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Demian Arancibia edited untitled.tex
almost 9 years ago
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\Delta I_m = {\frac{1}{\eta_s }}{\frac{SEFD}{\sqrt{2 \Delta \nu \tau_{acc}}}}
\end{equation}
in units of Janskys per synthesized beam area.
with $\eta_s$ most important factor being correlator efficiency $\eta_c = \frac{\text{correlator sensitivity}}{\text{sesitivity of a perfect analog correlator having the same } \tau_{acc}}$
(\citet*{sensitivity}). (see $\cite{sensitivity}$).
\subsubsection{Minimize SEFD}
\begin{equation}\label{eq:system_equivalent_flux_density}
SEFD = {\frac{T_{sys}}{\frac{\eta_a A}{2k_B}}}
\end{equation}
where $T_{sys}$ is the system temperature including contributions from receiver noise, feed losses, spillover, atmospheric emission, galactic background and cosmic background, $k_B = 1.380 \times 10^{-23}$ Joule $K^{-1}$ is the Boltzmann constant, $A$ is the antenna collecting area (thus we could also write $\pi \cdot D^2$), and $\eta_a$ is the antenna efficiency with $\eta_a = \eta_{\text{surface efficiency}} \cdot \eta_{\text{aperture blockage}} \cdot \eta_{\text{feed spillover efficiency}} \cdot \eta_{\text{illumination taper efficiency}}$
(\citet*{antenna}). (see $\cite{antenna}$).
\subsection{Minimize Operations Costs}
The operations cost is a complex problem divided in the sub-problems in this section.
\subsubsection{Minimize Maintenance Costs}
...
\subsubsection{Quantity of Construction Sites}
\subsubsection{Cost of Data Transmission Network Construction}
\subsubsection{Cost of Antennas Construction}
A commonly used rule of thumb for the cost of an antenna is that it is proportional to $D^{\alpha}$, where $\alpha \approx 2.7$ for values of $D$ from a few meters to tens of meters.
(\citet*{moran}) (see $\cite{moran}$)
\subsubsection{Cost of Antenna Electronics}
\subsubsection{Cost of Re-configuration Systems Construction}
\section{Array Performance Data Generation - Python Implementation}
...
\section{Conversation notes}
\subsection{Engineering cost vs. Calibration cost}
Tricky because you can compensate antenna quality with software. So the equations must capture this trade off.