\section{III. Methods}

\begin{quote}
3.1 Parabolic Antenna:-
\end{quote}

The detection of hydrogen lines through a dish-based antenna is a
powerful tool for studying the properties of hydrogen gas in the
universe. The process of detecting hydrogen lines using a dish-based
antenna is similar to using a radio telescope. The dish-based antenna
collects radiation emitted by hydrogen gas at a frequency of 1420.4058
MHz, which is in the radio wave part of the electromagnetic spectrum.
The dish-based antenna consists of a parabolic reflector that collects
the radiation emitted by the hydrogen gas and focuses it onto a
receiver. The receiver contains a detector that measures the voltage of
the collected radiation. This voltage signal is then processed by a
spectrometer to create a spectrum, which is a plot of the intensity of
the collected radiation as a function of frequency {[}{\color{blue}17}{]}. The
spectrum obtained from the dish-based antenna can reveal the properties
of the hydrogen gas emitting the radiation. The spectrum contains a
distinct peak at a frequency of 1420.4058 MHz, which corresponds to the
21 centimeter wavelength of the hydrogen emission. The intensity of the
peak can be used to measure the amount of hydrogen gas emitting the
radiation, while the shape of the peak can reveal information about the
motion and temperature of the gas. One of the advantages of using a
dish-based antenna for hydrogen line observations is its ability to
obtain high-resolution spectra. The dish-based antenna can be pointed at
specific regions of the sky to obtain detailed spectra of the hydrogen
gas in those regions. This allows astronomers to study the distribution
and motion of hydrogen gas in galaxies, the interstellar medium, and
even the early universe. In addition to mapping the distribution of
hydrogen gas in galaxies, the 21 centimeter line is also useful for
studying the interstellar medium (ISM) of galaxies. The ISM is the
material that fills the space between stars, and it consists of gas and
dust. By studying the 21 centimeter line emission from the ISM,
astronomers can learn about the physical properties of the gas, such as
its temperature, density, and motion. The 21 centimeter line is also a
useful tool for studying the early universe. Since the radiation from
the 21 centimeter line has been traveling through space for billions of
years, observing it can provide information about the conditions of the
universe in its early stages. In particular, the 21 centimeter line can
be used to study the epoch of reionization, which is the period when the
first stars and galaxies formed and began ionizing the hydrogen gas in
the universe.{[}{\color{blue}4}{]}

The standard formula for the parabolic reflector antenna gain is:

\begin{center}
\(G = 10logK(\pi D/\lambda)^{2}\)

\end{center}

The gain of the antennae in this manner is denoted as dBi.

\textbf{Where:\\
} G is gain over isotropic source in dB\\
k is the efficiency factor which is generally around 50\% to 60\%\\
D is diameter of parabolic reflector in meters\\
$\lambda$ is wavelength of signal in meters

The output of a real antenna is always smaller than this and most radio
sources are nearly unpolarized, so radio astronomers find it useful to
define the effective collecting area (Ae) of an antenna whose output
spectral power (Pv) in the response to an unpolarized point source of
total flux density (S) by
$$ Ae \equiv 2P\vartheta/S\vartheta$$
   $$ Where, P\vartheta = AS\vartheta $$