System equivalent flux density of a low-frequency polarimetric phased array interferometer

Abstract

This paper extends the treatment of system equivalent flux density (SEFD) in Sutinjo, A. T. et al. (2021) (Paper I) to interferometric phased array telescopes. The objective is to develop an SEFD formula involving only the most fundamental assumptions and one that is readily applicable to phased array interferometer radio observations. Then, we aimed at comparing the resultant SEFD expression against the often-used root-mean-square (RMS) SEFD approximation, SEFDrmsI = (1/2)(SEFD^2_XX + SEFD^2_YY)^(1/2) to study the inaccuracy of the SEFDrms. We take into account all mutual coupling and noise coupling within an array environment (intra-array coupling). This intra-array noise coupling is included in the SEFD expression through the realized noise resistance of the array, which accounts for the system noise. No assumption is made regarding the polarization (or lack thereof) of the sky nor the orthogonality of the antenna elements. The fundamental noise assumption is that, in phasor representation, the real and imaginary components of a given noise source are independent and equally distributed (iid) with zero mean. Noise sources that are mutually correlated and non-iid among themselves are allowed, provided the real and imaginary components of each noise source are iid. The system noise is uncorrelated between array entities separated by a baseline distance, which in the case of the Murchison Widefield Array (MWA) is typically tens of wavelengths or greater. By comparing the resulting SEFD formula to the SEFD_I^rms approximation, we proved that SEFD_I^rms always underestimates the SEFD, which leads to an overestimation of array sensitivity.

arXiv commentAccepted for publication in Astronomy & Astrophysics (30 Jan. 2022). 15 pages

References in corpus (15)

• LOFAR: The LOw-Frequency ARray
• The Murchison Widefield Array: the Square Kilometre Array Precursor at low radio frequencies
• WSClean: an implementation of a fast, generic wide-field imager for radio astronomy
• An Accurate Flux Density Scale from 50 MHz to 50 GHz
• The Very Large Array Low-frequency Sky Survey Redux (VLSSr)
• Parametrising Epoch of Reionization foregrounds: A deep survey of low-frequency point-source spectra with the MWA
• Characterization of a Low-Frequency Radio Astronomy Prototype Array in Western Australia
• Calibration and Stokes Imaging with Full Embedded Element Primary Beam Model for the Murchison Widefield Array
• Sensitivity of Antenna Arrays for Long-Wavelength Radio Astronomy
• The High Time and Frequency Resolution Capabilities of the Murchison Widefield Array
• Measuring Noise Temperatures of Phased-Array Antennas for Astronomy at CSIRO
• Noise Temperature of Phased Array Radio Telescope: The Murchison Widefield Array and the Engineering Development Array
• Cold-Source Noise Measurement of a Differential Input Single-Ended Output Low-Noise Amplifier Connected to a Low-Frequency Radio Astronomy Antenna
• Sensitivity of a Low-Frequency Polarimetric Radio Interferometer
• Calibration database for the Murchison Widefield Array All-Sky Virtual Observatory

Cited by in corpus (2)

• System equivalent flux density of Stokes I, Q, U, V of a polarimetric interferometer
• Beamforming approaches toward detecting the 21-cm global signal from Cosmic Dawn with radio array telescopes