\batchmode
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\usepackage{natbib}
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%
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%
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%
\providecommand{\tint}[1][]{\ensuremath{t_\ensuremath{\mathrm{#1}}}}%
\providecommand{\tonoff}{\ensuremath{t_\ensuremath{\mathrm{onoff}}}}%
\providecommand{\ton}{\ensuremath{t_\ensuremath{\mathrm{on}}}}%
\providecommand{\toff}{\ensuremath{t_\ensuremath{\mathrm{off}}}}%
\providecommand{\tsig}{\ensuremath{t_\ensuremath{\mathrm{sig}}}}%
\providecommand{\ttel}{\ensuremath{t_\ensuremath{\mathrm{tel}}}}%
\providecommand{\npol}{\ensuremath{n_\ensuremath{\mathrm{pol}}}} 

%
\providecommand{\noise}[1][]{\ensuremath{\sigma_\ensuremath{\mathrm{#1}}}}%
\providecommand{\Tsys}{\ensuremath{T_\ensuremath{\mathrm{sys}}}}%
\providecommand{\speceff}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}}%
\providecommand{\obseff}{\ensuremath{\eta_\ensuremath{\mathrm{tel}}}} 

%
\providecommand{\dnu}{\ensuremath{d\nu}} 

%
\providecommand{\Tas}{\ensuremath{T_\ensuremath{\mathrm{a}}^\star}}%
\providecommand{\Tatm}{\ensuremath{T_\ensuremath{\mathrm{atm}}}}%
\providecommand{\Tcab}{\ensuremath{T_\ensuremath{\mathrm{cab}}}}%
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\providecommand{\gim}{\ensuremath{G_\ensuremath{\mathrm{im}}}}%
\providecommand{\Feff}{\ensuremath{F_\ensuremath{\mathrm{eff}}}}%
\providecommand{\A}{\ensuremath{A}} 

%
\providecommand{\Amap}{\ensuremath{A_\ensuremath{\mathrm{map}}}}%
\providecommand{\Abeam}{\ensuremath{A_\ensuremath{\mathrm{beam}}}}%
\providecommand{\beam}{\ensuremath{\theta}}%
\providecommand{\grideff}{\ensuremath{\eta_\ensuremath{\mathrm{grid}}}}%
\providecommand{\nbeam}{\ensuremath{n_\ensuremath{\mathrm{beam}}}} 

%
\providecommand{\tontot}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{tot}}}}%
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%
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\providecommand{\tsigcover}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{cover}}}} 

%
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\providecommand{\varea}[1][]{\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{#1}}}}%
\providecommand{\vlinmax}{\ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{max}}}}%
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\providecommand{\rowseparation}{\ensuremath{\Delta\theta}} 

%
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\providecommand{\tstable}{\ensuremath{t_\ensuremath{\mathrm{stable}}}}%
\providecommand{\Asubmap}{\ensuremath{A_\ensuremath{\mathrm{submap}}}}%
\providecommand{\tsubmap}{\ensuremath{t_\ensuremath{\mathrm{submap}}}}%
\providecommand{\nsubmap}{\ensuremath{n_\ensuremath{\mathrm{submap}}}}%
\providecommand{\ncover}{\ensuremath{n_\ensuremath{\mathrm{cover}}}} 

%
\providecommand{\cint}[1]{\texttt{int(}#1\texttt{)}} 


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\lhead{\scshape IRAM-30m EMIR time/sensitivity estimator}
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%
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%
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\begin{displaymath}
    \ensuremath{n_\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{A_\ensuremath{\mathrm{beam}}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2917}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2919}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2921}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath303}%
\begin{displaymath}
    \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}+\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}}
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2933}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{tot}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2935}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{tot}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2943}%
\ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2945}%
\ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{max}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2947}%
\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2949}%
\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath320}%
\begin{displaymath}
    \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}= \ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{}}}\, \ensuremath{\Delta\theta},
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2961}%
\ensuremath{\Delta\theta}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath324}%
\begin{displaymath}
    \ensuremath{\Delta\theta}= \frac{\ensuremath{\theta}}{2.5}.
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath331}%
\begin{displaymath}
  \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{tot}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{tot}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath333}%
\begin{displaymath}
  \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{t_\ensuremath{\mathrm{onoff}}}}{\ensuremath{n_\ensuremath{\mathrm{beam}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath337}%
\begin{displaymath}
  \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}}{2} = \frac{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}}{2} = \frac{\ensuremath{t_\ensuremath{\mathrm{onoff}}}}{2\ensuremath{n_\ensuremath{\mathrm{beam}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath345}%
\begin{displaymath}
  \ensuremath{\sigma_\ensuremath{\mathrm{fsw}}} = \frac{\sqrt{2\,\ensuremath{n_\ensuremath{\mathrm{beam}}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\sqrt{\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath349}%
\begin{displaymath}
  \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{t_\ensuremath{\mathrm{onoff}}}} \le \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath359}%
\begin{displaymath}
  \ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{optimal}} = \sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}} \, \ensuremath{t_\ensuremath{\mathrm{on}}}
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3021}%
\ensuremath{n_\ensuremath{\mathrm{on/off}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath367}%
\begin{displaymath}
  \ensuremath{t_\ensuremath{\mathrm{sig}}}= \frac{\ensuremath{t_\ensuremath{\mathrm{on}}}}{1+\frac{1}{\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}}}
  \quad \mbox{and} \quad
  \ensuremath{\sigma_\ensuremath{\mathrm{}}}=
  \frac{\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\sqrt{\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{t_\ensuremath{\mathrm{on}}}}}\sqrt{1+\frac{1}{\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}}}.
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3045}%
\ensuremath{A_\ensuremath{\mathrm{submap}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3047}%
\ensuremath{n_\ensuremath{\mathrm{submap}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3049}%
\ensuremath{t_\ensuremath{\mathrm{stable}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3051}%
\ensuremath{t_\ensuremath{\mathrm{submap}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3053}%
\ensuremath{n_\ensuremath{\mathrm{cover}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3055}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3057}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{cover}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath392}%
\begin{displaymath}
    \ensuremath{n_\ensuremath{\mathrm{submap}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{A_\ensuremath{\mathrm{submap}}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath397}%
\begin{displaymath}
    \ensuremath{n_\ensuremath{\mathrm{on/off}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{submap}}}}{\ensuremath{A_\ensuremath{\mathrm{beam}}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath402}%
\begin{displaymath}
    \ensuremath{n_\ensuremath{\mathrm{beam}}}= \ensuremath{n_\ensuremath{\mathrm{submap}}}\,\ensuremath{n_\ensuremath{\mathrm{on/off}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath405}%
\begin{displaymath}
    \ensuremath{A_\ensuremath{\mathrm{submap}}}= \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}\, \ensuremath{t_\ensuremath{\mathrm{submap}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath409}%
\begin{displaymath}
    \ensuremath{t_\ensuremath{\mathrm{submap}}}= \ensuremath{n_\ensuremath{\mathrm{on/off}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath412}%
\begin{displaymath}
    \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}= \ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}
    \quad \mbox{and} \quad
    \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}= \ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{cover}}}
    \quad \mbox{with} \quad
    \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{cover}}}= \sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}.
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath417}%
\begin{displaymath}
    \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}= \ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{cover}}}
              = \frac{\ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{t_\ensuremath{\mathrm{submap}}}}{\ensuremath{n_\ensuremath{\mathrm{on/off}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath422}%
\begin{displaymath}
    \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{n_\ensuremath{\mathrm{submap}}}\,(\ensuremath{n_\ensuremath{\mathrm{on/off}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}+ \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{cover}}}).
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath426}%
\begin{displaymath}
    \ensuremath{t_\ensuremath{\mathrm{onoff}}}=
    \ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{t_\ensuremath{\mathrm{submap}}}\,\ensuremath{n_\ensuremath{\mathrm{submap}}}\,\ensuremath{\displaystyle\left(  1+\frac{1}{\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}} \right) }.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3511}%
$\ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{t_\ensuremath{\mathrm{submap}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath437}%
\begin{displaymath}
  \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}\,\ensuremath{n_\ensuremath{\mathrm{submap}}}\,\ensuremath{\displaystyle\left(  1+\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}} \right) }^2.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath442}%
\begin{displaymath}
  \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}\,\ensuremath{\displaystyle\left(  \sqrt{\ensuremath{n_\ensuremath{\mathrm{submap}}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{beam}}}} \right) }^2.
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath450}%
\begin{displaymath}
  \ensuremath{\sigma_\ensuremath{\mathrm{psw}}} =
  \frac{\ensuremath{\displaystyle\left(  \sqrt{\ensuremath{n_\ensuremath{\mathrm{beam}}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{submap}}}} \right) }\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\,\sqrt{\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3513}%
$\ensuremath{A_\ensuremath{\mathrm{map}}}/\ensuremath{A_\ensuremath{\mathrm{beam}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath465}%
\begin{displaymath}
    \ensuremath{n_\ensuremath{\mathrm{submap}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}\, \ensuremath{t_\ensuremath{\mathrm{submap}}}}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3515}%
$\ensuremath{t_\ensuremath{\mathrm{submap}}}=
  \ensuremath{t_\ensuremath{\mathrm{stable}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3517}%
$\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}= \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3519}%
$\ensuremath{t_\ensuremath{\mathrm{submap}}}\,\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath472}%
\begin{displaymath}
    \ensuremath{n_\ensuremath{\mathrm{submap}}}= 1+\texttt{int(}\ensuremath{n_\ensuremath{\mathrm{submap}}}\texttt{)}.
    
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3521}%
$\ensuremath{t_\ensuremath{\mathrm{submap}}}\,\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}<
  \ensuremath{t_\ensuremath{\mathrm{stable}}}\,\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4068}%
$\displaystyle 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4069}%
$\displaystyle \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{T_\ensuremath{\mathrm{sys}}}^2}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}^2\,\ensuremath{\sigma_\ensuremath{\mathrm{}}}^2\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4070}%
$\displaystyle 2.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4071}%
$\displaystyle \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}\,\ensuremath{\displaystyle\left(  \sqrt{\ensuremath{n_\ensuremath{\mathrm{submap}}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{beam}}}} \right) }^2,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4072}%
$\displaystyle 3.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4073}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}= \ensuremath{t_\ensuremath{\mathrm{onoff}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4076}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{on/off}}}= \frac{\ensuremath{n_\ensuremath{\mathrm{beam}}}}{\ensuremath{n_\ensuremath{\mathrm{submap}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4078}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{cover}}}= \frac{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}}{\ensuremath{t_\ensuremath{\mathrm{submap}}}}\ensuremath{\displaystyle\left(  \ensuremath{n_\ensuremath{\mathrm{on/off}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}} \right) },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4080}%
$\displaystyle \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{t_\ensuremath{\mathrm{submap}}}}{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4082}%
$\displaystyle \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3523}%
$\ensuremath{n_\ensuremath{\mathrm{cover}}}< 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3525}%
$\ensuremath{n_\ensuremath{\mathrm{cover}}}\ge 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3527}%
$\ensuremath{A_\ensuremath{\mathrm{submap}}}(= \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}\,
    \ensuremath{t_\ensuremath{\mathrm{submap}}})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3529}%
$\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}
    < \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath518}%
\begin{displaymath}
  \ensuremath{\sigma_\ensuremath{\mathrm{fsw}}} = \frac{\sqrt{2\,\ensuremath{n_\ensuremath{\mathrm{beam}}}}\,\ensuremath{T_\ensuremath{\mathrm{sys}}}}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}\sqrt{\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath527}%
\begin{displaymath}
  \frac{\ensuremath{\sigma_\ensuremath{\mathrm{psw}}}}{\ensuremath{\sigma_\ensuremath{\mathrm{fsw}}}} = \frac{1}{\sqrt{2}}\,\ensuremath{\displaystyle\left(  1+\sqrt{\frac{\ensuremath{n_\ensuremath{\mathrm{submap}}}}{\ensuremath{n_\ensuremath{\mathrm{beam}}}}} \right) }.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath535}%
\begin{displaymath}
  \frac{\ensuremath{n_\ensuremath{\mathrm{beam}}}}{\ensuremath{n_\ensuremath{\mathrm{submap}}}} = \ensuremath{n_\ensuremath{\mathrm{on/off}}}\ge \frac{1}{3-2\sqrt{2}} \sim 6.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3531}%
$\ensuremath{\sigma_\ensuremath{\mathrm{psw}}}/\ensuremath{\sigma_\ensuremath{\mathrm{fsw}}} \simeq 0.84$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3533}%
$\ensuremath{n_\ensuremath{\mathrm{on/off}}}= 30$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3535}%
$\simeq 0.78$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3537}%
$\ensuremath{n_\ensuremath{\mathrm{on/off}}}= 100$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath543}%
\begin{displaymath}
  \ensuremath{n_\ensuremath{\mathrm{on/off}}}= \frac{\ensuremath{t_\ensuremath{\mathrm{stable}}}}{\ensuremath{A_\ensuremath{\mathrm{beam}}}/\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\appendix
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3539}%
$\ensuremath{\eta_\ensuremath{\mathrm{tel}}}= 0.5.$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3541}%
$\ensuremath{T_\ensuremath{\mathrm{atm}}}= 250$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3543}%
$\ensuremath{T_\ensuremath{\mathrm{cab}}}= 290$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3545}%
$\ensuremath{F_\ensuremath{\mathrm{eff}}}= 0.95$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3547}%
$\ensuremath{T_\ensuremath{\mathrm{rec}}}= 75$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3549}%
$Trec = 95$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3551}%
$\ensuremath{G_\ensuremath{\mathrm{im}}}= 0.1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3553}%
$\ensuremath{\eta_\ensuremath{\mathrm{spec}}}= 0.87$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3555}%
$\ensuremath{t_\ensuremath{\mathrm{stable}}}= 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3557}%
$\ensuremath{\theta}= \,\frac{2460''}{\nu\,\ensuremath{\mathrm{GHz}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3559}%
$\ensuremath{f_\ensuremath{\mathrm{dump}}}= 2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath579}%
\begin{displaymath}
    \ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{max}}}= \ensuremath{f_\ensuremath{\mathrm{dump}}}\,\frac{\ensuremath{\theta}}{4}\,\ensuremath{\mathrm{arcsec/s}}
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath584}%
\begin{displaymath}
    \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}= \ensuremath{f_\ensuremath{\mathrm{dump}}}\,\frac{\ensuremath{\theta}}{2.5}\,\frac{\ensuremath{\theta}}{4}\,\ensuremath{\mathrm{arcsec^2/s}}
    \quad \mbox{or} \quad
    \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}= \ensuremath{f_\ensuremath{\mathrm{dump}}}\,\frac{\ensuremath{\theta}^2}{10}\,\ensuremath{\mathrm{arcsec^2/s}}
  \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath602}%
\begin{displaymath}
  \ensuremath{t_\ensuremath{\mathrm{off}}}= \alpha \, \ensuremath{t_\ensuremath{\mathrm{on}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3561}%
$\alpha$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3563}%
$\ensuremath{t_\ensuremath{\mathrm{onoff}}}
= \ensuremath{n_\ensuremath{\mathrm{on/off}}}\ensuremath{t_\ensuremath{\mathrm{on}}}+ \ensuremath{t_\ensuremath{\mathrm{off}}}= (\ensuremath{n_\ensuremath{\mathrm{on/off}}}+\alpha)\,\ensuremath{t_\ensuremath{\mathrm{on}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath605}%
\begin{displaymath}
  \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \frac{\ensuremath{T_\ensuremath{\mathrm{sys}}}^2}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}^2\,\sigma^2\,\ensuremath{d\nu}} \ensuremath{\displaystyle\left(  1+\ensuremath{n_\ensuremath{\mathrm{on/off}}}+\alpha+\frac{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}{\alpha} \right) }.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath611}%
\begin{displaymath}
  \frac{d\ensuremath{t_\ensuremath{\mathrm{onoff}}}}{d\alpha} \propto 1-\frac{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}{\alpha^2}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath617}%
\begin{displaymath}
  \alpha = \sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}} \quad \mbox{or} \quad
  \ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{optimal}} = \sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}} \, \ensuremath{t_\ensuremath{\mathrm{on}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}


\end{document}
