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%
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\providecommand{\eg}{{\em e.g.}}%
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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}}}}%
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\providecommand{\A}{\ensuremath{A}} 

%
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\providecommand{\nbeam}{\ensuremath{n_\ensuremath{\mathrm{beam}}}} 

%
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%
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%
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\providecommand{\rowseparation}{\ensuremath{\Delta\theta}} 

%
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\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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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3968}%
$\displaystyle \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}}}}
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2896}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{tot}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2898}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{tot}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2906}%
\ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2908}%
\ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{max}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2910}%
\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2912}%
\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3981}%
$\displaystyle \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}= \ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{}}}\, \ensuremath{\Delta\theta},
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2924}%
\ensuremath{\Delta\theta}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3984}%
$\displaystyle \ensuremath{\Delta\theta}= \frac{\ensuremath{\theta}}{2.5}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3987}%
$\displaystyle \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{tot}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{tot}}},
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3989}%
$\displaystyle \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}}}},
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3991}%
$\displaystyle \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}}}},
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3993}%
$\displaystyle \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}}}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3995}%
$\displaystyle \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{t_\ensuremath{\mathrm{onoff}}}} \le \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay3999}%
$\displaystyle \ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{optimal}} = \sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}} \, \ensuremath{t_\ensuremath{\mathrm{on}}}
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2984}%
\ensuremath{n_\ensuremath{\mathrm{on/off}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4003}%
$\displaystyle \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}}}}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3008}%
\ensuremath{A_\ensuremath{\mathrm{submap}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3010}%
\ensuremath{n_\ensuremath{\mathrm{submap}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3012}%
\ensuremath{t_\ensuremath{\mathrm{stable}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3014}%
\ensuremath{t_\ensuremath{\mathrm{submap}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3016}%
\ensuremath{n_\ensuremath{\mathrm{cover}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3018}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3020}%
\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{cover}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4016}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{submap}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{A_\ensuremath{\mathrm{submap}}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4018}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{on/off}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{submap}}}}{\ensuremath{A_\ensuremath{\mathrm{beam}}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4020}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{beam}}}= \ensuremath{n_\ensuremath{\mathrm{submap}}}\,\ensuremath{n_\ensuremath{\mathrm{on/off}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4022}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{submap}}}= \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}\, \ensuremath{t_\ensuremath{\mathrm{submap}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4025}%
$\displaystyle \ensuremath{t_\ensuremath{\mathrm{submap}}}= \ensuremath{n_\ensuremath{\mathrm{on/off}}}\,\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4027}%
$\displaystyle \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}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4029}%
$\displaystyle \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}}}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4031}%
$\displaystyle \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}}}).
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4033}%
$\displaystyle \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) }.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3474}%
$\ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{t_\ensuremath{\mathrm{submap}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4038}%
$\displaystyle \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.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4041}%
$\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_indisplay4043}%
$\displaystyle \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}}}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3476}%
$\ensuremath{A_\ensuremath{\mathrm{map}}}/\ensuremath{A_\ensuremath{\mathrm{beam}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4056}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{submap}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}}}{\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}\, \ensuremath{t_\ensuremath{\mathrm{submap}}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3478}%
$\ensuremath{t_\ensuremath{\mathrm{submap}}}=
  \ensuremath{t_\ensuremath{\mathrm{stable}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3480}%
$\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}= \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3482}%
$\ensuremath{t_\ensuremath{\mathrm{submap}}}\,\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4063}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{submap}}}= 1+\texttt{int(}\ensuremath{n_\ensuremath{\mathrm{submap}}}\texttt{)}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3484}%
$\ensuremath{t_\ensuremath{\mathrm{submap}}}\,\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}<
  \ensuremath{t_\ensuremath{\mathrm{stable}}}\,\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4069}%
$\displaystyle 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4070}%
$\displaystyle \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{T_\ensuremath{\mathrm{sys}}}^2}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}^2\,\ensuremath{\sigma_\ensuremath{\mathrm{}}}^2\,\ensuremath{d\nu}\,\ensuremath{n_\ensuremath{\mathrm{pol}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4071}%
$\displaystyle 2.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4072}%
$\displaystyle \ensuremath{t_\ensuremath{\mathrm{onoff}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}\,\ensuremath{\displaystyle\left(  \sqrt{\ensuremath{n_\ensuremath{\mathrm{submap}}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{beam}}}} \right) }^2,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4073}%
$\displaystyle 3.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4074}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}= \ensuremath{t_\ensuremath{\mathrm{onoff}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4077}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{on/off}}}= \frac{\ensuremath{n_\ensuremath{\mathrm{beam}}}}{\ensuremath{n_\ensuremath{\mathrm{submap}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4079}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{cover}}}= \frac{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}}{\ensuremath{t_\ensuremath{\mathrm{submap}}}}\ensuremath{\displaystyle\left(  \ensuremath{n_\ensuremath{\mathrm{on/off}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}} \right) },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4081}%
$\displaystyle \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}= \frac{\ensuremath{n_\ensuremath{\mathrm{cover}}}\,\ensuremath{t_\ensuremath{\mathrm{submap}}}}{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4083}%
$\displaystyle \ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}= \ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}\,\sqrt{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3486}%
$\ensuremath{n_\ensuremath{\mathrm{cover}}}< 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3488}%
$\ensuremath{n_\ensuremath{\mathrm{cover}}}\ge 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3490}%
$\ensuremath{A_\ensuremath{\mathrm{submap}}}(= \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}\,
    \ensuremath{t_\ensuremath{\mathrm{submap}}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3492}%
$\ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{}}}< \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{max}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4106}%
$\displaystyle \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}}}}},
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4108}%
$\displaystyle \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}}}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4110}%
$\displaystyle \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) }.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4112}%
$\displaystyle \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.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3494}%
$\ensuremath{\sigma_\ensuremath{\mathrm{psw}}}/\ensuremath{\sigma_\ensuremath{\mathrm{fsw}}} \simeq 0.84$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3496}%
$\ensuremath{n_\ensuremath{\mathrm{on/off}}}= 30$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3498}%
$\simeq 0.78$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3500}%
$\ensuremath{n_\ensuremath{\mathrm{on/off}}}= 100$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4118}%
$\displaystyle \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}}}},
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\appendix
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3502}%
$\ensuremath{\eta_\ensuremath{\mathrm{tel}}}= 0.5.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3504}%
$\ensuremath{T_\ensuremath{\mathrm{atm}}}= 250$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3506}%
$\ensuremath{T_\ensuremath{\mathrm{cab}}}= 290$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3508}%
$\ensuremath{F_\ensuremath{\mathrm{eff}}}= 0.95$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3510}%
$\ensuremath{T_\ensuremath{\mathrm{rec}}}= 75$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3512}%
$Trec = 95$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3514}%
$\ensuremath{G_\ensuremath{\mathrm{im}}}= 0.1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3516}%
$\ensuremath{\eta_\ensuremath{\mathrm{spec}}}= 0.87$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3518}%
$\ensuremath{t_\ensuremath{\mathrm{stable}}}= 2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3520}%
$\ensuremath{\theta}= \,\frac{2460''}{\nu\,\ensuremath{\mathrm{GHz}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3522}%
$\ensuremath{f_\ensuremath{\mathrm{dump}}}= 2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4141}%
$\displaystyle \ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{max}}}= \ensuremath{f_\ensuremath{\mathrm{dump}}}\,\frac{\ensuremath{\theta}}{4}\,\ensuremath{\mathrm{arcsec/s}}
  $%
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$\displaystyle \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}}
  $%
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$\displaystyle \ensuremath{t_\ensuremath{\mathrm{off}}}= \alpha \, \ensuremath{t_\ensuremath{\mathrm{on}}},
$%
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$\alpha$%
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$\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}}}$%
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$\displaystyle \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) }.
$%
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$\displaystyle \frac{d\ensuremath{t_\ensuremath{\mathrm{onoff}}}}{d\alpha} \propto 1-\frac{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}{\alpha^2}
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$\displaystyle \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}}}.
$%
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\end{document}
