A Model for Phased Array Feed. (arXiv:1902.01516v1 [astro-ph.IM])

A Model for Phased Array Feed. (arXiv:1902.01516v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Roshi_D/0/1/0/all/0/1">D. Anish Roshi</a> (1), <a href="http://arxiv.org/find/astro-ph/1/au:+Fisher_J/0/1/0/all/0/1">J. Richard Fisher</a> (1) (1. National Radio Astronomy Observatory, Charlottesville, USA)

In this report we present a model for phased array feed (PAF) and compare the
model predictions with measurements. A theory for loss-less PAF is presented
first. To develop the theory we ask the question — what is the best
$T_{sys}/eta_{ap}$ that can be achieved when a PAF is used on a telescope to
observe a source at an angle $theta_s, phi_s$ from the boresight direction ?
We show that a characteristic matrix for the {em system} (i.e.
PAF+telescope+receiver) can be constructed starting from the signal-to-noise
ratio of the observations and the best $T_{sys}/eta_{ap}$ can be obtained from
the maximum eigenvalue of the characteristic matrix. For constructing the
characteristic matrix, we derive the open-circuit voltage at the output of the
antenna elements in the PAF due to (a) radiation from source, (b) radiation
from ground (spillover), (c) radiation from sky background and (d) noise due to
the receiver. The characteristic matrix is then obtained from the correlation
matrices of these voltages. We then describe a modeling program developed to
implement the theory presented here. Finally the model predictions are compared
with results from test observations made toward Virgo A with a prototype PAF
(Kite array) on the GBT (Roshi et al. 2015).

In this report we present a model for phased array feed (PAF) and compare the
model predictions with measurements. A theory for loss-less PAF is presented
first. To develop the theory we ask the question — what is the best
$T_{sys}/eta_{ap}$ that can be achieved when a PAF is used on a telescope to
observe a source at an angle $theta_s, phi_s$ from the boresight direction ?
We show that a characteristic matrix for the {em system} (i.e.
PAF+telescope+receiver) can be constructed starting from the signal-to-noise
ratio of the observations and the best $T_{sys}/eta_{ap}$ can be obtained from
the maximum eigenvalue of the characteristic matrix. For constructing the
characteristic matrix, we derive the open-circuit voltage at the output of the
antenna elements in the PAF due to (a) radiation from source, (b) radiation
from ground (spillover), (c) radiation from sky background and (d) noise due to
the receiver. The characteristic matrix is then obtained from the correlation
matrices of these voltages. We then describe a modeling program developed to
implement the theory presented here. Finally the model predictions are compared
with results from test observations made toward Virgo A with a prototype PAF
(Kite array) on the GBT (Roshi et al. 2015).

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