope arrays with only N logN computational cost |
| title_short | Omniscopes: Large area telescope arrays with only N logN computational cost |
| title_sort | omniscopes large area telescope arrays with only n logn computational cost |
| url | http://hdl.handle.net/1721.1/116597 https://orcid.org/0000-0001-7670-7190 |
| work_keys_str_mv | AT zaldarriagamatias omniscopeslargeareatelescopearrayswithonlynlogncomputationalcost AT tegmarkmaxerik omniscopeslargeareatelescopearrayswithonlynlogncomputationalcost |