Algorithms for FFT Beamforming Radio Interferometers

Masui, Kiyoshi; Shaw, J. Richard; Ng, Cherry; Smith, Kendrick M.; Vanderlinde, K.; Paradise, Adiv

doi:10.3847/1538-4357/ab229e

Cited by 26 publications

(20 citation statements)

References 40 publications

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“…The most efficient instrument for such a wide-field monitoring is a regular array of antennas or small dishes with a beamformer based on a two-dimensional Fast Fourier Transform as proposed by Otobe et al (1994) and Tegmark & Zaldarriaga (2009). A one-dimensional version of this approach is already being used by CHIME-FRB (Ng et al 2017;Masui et al 2019), and an application for the two-dimensional case is straight forward. Appropriate antenna arrays were developed as design studies for the Square Kilometre Array (SKA).…”

Section: Finding Lensed Frbsmentioning

confidence: 99%

Cosmology with gravitationally lensed repeating fast radio bursts

Wucknitz

Spitler

Pen

2021

A&A

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High-precision cosmological probes have revealed a small but significant tension between the parameters measured with different techniques, among which there is one based on time delays in gravitational lenses. We discuss a new way of using time delays for cosmology, taking advantage of the extreme precision expected for lensed fast radio bursts, which are short flashes of radio emission originating at cosmological distances. With coherent methods, the achievable precision is sufficient for measuring how time delays change over the months and years, which can also be interpreted as differential redshifts between the images. It turns out that uncertainties arising from the unknown mass distribution of gravitational lenses can be eliminated by combining time delays with their time derivatives. Other effects, most importantly relative proper motions, can be measured accurately and disentangled from the cosmological effects. With a mock sample of simulated lenses, we show that it may be possible to attain strong constraints on cosmological parameters. Finally, the lensed images can be used as galactic interferometer to resolve structures and motions of the burst sources with incredibly high resolution and help reveal their physical nature, which is currently unknown.

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Section: Finding Lensed Frbsmentioning

confidence: 99%

Cosmology with gravitationally lensed repeating fast radio bursts

Wucknitz

Spitler

Pen

2021

A&A

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“…4.1 for these instruments, by computing n(u, ν) and also making appropriate modifications to account for a drift-scan observation strategy. However, for a close-packed distribution of feeds or dishes, one may use a simpler formalism in which the instrument is treated as having a single large collecting area observing the sky with multiple simultaneous beams [81] (this approach, realizable in practice with FFT beamforming [82], contains the same information as stacking measurements from redundant baselines). In this case, the noise angular power spectrum is given by [81,83]…”

Section: Chime and Hiraxmentioning

confidence: 99%

“…For CHIME, n x = 4, n y = 256, and A e = (20 × 80/256) m 2 = 6.25m 2 (since only 80m of each cylinder are instrumented with feeds), while for HIRAX, n x = n y = 32 and A e = (π3 2 /4) m 2 ≈ 28m 2 . In FFT beamforming, the maximum number of beams with non-redundant information is n beams = (2n x − 1)(2n y − 1) [82], so we use that for each experiment. The window function W ( ) encodes the effective scale-dependence of the instrument response.…”

Section: Chime and Hiraxmentioning

confidence: 99%

Lensing reconstruction from line intensity maps: the impact of gravitational nonlinearity

Foreman

Meerburg

Engelen

et al. 2018

J. Cosmol. Astropart. Phys.

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We investigate the detection prospects for gravitational lensing of three-dimensional maps from upcoming line intensity surveys, focusing in particular on the impact of gravitational nonlinearities on standard quadratic lensing estimators. Using perturbation theory, we show that these nonlinearities can provide a significant contaminant to lensing reconstruction, even for observations at reionization-era redshifts. However, we show how this contamination can be mitigated with the use of a "bias-hardened" estimator. Along the way, we present an estimator for reconstructing longwavelength density modes, in the spirit of the "tidal reconstruction" technique that has been proposed elsewhere, and discuss the dominant biases on this estimator. After applying bias-hardening, we find that a detection of the lensing potential power spectrum will still be challenging for the first phase of SKA-Low, CHIME, and HIRAX, with gravitational nonlinearities decreasing the signal to noise by a factor of a few compared to forecasts that ignore these effects. On the other hand, cross-correlations between lensing and galaxy clustering or cosmic shear from a large photometric survey look promising, provided that systematics can be sufficiently controlled. We reach similar conclusions for a single-dish survey inspired by CII measurements planned for CCAT-prime, suggesting that lensing is an interesting science target not just for 21cm surveys, but also for intensity maps of other lines.

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“…The DFT architecture would be most applicable for a non-redundant and sparse array with many elements, where high time resolution imaging is a valuable observation mode. Redundant arrays can use FFT beamforming approaches (Masui et al 2019) for reducing data rates, and dense arrays can use the EPIC correlator Thyagarajan et al (2017); Kent et al (2019) for direct radio imaging. A combination of these schemes can also be utilised, depending on the interferometer configuration, geometry, and science goals.…”

Section: Dft Applicabilitymentioning

confidence: 99%

Direct wide-field radio imaging in real-time at high time resolution using antenna electric fields

Kent

Beardsley

Bester

et al. 2019

Monthly Notices of the Royal Astronomical Society

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The recent demonstration of a real-time direct imaging radio interferometry correlator represents a new capability in radio astronomy. However wide field imaging with this method is challenging since wide-field effects and array non-coplanarity degrade image quality if not compensated for. Here we present an alternative direct imaging correlation strategy using a Direct Fourier Transform (DFT), modelled as a linear operator facilitating a matrix multiplication between the DFT matrix and a vector of the electric fields from each antenna. This offers perfect correction for wide field and non-coplanarity effects. When implemented with data from the Long Wavelength Array (LWA), it offers comparable computational performance to previously demonstrated direct imaging techniques, despite having a theoretically higher floating point cost. It also has additional benefits, such as imaging sparse arrays and control over which sky co-ordinates are imaged, allowing variable pixel placement across an image. It is in practice a highly flexible and efficient method of direct radio imaging when implemented on suitable arrays. A functioning Electric Field Direct imaging architecture using the DFT is presented, alongside an exploration of techniques for wide-field imaging similar to those in visibility based imaging, and an explanation of why they do not fit well to imaging directly with the digitized electric field data. The DFT imaging method is demonstrated on real data from the LWA telescope, alongside a detailed performance analysis, as well as an exploration of its applicability to other arrays.

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Algorithms for FFT Beamforming Radio Interferometers

Cited by 26 publications

References 40 publications

Cosmology with gravitationally lensed repeating fast radio bursts

Cosmology with gravitationally lensed repeating fast radio bursts

Lensing reconstruction from line intensity maps: the impact of gravitational nonlinearity

Direct wide-field radio imaging in real-time at high time resolution using antenna electric fields

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