OPTIMIZED BEAM SCULPTING WITH GENERALIZED FRINGE-RATE FILTERS

Draft version March 20, 2015 Preprint typeset using L A TEX style emulateapj v. 5/2/11 OPTIMIZED BEAM SCULPTING WITH GENERALIZED FRINGE-RATE FILTERS Aaron R. Parsons 1,2 , Adrian Liu 1,3 , Zaki S. Ali 1 , Carina Cheng 1 arXiv:1503.05564v1 [astro-ph.IM] 18 Mar 2015 Draft version March 20, 2015 ABSTRACT We generalize the technique of fringe-rate filtering, whereby visibilities measured by a radio inter- ferometer are re-weighted according to their temporal variation. As the Earth rotates, radio sources traverse through an interferometer’s fringe pattern at rates that depend on their position on the sky. Capitalizing on this geometric interpretation of fringe rates, we employ time-domain convolution ker- nels to enact fringe-rate filters that sculpt the effective primary beam of antennas in an interferometer. As we show, beam sculpting through fringe-rate filtering can be used to optimize measurements for a variety of applications, including mapmaking, minimizing polarization leakage, suppressing instru- mental systematics, and enhancing the sensitivity of power-spectrum measurements. We show that fringe-rate filtering arises naturally in minimum variance treatments of many of these problems, en- abling optimal visibility-based approaches to analyses of interferometric data that avoid systematics potentially introduced by traditional approaches such as imaging. Our techniques have recently been demonstrated in Ali et al. (2015), where new upper limits were placed on the 21 cm power spectrum from reionization, showcasing the ability of fringe-rate filtering to successfully boost sensitivity and reduce the impact of systematics in deep observations. 1. INTRODUCTION In recent years, low-frequency radio interferometers have undergone dramatic changes in design. These trans- formations have been driven by new science applications such as 21 cm cosmology, where one uses the highly red- shifted emission from the 21 cm hyperfine transition of neutral hydrogen to map our early Universe. Observers in 21 cm cosmology seek to measure small fluctuations (both spatially and spectrally) in a dim, diffuse back- ground that is obscured by bright foreground emission orders of magnitude brighter in brightness temperature. This stands in contrast to many traditional observations in radio astronomy, which more usually target bright, compact objects in front of a dim background, often over a small selection of frequencies. These differences have led to the design, construction, and usage of new inter- ferometers that only have moderate angular resolution, but are comprised of a large number of receiving elements with wide fields of view operating over a wide bandwidth. Examples of new interferometers that broadly fit this de- scription include the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER; Parsons et al. 2010), the Murchison Widefield Array (MWA; Tin- gay et al. 2013; Bowman et al. 2013), the LOw Frequency ARray (LOFAR; van Haarlem et al. 2013), the Canadian Hydrogen Intensity Mapping Experiment (CHIME; Ban- dura et al. 2014), the MIT Epoch of Reionization exper- iment (MITEoR; Zheng et al. 2014), the Large Aperture Experiment to Detect the Dark Ages (LEDA; Greenhill & Bernardi 2012), and the Hydrogen Epoch of Reioniza- tion Array (HERA; Pober et al. 2014). Further deviating from conventional array designs, the PAPER, MITEoR, CHIME, HERA projects have also maximized sensitivity by choosing to place their antenna elements in regular, redundant grids (Parsons et al. 2012a). Astronomy Dept., U. California, Berkeley, CA Radio Astronomy Lab., U. California, Berkeley, CA Berkeley Center for Cosmological Physics, Berkeley, CA With new interferometer designs, it is natural to expect new approaches to data analysis. In this paper, we criti- cally examine methods for time integration. Integrating in time is a crucial step for the high-sensitivity appli- cations of modern low-frequency radio astronomy. Con- sider the measurement of the high-redshift 21 cm power spectrum as an example application. At the relevant red- shifts (z ∼ 6 to 20), theoretical models suggest that this cosmological signal will be faint — on the order of 1 mK in brightness temperature. The noise power spectrum on such measurements reaches comparable magnitudes only after long integration (& 1000 hrs) on instruments opti- mized for such a measurement (Harker et al. 2010; Par- sons et al. 2012a; Beardsley et al. 2013; Pober et al. 2014), and even then, often only for the largest spatial modes (depending on the instrument). Long time-integrations are therefore crucial not only for generating the requisite sensitivity for a detection of the cosmological signal, but also to allow faint systematics to be detected and excised from the data. In this paper, we extend ideas introduced in Parsons & Backer (2009) (as well as similar ideas in Offringa et al. 2012 and Shaw et al. 2013a) to optimize the pro- cess of combining time-ordered data. The key realization is that fringe-rate—the Fourier dual to time—is a more natural space to enact time-averaging. Traditional time- averaging (say, a running box-car average) is equivalent to multiplying by a sinc filter in the fringe-rate domain. Generalizing this process, the convolution theorem en- sures that time integration can be achieved by weighting the data in the fringe-rate domain. The fringe-rate do- main provides a natural basis for time-averaging interfer- ometric data because astronomical sources are locked to the celestial sphere, and therefore appear at predictable fringe-rates in the data. In particular, for a given in- terferometric baseline, there exists a maximum allow- able fringe-rate, beyond which there is only instrumental noise. Fringe-rate filtering allows the clean elimination of such noise-like modes.