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%
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%
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%
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%
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%
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%
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%
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\providecommand{\Tatm}{\ensuremath{T_\ensuremath{\mathrm{atm}}}}%
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%
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%
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%
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\providecommand{\dpow}{\ensuremath{dw}}%
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%
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\lhead{\scshape NOEMA sensitivity estimator}
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%
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%
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$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{atm}}}{} = e^{-\frac{\ensuremath{\phi_\ensuremath{\mathrm{rms}}}^2}{2}} \le 1.0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7220}%
$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{\displaystyle\left<  \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}} \right> }}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{\Delta t_\ensuremath{\mathrm{}}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7223}%
$\displaystyle \boxed{%
    \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{\displaystyle\left<  \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}} \right> }}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{\Delta t_\ensuremath{\mathrm{}}}}},
\quad \mbox{with} \quad
\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}} = \frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{sd}}}}{\ensuremath{\eta_\ensuremath{\mathrm{atm}}}}
\quad \mbox{and} \quad
\ensuremath{\eta_\ensuremath{\mathrm{atm}}}{} = e^{-\frac{\ensuremath{\phi_\ensuremath{\mathrm{rms}}}^2}{2}} \le 1.0,
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7225}%
$ \sigma_\ensuremath{\mathrm{Jy}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7239}%
$ \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7242}%
$ uv$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7244}%
$ \ensuremath{\lambda}/\ensuremath{\mathrm{FWHM}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7247}%
$ \Omega_\ensuremath{\mathrm{ant}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7251}%
$ \lambda$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7253}%
$\displaystyle \ensuremath{\Omega_\ensuremath{\mathrm{ant}}} \, \ensuremath{A_\ensuremath{\mathrm{eff}}}= \ensuremath{\lambda}^2.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7255}%
$\displaystyle \ensuremath{F_\ensuremath{\mathrm{}}}= \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{}}}\ensuremath{T_\ensuremath{\mathrm{A}}^\star}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7256}%
$\displaystyle \quad
\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{}}}= \frac{2\ensuremath{k}\,\ensuremath{\Omega_\ensuremath{\mathrm{ant}}}\,\ensuremath{F_\ensuremath{\mathrm{eff}}}}{\ensuremath{\lambda}^2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7258}%
$ \ensuremath{\Omega_\ensuremath{\mathrm{prim}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7264}%
$\displaystyle \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}
= \frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{sd}}}}{\ensuremath{\eta_\ensuremath{\mathrm{atm}}}}
= \frac{1}{\ensuremath{\eta_\ensuremath{\mathrm{atm}}}}\,\frac{\ensuremath{F_\ensuremath{\mathrm{eff}}}}{\ensuremath{B_\ensuremath{\mathrm{eff}}}}\,\frac{2\ensuremath{k}\,\ensuremath{\Omega_\ensuremath{\mathrm{prim}}}}{\ensuremath{\lambda}^2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7266}%
$ \ensuremath{\Omega_\ensuremath{\mathrm{syn}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7268}%
$ J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{syn}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7270}%
$ \ensuremath{B_\ensuremath{\mathrm{eff}}}^\ensuremath{\mathrm{int}} = 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7272}%
$ \ensuremath{F_\ensuremath{\mathrm{eff}}}^\ensuremath{\mathrm{int}} = 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7274}%
$\displaystyle \ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{syn}}}
= \frac{2\ensuremath{k}\,\ensuremath{\Omega_\ensuremath{\mathrm{syn}}}}{\ensuremath{\lambda}^2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7278}%
$\displaystyle \boxed{%
    \ensuremath{\sigma_\ensuremath{\mathrm{K}}} = \frac{\ensuremath{\sigma_\ensuremath{\mathrm{Jy}}}}{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{syn}}}}
\quad \mbox{with} \quad
\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{syn}}} = \frac{2\pi\,\ensuremath{k}\,\ensuremath{\theta_\ensuremath{\mathrm{maj}}}\ensuremath{\theta_\ensuremath{\mathrm{min}}}}{4\,\ln{2}\,\ensuremath{\lambda}^2},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7280}%
$\displaystyle \boxed{%
    \ensuremath{\sigma_\ensuremath{\mathrm{K}}}
= \frac{\ensuremath{\Omega_\ensuremath{\mathrm{prim}}}}{\ensuremath{\Omega_\ensuremath{\mathrm{syn}}}}\,\ensuremath{\displaystyle\left<  \frac{\ensuremath{F_\ensuremath{\mathrm{eff}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{B_\ensuremath{\mathrm{eff}}}\,\ensuremath{\eta_\ensuremath{\mathrm{atm}}}} \right> }\,\frac{1}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\, \sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{\Delta t_\ensuremath{\mathrm{}}}}}
= \frac{\ensuremath{\theta_\ensuremath{\mathrm{prim}}}^2}{\ensuremath{\theta_\ensuremath{\mathrm{maj}}}\,\ensuremath{\theta_\ensuremath{\mathrm{min}}}}\,\ensuremath{\displaystyle\left<  \frac{\ensuremath{F_\ensuremath{\mathrm{eff}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{B_\ensuremath{\mathrm{eff}}}\,\ensuremath{\eta_\ensuremath{\mathrm{atm}}}} \right> }\,\frac{1}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\, \sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{\Delta t_\ensuremath{\mathrm{}}}}},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7284}%
$ \theta_\ensuremath{\mathrm{prim}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7286}%
$ \theta_\ensuremath{\mathrm{maj}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7288}%
$ \theta_\ensuremath{\mathrm{min}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7293}%
$ 4 (=2^2)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7295}%
$ 16 (=2^4)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7300}%
$ \ensuremath{T_\ensuremath{\mathrm{sys}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7304}%
\includegraphics[width=0.80\linewidth]{astro-noema-sensitivity-estimator-tsys-table-sbr}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7308}%
\includegraphics[width=0.80\linewidth]{astro-noema-sensitivity-estimator-tsys-table-dbr}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7316}%
\includegraphics[width=0.775\linewidth]{astro-noema-sensitivity-estimator-tsys-minmax-sbr}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7320}%
\includegraphics[width=0.775\linewidth]{astro-noema-sensitivity-estimator-tsys-minmax-dbr}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7328}%
\includegraphics[width=0.80\linewidth]{astro-noema-sensitivity-estimator-tsys-cont-sbr}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7332}%
\includegraphics[width=0.80\linewidth]{astro-noema-sensitivity-estimator-tsys-cont-dbr}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7337}%
$\displaystyle \ensuremath{T_\ensuremath{\mathrm{sys}}}= \frac{\ensuremath{\displaystyle\left(  1+\ensuremath{G_\ensuremath{\mathrm{im}}} \right) }\exp\ensuremath{\displaystyle\left\{ \ensuremath{\tau_\ensuremath{\mathrm{s}}}\,\ensuremath{A} \right\}}}{\ensuremath{F_\ensuremath{\mathrm{eff}}}}
\ensuremath{\displaystyle\left[  \ensuremath{F_\ensuremath{\mathrm{eff}}}\,\ensuremath{T_\ensuremath{\mathrm{atm}}}\,\ensuremath{\displaystyle\left(  1-\exp\ensuremath{\displaystyle\left\{ -\ensuremath{\tau_\ensuremath{\mathrm{s}}}\,\ensuremath{A} \right\}} \right) }+\ensuremath{\displaystyle\left(  1-\ensuremath{F_\ensuremath{\mathrm{eff}}} \right) }\ensuremath{T_\ensuremath{\mathrm{cab}}}+\ensuremath{T_\ensuremath{\mathrm{rec}}} \right] },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7339}%
$ G_\ensuremath{\mathrm{im}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7341}%
$ F_\ensuremath{\mathrm{eff}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7343}%
$ \ensuremath{A}= 1/\sin(\ensuremath{\mathrm{elevation}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7345}%
$ \tau_\ensuremath{\mathrm{s}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7347}%
$ T_\ensuremath{\mathrm{atm}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7349}%
$ T_\ensuremath{\mathrm{cab}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7351}%
$ T_\ensuremath{\mathrm{rec}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7362}%
$\displaystyle \boxed{%
    \frac{1}{<\ensuremath{T_\ensuremath{\mathrm{sys}}}>^2} = \frac{1}{N} \sum \frac{1}{\ensuremath{T_\ensuremath{\mathrm{sys}}}^2}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7367}%
\includegraphics[width=0.80\linewidth]{astro-noema-sensitivity-estimator-trec-dichroic-summary}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7373}%
$ \backslash$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7375}%
$ 2 \times 8\,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7378}%
$ n_\ensuremath{\mathrm{pol}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7380}%
$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7387}%
$\displaystyle \boxed{%
    \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} =
\frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}}
\quad \mbox{with} \quad
\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}} = \frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{sd}}}}{\ensuremath{\eta_\ensuremath{\mathrm{atm}}}}
\quad \mbox{and} \quad
\ensuremath{\eta_\ensuremath{\mathrm{atm}}}{} = e^{-\frac{\ensuremath{\phi_\ensuremath{\mathrm{rms}}}^2}{2}} \le 1.0,
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7395}%
$\displaystyle \boxed{%
    \ensuremath{\sigma_\ensuremath{\mathrm{K}}} = \frac{\ensuremath{\sigma_\ensuremath{\mathrm{Jy}}}}{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{syn}}}}
\quad \mbox{with} \quad
\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{syn}}} =
\frac{2\pi\,\ensuremath{k}\,\ensuremath{\theta_\ensuremath{\mathrm{maj}}}\ensuremath{\theta_\ensuremath{\mathrm{min}}}}{4\,\ln{2}\,\ensuremath{\lambda}^2}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7398}%
$ \Delta t_\ensuremath{\mathrm{tel}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7400}%
$ \Delta t_\ensuremath{\mathrm{on}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7405}%
$ \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}\sim 40$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7407}%
$ \Delta t_\ensuremath{\mathrm{setup}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7409}%
$\displaystyle \boxed{%
      \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}= \ensuremath{\Delta t_\ensuremath{\mathrm{setup min}}}+ (\ensuremath{n_\ensuremath{\mathrm{freq}}}-1) \, \ensuremath{\Delta t_\ensuremath{\mathrm{setup/freq}}},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7411}%
$ \Delta t_\ensuremath{\mathrm{setup min}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7413}%
$ \Delta t_\ensuremath{\mathrm{setup/freq}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7419}%
$ n_\ensuremath{\mathrm{track}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7421}%
$ \ensuremath{n_\ensuremath{\mathrm{track}}}\times \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7423}%
$ \Delta t_\ensuremath{\mathrm{obs}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7425}%
$\displaystyle \boxed{%
      \ensuremath{\Delta t_\ensuremath{\mathrm{obs}}}= \ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}- \ensuremath{n_\ensuremath{\mathrm{track}}}\times \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7427}%
$\displaystyle \boxed{%
      \ensuremath{n_\ensuremath{\mathrm{track}}}= \frac{\ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{visible}}}}+ \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7429}%
$ \ensuremath{\Delta t_\ensuremath{\mathrm{visible}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7431}%
$ 0 \deg$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7435}%
$ -10 \deg$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7437}%
$ -20 \deg$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7439}%
$ -30 \deg$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7447}%
$ \ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}< \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{visible}}}}+ \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7465}%
$\displaystyle \boxed{%
      \ensuremath{\Delta t_\ensuremath{\mathrm{on}}}= \ensuremath{\Delta t_\ensuremath{\mathrm{obs}}}\times \ensuremath{\eta_\ensuremath{\mathrm{obs}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7467}%
$ \ensuremath{\eta_\ensuremath{\mathrm{obs}}}{} < 1.0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7469}%
$ \eta_\ensuremath{\mathrm{obs}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7471}%
$ \ensuremath{n_\ensuremath{\mathrm{gain cal}}}= 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7473}%
$\displaystyle \boxed{%
      \ensuremath{\eta_\ensuremath{\mathrm{obs}}}= \frac{1}{\ensuremath{\Omega_\ensuremath{\mathrm{obs}}}}
\quad \mbox{with} \quad
\ensuremath{\Omega_\ensuremath{\mathrm{obs}}}= \ensuremath{\Omega_\ensuremath{\mathrm{min}}}+ \ensuremath{n_\ensuremath{\mathrm{gain cal}}}\,\ensuremath{n_\ensuremath{\mathrm{freq}}}\,\ensuremath{\Omega_\ensuremath{\mathrm{/freq/gaincal}}},
\quad
\ensuremath{\Omega_\ensuremath{\mathrm{min}}}= 1.3,
\quad \mbox{and} \quad
\ensuremath{\Omega_\ensuremath{\mathrm{/freq/gaincal}}}= 0.3.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7475}%
$ \Omega_\ensuremath{\mathrm{min}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7477}%
$ \Omega_\ensuremath{\mathrm{/freq/gaincal}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7479}%
$ \ensuremath{\Omega_\ensuremath{\mathrm{obs}}}= 1.6$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7481}%
$ \ensuremath{\Omega_\ensuremath{\mathrm{obs}}}= 1.9,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7490}%
$ \ensuremath{\lambda}/(2\ensuremath{d_\ensuremath{\mathrm{prim}}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7492}%
$ d_\ensuremath{\mathrm{prim}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7494}%
$ \eta_\ensuremath{\mathrm{tot}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7496}%
$\displaystyle \boxed{%
      \ensuremath{\eta_\ensuremath{\mathrm{tot}}}= \frac{\Sigma \ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}{\ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}}
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7498}%
$ \ensuremath{\eta_\ensuremath{\mathrm{tot}}}\le 0.25$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7501}%
$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7507}%
$\displaystyle \boxed{%
    \ensuremath{\Delta t_\ensuremath{\mathrm{on}}}= \ensuremath{\eta_\ensuremath{\mathrm{obs}}}\, \ensuremath{\eta_\ensuremath{\mathrm{freq}}}\, \ensuremath{\displaystyle\left(  \ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}\,-\,  \ensuremath{n_\ensuremath{\mathrm{track}}}\times \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}} \right) },
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7509}%
$ \eta_\ensuremath{\mathrm{freq}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7513}%
$ \ensuremath{\eta_\ensuremath{\mathrm{freq}}}= 1.0$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7515}%
$ \ensuremath{\eta_\ensuremath{\mathrm{freq}}}\sim 0.5$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7517}%
$ \ensuremath{\eta_\ensuremath{\mathrm{freq}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7520}%
$ n_\ensuremath{\mathrm{sou}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7522}%
$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7524}%
$\displaystyle \quad
\boxed{%
    \ensuremath{\Delta t_\ensuremath{\mathrm{on}}}=  \ensuremath{\eta_\ensuremath{\mathrm{obs}}}\, \ensuremath{\eta_\ensuremath{\mathrm{freq}}}\ensuremath{\displaystyle\left(  \frac{\ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}\,-\,  \ensuremath{n_\ensuremath{\mathrm{track}}}\times  \ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}}{\ensuremath{n_\ensuremath{\mathrm{sou}}}} \right) }.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7527}%
$ A_\ensuremath{\mathrm{map}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7529}%
$ n_\ensuremath{\mathrm{beam}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7531}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{A_\ensuremath{\mathrm{beam}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7533}%
$ A_\ensuremath{\mathrm{beam}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7535}%
$ \theta_\ensuremath{\mathrm{}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7537}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{beam}}}= \frac{0.8\,\pi\,\ensuremath{\theta_\ensuremath{\mathrm{prim}}}^2}{4\,\ln(2)},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7541}%
$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} = \frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7543}%
$\displaystyle \quad
\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}= \ensuremath{\eta_\ensuremath{\mathrm{obs}}}\ensuremath{\eta_\ensuremath{\mathrm{mos}}}\ensuremath{\displaystyle\left(  \frac{\ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}\,-\, \ensuremath{n_\ensuremath{\mathrm{track}}}\times
\ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}}{\ensuremath{n_\ensuremath{\mathrm{beam}}}} \right) },
\quad \mbox{and} \quad
\ensuremath{\eta_\ensuremath{\mathrm{mos}}}= \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7545}%
$ \ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7547}%
$ \ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7555}%
$ n_\ensuremath{\mathrm{point}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7559}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{point}}}= \ensuremath{n_\ensuremath{\mathrm{beam}}}\, \ensuremath{\displaystyle\left(  \frac{7}{4} \right) }^2,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7565}%
$ \eta_\ensuremath{\mathrm{mos}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7569}%
$\displaystyle \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{min}}}}\le \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7570}%
$\displaystyle \quad
\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{min}}}}= 10\,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7571}%
$\displaystyle .$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7575}%
$\displaystyle \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}}{1 s} << \frac{6900}{\ensuremath{\theta_\ensuremath{\mathrm{alias}}} / \ensuremath{\theta_\ensuremath{\mathrm{syn}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7577}%
$ \ensuremath{\theta_\ensuremath{\mathrm{alias}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7579}%
$ \ensuremath{\theta_\ensuremath{\mathrm{syn}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7581}%
$\displaystyle \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}\le \eta\,\frac{6\,900}{1\,\ensuremath{\mathrm{sec}}}\,
\sqrt{\frac{\ensuremath{\theta_\ensuremath{\mathrm{maj}}}\ensuremath{\theta_\ensuremath{\mathrm{min}}}}{\ensuremath{A_\ensuremath{\mathrm{map}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7583}%
$ \eta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7585}%
$ \mathrm{\,sec}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7587}%
$\displaystyle 10\,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7588}%
$\displaystyle \le \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}= \ensuremath{\mathrm{min}}\ensuremath{\displaystyle\left(  45\ensuremath{\mathrm{\,sec}},\eta\,\frac{6\,900}{1\,\ensuremath{\mathrm{sec}}}\,
\sqrt{\frac{\ensuremath{\theta_\ensuremath{\mathrm{maj}}}\ensuremath{\theta_\ensuremath{\mathrm{min}}}}{\ensuremath{A_\ensuremath{\mathrm{map}}}}} \right) }
\quad \mbox{with} \quad
\eta = 0.5.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7590}%
$ \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}= 11\,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7592}%
$\displaystyle 0.47 \le \ensuremath{\eta_\ensuremath{\mathrm{mos}}}\le 1.0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7594}%
$ \ensuremath{\eta_\ensuremath{\mathrm{mos}}}= 0.67$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7596}%
$ \ensuremath{\Delta t_\ensuremath{\mathrm{min}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7598}%
$ n_\ensuremath{\mathrm{repeat/point/cycle}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7600}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{mos}}}= \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7601}%
$\displaystyle \quad
\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cycle}}}}= \ensuremath{n_\ensuremath{\mathrm{point/track}}}\,\ensuremath{\displaystyle\left(  \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}} \right) },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7603}%
$\displaystyle \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}= \ensuremath{n_\ensuremath{\mathrm{repeat/point/cycle}}}\,\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7605}%
$ \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cal max}}}}= 25\,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7607}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{repeat/point/cycle}}^\ensuremath{\mathrm{max}}}= \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cal max}}}}/\ensuremath{n_\ensuremath{\mathrm{point/track}}}-\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7608}%
$\displaystyle \quad
\ensuremath{\eta_\ensuremath{\mathrm{mos}}}=  1 - \frac{\ensuremath{n_\ensuremath{\mathrm{point/track}}}\,\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cal max}}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7610}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{large}}}= \ensuremath{\mathrm{floor}}\ensuremath{\displaystyle\left(  \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cal max}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}} \right) }.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7612}%
$ \ensuremath{\Delta t_\ensuremath{\mathrm{cycle max}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7614}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{max}}}= \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cycle max}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{min}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}} \sim 150.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7618}%
$\displaystyle \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}= \ensuremath{\mathrm{min}}\ensuremath{\displaystyle\left\{ \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}},\ensuremath{\displaystyle\left(  \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cycle max}}}}}{\ensuremath{n_\ensuremath{\mathrm{point/track}}}}-\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}} \right) } \right\}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7620}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{min}}}= \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{min}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{min}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}} = 0.47.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7622}%
$\displaystyle \boxed{%
      \ensuremath{n_\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{A_\ensuremath{\mathrm{beam}}}},
\quad \mbox{where} \quad
\ensuremath{A_\ensuremath{\mathrm{beam}}}= \frac{0.8\,\pi\,\ensuremath{\theta_\ensuremath{\mathrm{prim}}}^2}{4\,\ln(2)}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7624}%
$\displaystyle \boxed{%
      \ensuremath{n_\ensuremath{\mathrm{point}}}= \ensuremath{n_\ensuremath{\mathrm{beam}}}\, \ensuremath{\displaystyle\left(  \frac{7}{4} \right) }^2,
\quad \mbox{and} \quad
\ensuremath{n_\ensuremath{\mathrm{point/track}}}= \ensuremath{\mathrm{min}}\ensuremath{\displaystyle\left(  \ensuremath{n_\ensuremath{\mathrm{point}}},\frac{\ensuremath{n_\ensuremath{\mathrm{point}}}}{\ensuremath{n_\ensuremath{\mathrm{track}}}} \right) }.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7626}%
$\displaystyle \boxed{%
        10\,\mbox{sec} \le \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}= \ensuremath{\mathrm{min}}\ensuremath{\displaystyle\left(  45\ensuremath{\mathrm{\,sec}},\eta\,\frac{6\,900}{1\,\ensuremath{\mathrm{sec}}}\,
\sqrt{\frac{\ensuremath{\theta_\ensuremath{\mathrm{maj}}}\ensuremath{\theta_\ensuremath{\mathrm{min}}}}{\ensuremath{A_\ensuremath{\mathrm{map}}}}} \right) }
\quad \mbox{with} \quad
\eta = 0.5.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7628}%
$\displaystyle \boxed{%
      \ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{large}}}= \ensuremath{\mathrm{floor}}\ensuremath{\displaystyle\left(  \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cal max}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}} \right) },
\quad \mbox{where} \quad
\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}= 11\ensuremath{\mathrm{\,sec}},
\quad \mbox{and} \quad
\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cal max}}}}= 25\ensuremath{\mathrm{\,min}}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7630}%
$ (\ensuremath{n_\ensuremath{\mathrm{point/track}}}\le \ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{large}}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7632}%
$\displaystyle \boxed{%
      \ensuremath{n_\ensuremath{\mathrm{repeat/point/cycle}}^\ensuremath{\mathrm{max}}}= \frac{\frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cal max}}}}}{\ensuremath{n_\ensuremath{\mathrm{point/track}}}}-\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7634}%
$ (\ensuremath{n_\ensuremath{\mathrm{point/track}}}> \ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{large}}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7636}%
$ \ensuremath{n_\ensuremath{\mathrm{repeat/point/cycle}}^\ensuremath{\mathrm{max}}}= 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7638}%
$\displaystyle \boxed{%
      \ensuremath{n_\ensuremath{\mathrm{point/track}}}\le \ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{max}}},
\quad \mbox{where} \quad
\ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{max}}}= \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cycle max}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{min}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}} \sim 150,
\quad \mbox{and} \quad
\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cycle max}}}}= 60\ensuremath{\mathrm{\,min}}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7642}%
$\displaystyle \boxed{%
      \mbox{if} \quad
\ensuremath{n_\ensuremath{\mathrm{point/track}}}> \ensuremath{n_\ensuremath{\mathrm{point/track}}^\ensuremath{\mathrm{large}}},
\quad \mbox{then} \quad
\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}}= \ensuremath{\mathrm{min}}\ensuremath{\displaystyle\left\{ \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}},\ensuremath{\displaystyle\left(  \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cycle max}}}}}{\ensuremath{n_\ensuremath{\mathrm{point/track}}}}-\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}} \right) } \right\}}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7644}%
$\displaystyle \boxed{%
      \ensuremath{\eta_\ensuremath{\mathrm{mos}}}= \frac{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}}{\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}}},
\quad \mbox{and} \quad
\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}= \ensuremath{n_\ensuremath{\mathrm{repeat/point/cycle}}^\ensuremath{\mathrm{max}}}\,\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{int/scan}}}},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7646}%
$\displaystyle \boxed{%
      \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{cycle}}}}= \ensuremath{n_\ensuremath{\mathrm{point/track}}}\,\ensuremath{\displaystyle\left(  \ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{point/cycle}}}}+\ensuremath{\ensuremath{\Delta t_\ensuremath{\mathrm{slew}}}} \right) }.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7648}%
$\displaystyle \boxed{
\ensuremath{\sigma_\ensuremath{\mathrm{Jy}}} =
\frac{\ensuremath{J_\ensuremath{\mathrm{ant}}^\ensuremath{\mathrm{int}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{ant}}}\,(\ensuremath{n_\ensuremath{\mathrm{ant}}}-1)\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}}},
\quad \mbox{and} \quad
\ensuremath{\Delta t_\ensuremath{\mathrm{on}}}= \ensuremath{\eta_\ensuremath{\mathrm{obs}}}\ensuremath{\eta_\ensuremath{\mathrm{mos}}}\ensuremath{\displaystyle\left(  \frac{\ensuremath{\Delta t_\ensuremath{\mathrm{tel}}}\,-\, \ensuremath{n_\ensuremath{\mathrm{track}}}\times
\ensuremath{\Delta t_\ensuremath{\mathrm{setup}}}}{\ensuremath{n_\ensuremath{\mathrm{beam}}}} \right) }.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\appendix
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7655}%
$ P_\ensuremath{\mathrm{ant}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7657}%
$ \theta_{},\phi_{}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7659}%
$ \nu$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7661}%
$ \theta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7663}%
$ \phi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7665}%
$\displaystyle \boxed{%
    \ensuremath{\Omega_\ensuremath{\mathrm{ant}}}(\ensuremath{\nu}) = \ensuremath{\int\!\!\!\!\int_{4\pi} \ensuremath{P_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7669}%
$ \mathrm{sr}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7673}%
$ \mathrm{dimensionless}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7675}%
$ d\Omega$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7679}%
$ (= \sin \theta\,d\theta\,d\phi)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7690}%
$ 2\pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7692}%
$\displaystyle \boxed{%
    \ensuremath{\Omega_\ensuremath{\mathrm{fb}}}(\ensuremath{\nu}) = \ensuremath{\int\!\!\!\!\int_{2\pi} \ensuremath{P_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}}, %
    \quad \mbox{and} \quad %
    \ensuremath{\Omega_\ensuremath{\mathrm{mb}}}(\ensuremath{\nu}) = \ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{main\,\,lobe}}} \ensuremath{P_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7694}%
$\displaystyle \boxed{%
    \ensuremath{F_\ensuremath{\mathrm{eff}}}= \frac{\ensuremath{\Omega_\ensuremath{\mathrm{fb}}}}{\ensuremath{\Omega_\ensuremath{\mathrm{ant}}}}, %
    \quad \mbox{and} \quad %
    \ensuremath{B_\ensuremath{\mathrm{eff}}}= \frac{\ensuremath{\Omega_\ensuremath{\mathrm{mb}}}}{\ensuremath{\Omega_\ensuremath{\mathrm{ant}}}}. %
  }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7697}%
$\displaystyle \boxed{%
    \ensuremath{F_\ensuremath{\mathrm{sou}}}(\ensuremath{\nu}) = \ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7699}%
$ F_\ensuremath{\mathrm{sou}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7701}%
$ \mathrm{W\,m^{-2}\,Hz^{-1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7703}%
$ B_{}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7705}%
$ \mathrm{W\,m^{-2}\,Hz^{-1}\,sr^{-1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7724}%
$ \theta_{0},\phi_{0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7726}%
$\displaystyle \ensuremath{F_\ensuremath{\mathrm{obs}}}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu}) = \ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{P_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{}-\theta_{0},\phi_{}-\phi_{0}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7728}%
$ F_\ensuremath{\mathrm{obs}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7760}%
$\displaystyle \ensuremath{F_\ensuremath{\mathrm{obs}}}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu}) = \ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7762}%
$\displaystyle \quad %
  \ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) = \ensuremath{P_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{}-\theta_{0},\phi_{}-\phi_{0}},\ensuremath{\nu}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7767}%
$\displaystyle \boxed{%
    \ensuremath{B_{\ensuremath{\mathrm{obs}}}}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu}) = \frac{1}{\ensuremath{\Omega_\ensuremath{\mathrm{}}}}\,\ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}},
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7769}%
$ B_{obs}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7779}%
$ \Omega_\ensuremath{\mathrm{}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7808}%
$ \Omega_\ensuremath{\mathrm{fb}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7810}%
$ \Omega_\ensuremath{\mathrm{mb}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7811}%
$\displaystyle \ensuremath{B_{\ensuremath{\mathrm{ant}}}}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7812}%
$\displaystyle = \frac{1}{\ensuremath{\Omega_\ensuremath{\mathrm{ant}}}}\,\ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7813}%
$\displaystyle \ensuremath{B_{\ensuremath{\mathrm{fb}}}}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7814}%
$\displaystyle = \frac{1}{\ensuremath{\Omega_\ensuremath{\mathrm{fb}}}}\,\ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7815}%
$\displaystyle \quad
\ensuremath{B_{\ensuremath{\mathrm{mb}}}}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7816}%
$\displaystyle = \frac{1}{\ensuremath{\Omega_\ensuremath{\mathrm{mb}}}}\,\ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7818}%
$\displaystyle \boxed{%
    \ensuremath{B_{\ensuremath{\mathrm{fb}}}} = \frac{1}{\ensuremath{F_\ensuremath{\mathrm{eff}}}}\,\ensuremath{B_{\ensuremath{\mathrm{ant}}}} %
    \quad \mbox{and} \quad
\ensuremath{B_{\ensuremath{\mathrm{mb}}}} = \frac{\ensuremath{F_\ensuremath{\mathrm{eff}}}}{\ensuremath{B_\ensuremath{\mathrm{eff}}}}\,\ensuremath{B_{\ensuremath{\mathrm{fb}}}}. %
  }$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7821}%
$\displaystyle \ensuremath{dw}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu}) = \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\cos \theta \,\ensuremath{d\Omega}\,\ensuremath{dA},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7823}%
$ dw$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7825}%
$ \mathrm{W\,Hz^{-1}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7849}%
$ dA$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7851}%
$ \mathrm{m^{2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7876}%
$ R$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7878}%
$ T_{}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7880}%
$\displaystyle \ensuremath{dw}= \ensuremath{k}\,\ensuremath{T_{}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7882}%
$\displaystyle \ensuremath{T_{\ensuremath{\mathrm{mb}}}}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu}) = \frac{1}{\ensuremath{\Omega_\ensuremath{\mathrm{mb}}}}\,\ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7885}%
$ (h\ensuremath{\nu}\ll \ensuremath{k}\ensuremath{T_{}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7887}%
$ h\ensuremath{\nu}\sim \ensuremath{k}\ensuremath{T_{}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7889}%
$ \ensuremath{k}= 1.380658\times
10^{23}\ensuremath{\mathrm{\,J\,K^{-1}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7894}%
$\displaystyle \ensuremath{dw}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu}) = \frac{1}{2}\,\ensuremath{A_\ensuremath{\mathrm{eff}}}\ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7896}%
$ \mathrm{m^{-2}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7898}%
$ \eta_\ensuremath{\mathrm{ant}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7900}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{ant}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{eff}}}}{\ensuremath{A_\ensuremath{\mathrm{geo}}}} < 1, %
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7901}%
$\displaystyle \quad %
  \ensuremath{A_\ensuremath{\mathrm{geo}}}= \pi \ensuremath{\displaystyle\left(  \frac{D_\ensuremath{\mathrm{ant}}}{2} \right) }^2.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7905}%
$\displaystyle \boxed{%
    \ensuremath{A_\ensuremath{\mathrm{eff}}}(\ensuremath{\nu})\,\ensuremath{\Omega_\ensuremath{\mathrm{ant}}}(\ensuremath{\nu}) = \ensuremath{\lambda}^2,
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7912}%
$\displaystyle \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu}) = \frac{2\,\ensuremath{k}\ensuremath{T_{}}}{\ensuremath{\lambda}^2},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7914}%
$\displaystyle \ensuremath{dw}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu})
= \frac{1}{2}\,\ensuremath{A_\ensuremath{\mathrm{eff}}}\ensuremath{\int\!\!\!\!\int_{\ensuremath{\mathrm{source}}} \ensuremath{B_{}}(\ensuremath{\theta_{},\phi_{}},\ensuremath{\nu})\,\ensuremath{\tilde{P}_\ensuremath{\mathrm{ant}}}(\ensuremath{\theta_{0}-\theta_{},\phi_{0}-\phi_{}},\ensuremath{\nu}) \, d\ensuremath{\Omega_\ensuremath{\mathrm{}}}}
= \frac{1}{2}\,\ensuremath{A_\ensuremath{\mathrm{eff}}}\,\ensuremath{\Omega_\ensuremath{\mathrm{ant}}}(\ensuremath{\nu}) \,\frac{2\,\ensuremath{k}\ensuremath{T_{}}}{\ensuremath{\lambda}^2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7916}%
$\displaystyle \ensuremath{dw}(\ensuremath{\theta_{0},\phi_{0}},\ensuremath{\nu}) = \ensuremath{k}\,\ensuremath{T_{}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7921}%
$ 4\pi\ensuremath{\mathrm{\,sr}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7923}%
$\displaystyle \boxed{%
    \ensuremath{A_\ensuremath{\mathrm{eff}}}(\ensuremath{\nu})\,\ensuremath{\Omega_\ensuremath{\mathrm{fb}}}(\ensuremath{\nu}) = \ensuremath{\lambda}^2\,\ensuremath{F_\ensuremath{\mathrm{eff}}}(\ensuremath{\nu}) %
    \quad \mbox{and} \quad %
    \ensuremath{A_\ensuremath{\mathrm{eff}}}(\ensuremath{\nu})\,\ensuremath{\Omega_\ensuremath{\mathrm{mb}}}(\ensuremath{\nu}) = \ensuremath{\lambda}^2\,\ensuremath{B_\ensuremath{\mathrm{eff}}}(\ensuremath{\nu}).
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7925}%
$\displaystyle \ensuremath{B_\ensuremath{\mathrm{eff}}}(\ensuremath{\nu}) = \ensuremath{\eta_\ensuremath{\mathrm{ant}}}\,\ensuremath{A_\ensuremath{\mathrm{geo}}}\,\frac{\ensuremath{\Omega_\ensuremath{\mathrm{mb}}}(\ensuremath{\nu})}{\ensuremath{\lambda}^2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7927}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{geo}}}= \frac{\pi}{4}\,D^2,
\quad
\frac{\ensuremath{\Omega_\ensuremath{\mathrm{mb}}}(\ensuremath{\nu})}{\ensuremath{\lambda}^2} = \frac{\pi}{4\ln2}\,\ensuremath{\displaystyle\left(  \frac{\ensuremath{\theta_\ensuremath{\mathrm{mb}}}}{\ensuremath{\lambda}} \right) }^2,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7928}%
$\displaystyle \quad
\ensuremath{\theta_\ensuremath{\mathrm{mb}}} = \ensuremath{\alpha}\frac{\ensuremath{\lambda}}{D},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7930}%
$\displaystyle \boxed{%
    \ensuremath{B_\ensuremath{\mathrm{eff}}}(\ensuremath{\nu})
= \frac{\pi^2}{16\ln2}\ensuremath{\alpha}^2\,\,\ensuremath{\eta_\ensuremath{\mathrm{ant}}}(\ensuremath{\nu})
\simeq 0.8899\,\ensuremath{\alpha}^2\,\ensuremath{\eta_\ensuremath{\mathrm{ant}}}(\ensuremath{\nu}).
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7932}%
$ \alpha$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7934}%
$ \ensuremath{\alpha}\sim
1.2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7936}%
$ (\sigma)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7938}%
$\displaystyle \boxed{%
    \ensuremath{\eta_\ensuremath{\mathrm{ant}}}(\ensuremath{\nu}) = \ensuremath{\eta_\ensuremath{\mathrm{ant}}}^0 \, \exp \ensuremath{\displaystyle\left\{ - \ensuremath{\displaystyle\left(  \frac{4\pi\sigma}{\ensuremath{\lambda}} \right) }^2 \right\}}.
}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}


\end{document}
