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\usepackage{natbib}
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\pagestyle{fancy}

\fancyhf{} % Clears all fields.

\lhead{\scshape IRAM-30m HERA time/sensitivity estimator}
\rhead{\scshape \nouppercase{\rightmark}}   %
\fancyfoot[C]{\bfseries\thepage {}}

%
\renewcommand{\headrulewidth}{0pt}    %
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\renewcommand{\footrulewidth}{0pt}    %

%
\renewcommand{\sectionmark}[1]{%
  \markright{\thesection. \MakeLowercase{#1}}}
%
\renewcommand{\subsectionmark}[1]{}

%
\providecommand{\ie}{{\em i.e.}}%
\providecommand{\eg}{{\em e.g.}}%
\providecommand{\cf}{cf.} 

%
\providecommand{\emm}[1]{\ensuremath{#1}}    % Ensures math mode.%
\providecommand{\emr}[1]{\ensuremath{\mathrm{#1}}}  % Uses math roman fonts.%
\providecommand{\nds}[1]{\ensuremath{\displaystyle#1}}  % Normal display size for array and tabular environment.%
\providecommand{\paren}[1]{\ensuremath{\displaystyle\left(  #1 \right) }}  % Parenthesis.%
\providecommand{\cbrace}[1]{\ensuremath{\displaystyle\left\{ #1 \right\}}}  % Curly Braces.%
\providecommand{\bracket}[1]{\ensuremath{\displaystyle\left[  #1 \right] }}  % Brackets.%
\providecommand{\abs}[1]{\ensuremath{\left| #1 \right|}}  % Absolute value.

%
\providecommand{\tint}[1][]{\ensuremath{t_\ensuremath{\mathrm{#1}}}}%
\providecommand{\tonoff}{\ensuremath{t_\ensuremath{\mathrm{onoff}}}}%
\providecommand{\tonoffpix}{\ensuremath{\mathrm{\ensuremath{t_\ensuremath{\mathrm{onoff}}}^{pix}}}}%
\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{\noise}[1][]{\ensuremath{\sigma_\ensuremath{\mathrm{#1}}}}%
\providecommand{\Tsys}{\ensuremath{T_\ensuremath{\mathrm{sys}}}}%
\providecommand{\obseff}{\ensuremath{\eta_\ensuremath{\mathrm{tel}}}}%
\providecommand{\speceff}{\ensuremath{\eta_\ensuremath{\mathrm{spec}}}}%
\providecommand{\edgeeff}{\ensuremath{\eta_\ensuremath{\mathrm{edge}}}}%
\providecommand{\edgeeffmin}{\ensuremath{\eta_\ensuremath{\mathrm{edge}}^\ensuremath{\mathrm{min}}}} 

%
\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}}}}%
\providecommand{\Trec}{\ensuremath{T_\ensuremath{\mathrm{rec}}}}%
\providecommand{\taus}{\ensuremath{\tau_\ensuremath{\mathrm{s}}}}%
\providecommand{\gim}{\ensuremath{G_\ensuremath{\mathrm{im}}}}%
\providecommand{\Feff}{\ensuremath{F_\ensuremath{\mathrm{eff}}}}%
\providecommand{\A}{\ensuremath{A}} 

%
\providecommand{\Aedge}{\ensuremath{A_\ensuremath{\mathrm{edge}}}}%
\providecommand{\Amap}[1][]{\ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{#1}}}}%
\providecommand{\Atarget}{\ensuremath{A_\ensuremath{\mathrm{target}}}}%
\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{\nbeampix}{\ensuremath{n_\ensuremath{\mathrm{beam}}^\ensuremath{\mathrm{pix}}}} 

%
\providecommand{\tontot}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{tot}}}}%
\providecommand{\tofftot}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{tot}}}} 

%
\providecommand{\tonbeam}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{beam}}}}%
\providecommand{\toncover}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{on}}}^\ensuremath{\mathrm{cover}}}}%
\providecommand{\toffbeam}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{beam}}}}%
\providecommand{\toffcover}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{off}}}^\ensuremath{\mathrm{cover}}}}%
\providecommand{\tsigbeam}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{beam}}}}%
\providecommand{\tsigcover}{\ensuremath{\ensuremath{t_\ensuremath{\mathrm{sig}}}^\ensuremath{\mathrm{cover}}}} 

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

%
\providecommand{\nonperoff}{\ensuremath{n_\ensuremath{\mathrm{on/off}}}}%
\providecommand{\tstable}{\ensuremath{t_\ensuremath{\mathrm{stable}}}}%
\providecommand{\Achunk}{\ensuremath{A_\ensuremath{\mathrm{chunk}}}}%
\providecommand{\tchunk}{\ensuremath{t_\ensuremath{\mathrm{chunk}}}}%
\providecommand{\Achunknew}{\ensuremath{A_\ensuremath{\mathrm{chunk}}^\ensuremath{\mathrm{new}}}}%
\providecommand{\tchunknew}{\ensuremath{t_\ensuremath{\mathrm{chunk}}^\ensuremath{\mathrm{new}}}}%
\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{\Asubmappix}{\ensuremath{A_\ensuremath{\mathrm{submap}}^\ensuremath{\mathrm{pix}}}}%
\providecommand{\nsubmappix}{\ensuremath{n_\ensuremath{\mathrm{submap}}^\ensuremath{\mathrm{pix}}}} 

%
\providecommand{\nsubscan}{\ensuremath{n_\ensuremath{\mathrm{subscan}}}}%
\providecommand{\sqrtnpix}{\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}}%
\providecommand{\npix}{\ensuremath{n_\ensuremath{\mathrm{pix}}}}%
\providecommand{\npol}{\ensuremath{n_\ensuremath{\mathrm{pol}}}}%
\providecommand{\weight}{\ensuremath{w}}%
\providecommand{\Tsysave}{\ensuremath{\overline{T}_\ensuremath{\mathrm{sys}}}} 

%
\providecommand{\beamsep}{\ensuremath{\Delta}}%
\providecommand{\rowsep}{\ensuremath{\delta}}%
\providecommand{\groupsep}{\ensuremath{\delta'}} 
%
\renewcommand{\angle}{\ensuremath{\alpha}}%
\providecommand{\nperp}{\ensuremath{n_\bot}}%
\providecommand{\dperp}{\ensuremath{d_\bot}}%
\providecommand{\dpara}{\ensuremath{d_\|}}%
\providecommand{\dedge}{\ensuremath{d_\ensuremath{\mathrm{edge}}}}%
\providecommand{\aspect}{\ensuremath{a}}%
\providecommand{\tedgepix}{\ensuremath{t_\ensuremath{\mathrm{edge}}^\ensuremath{\mathrm{pix}}}} 

%
\providecommand{\floor}{\ensuremath{\mathrm{floor}}} 

%
\providecommand{\TabEdge}{%
  \begin{table}
    \centering
    \caption{Mapping strategy to minimize edge effects.}
    \begin{tabular}{cccc}
      \hline
      \hline
      \ensuremath{t_\ensuremath{\mathrm{chunk}}}{} & \ensuremath{n_\bot}{} & \ensuremath{a}{} & \ensuremath{\eta_\ensuremath{\mathrm{edge}}}{} \\
         min.    &          &           &            \\
      \hline
       1  & 1 & 3.7 & 0.83 \\
       2  & 2 & 1.9 & 0.83 \\
       5  & 4 & 1.2 & 0.86 \\
       10 & 6 & 1.1 & 0.90 \\
      \hline
    \end{tabular}
    \label{tab:edge}
  \end{table}} 



\usepackage{xcolor}



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$\deg$%
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$\displaystyle \frac{\ensuremath{n_\ensuremath{\mathrm{pol}}}\,\ensuremath{n_\ensuremath{\mathrm{pix}}}}{\ensuremath{\overline{T}_\ensuremath{\mathrm{sys}}}^2} = \sum_{i=1,\ensuremath{n_\ensuremath{\mathrm{pol}}},\,j=1,\ensuremath{n_\ensuremath{\mathrm{pix}}}} \frac{1}{T^2_{\ensuremath{\mathrm{sys}}_{ij}}}.
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$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{psw}}}^\ensuremath{\mathrm{track}} = \frac{2\,\ensuremath{\overline{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}}}}},
  \quad \mbox{and} \quad
  \ensuremath{\sigma_\ensuremath{\mathrm{fsw}}}^\ensuremath{\mathrm{track}} = \frac{\sqrt{2}\,\ensuremath{\overline{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{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3690}%
$\ensuremath{\Delta}=
\ensuremath{\theta}/2.5$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3692}%
$4''$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3694}%
$\ensuremath{\Delta}\simeq 2\ensuremath{\theta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3072}%
\ensuremath{\alpha}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3076}%
\ensuremath{\Delta}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3696}%
$\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}\times\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3082}%
\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3084}%
\ensuremath{\delta'}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4177}%
$\displaystyle \ensuremath{\delta}= \ensuremath{\Delta}\,\sin\ensuremath{\alpha}\quad \mbox{and} \quad
  \ensuremath{\delta'}= \ensuremath{\Delta}\,\cos\ensuremath{\alpha}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4179}%
$\displaystyle \ensuremath{\delta'}= \ensuremath{n_\ensuremath{\mathrm{subscan}}}\,\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}\,\ensuremath{\delta},
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4181}%
$\displaystyle \tan\ensuremath{\alpha}= \frac{1}{\ensuremath{n_\ensuremath{\mathrm{subscan}}}\,\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3698}%
$\ensuremath{n_\ensuremath{\mathrm{subscan}}}=1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3700}%
$\ensuremath{n_\ensuremath{\mathrm{subscan}}}=2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3702}%
$\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}= 3$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3706}%
$\sim 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3710}%
$\ensuremath{\alpha}=
18.4^\circ$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3712}%
$\ensuremath{\Delta}\sim 12''$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3716}%
$\ensuremath{\alpha}=
9.5^\circ$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3718}%
$\ensuremath{\Delta}\sim 24''$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3722}%
$9.5^\circ$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3726}%
$3\ensuremath{\delta}= 12''$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3728}%
$\ensuremath{d_\bot}= \ensuremath{n_\ensuremath{\mathrm{subscan}}}\ensuremath{n_\ensuremath{\mathrm{pix}}}\ensuremath{\delta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3144}%
\ensuremath{d_\|}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3146}%
\ensuremath{A_\ensuremath{\mathrm{target}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3148}%
\ensuremath{n_\bot}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3730}%
$\ensuremath{d_\bot}\times\ensuremath{d_\|}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4204}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{target}}}= \ensuremath{n_\bot}\,\ensuremath{d_\bot}\,\ensuremath{d_\|}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3162}%
\ensuremath{A_\ensuremath{\mathrm{edge}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3732}%
$\ensuremath{n_\bot}\,\ensuremath{d_\bot}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4209}%
$\displaystyle \ensuremath{d_\ensuremath{\mathrm{edge}}}= (\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}-1)\,\ensuremath{\Delta}\,(\cos\ensuremath{\alpha}+\sin\ensuremath{\alpha}) 
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4211}%
$\displaystyle \ensuremath{d_\ensuremath{\mathrm{edge}}}= (\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}-1)\,(1+\ensuremath{n_\ensuremath{\mathrm{subscan}}}\,\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}})\ensuremath{\delta}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3190}%
\ensuremath{\eta_\ensuremath{\mathrm{edge}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4214}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{edge}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{target}}}}{\ensuremath{A_\ensuremath{\mathrm{target}}}+\ensuremath{A_\ensuremath{\mathrm{edge}}}},
  \quad \mbox{with} \quad
  \ensuremath{A_\ensuremath{\mathrm{edge}}}= \ensuremath{n_\bot}\,\ensuremath{d_\bot}\,\ensuremath{d_\ensuremath{\mathrm{edge}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4218}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{edge}}}= \frac{1}{1+\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{d_\|}}}
           = \frac{1}{1+\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{a}\,\ensuremath{n_\bot}\,\ensuremath{d_\bot}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4220}%
$\displaystyle \ensuremath{a}= \frac{\ensuremath{d_\|}}{\ensuremath{n_\bot}\,\ensuremath{d_\bot}}
  \quad \mbox{with} \quad
  \ensuremath{a}> 1
  \quad \mbox{and} \quad
  \ensuremath{n_\bot}\mbox{ integer.}
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3240}%
\ensuremath{A_\ensuremath{\mathrm{chunk}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3242}%
\ensuremath{t_\ensuremath{\mathrm{chunk}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4225}%
$\displaystyle \ensuremath{n_\bot}\,\ensuremath{d_\bot}\,(\ensuremath{d_\|}+\ensuremath{d_\ensuremath{\mathrm{edge}}}) = \ensuremath{A_\ensuremath{\mathrm{chunk}}}\quad \mbox{with} \quad
  \ensuremath{A_\ensuremath{\mathrm{chunk}}}= \ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{}}}\,\ensuremath{d_\bot}\,\ensuremath{t_\ensuremath{\mathrm{chunk}}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3734}%
$\ensuremath{a}\,\ensuremath{n_\bot}\,\ensuremath{d_\bot}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4229}%
$\displaystyle \ensuremath{n_\bot}^2 + \ensuremath{n_\bot}\,\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{a}\,\ensuremath{d_\bot}} - \frac{\ensuremath{A_\ensuremath{\mathrm{chunk}}}}{\ensuremath{a}\,\ensuremath{d_\bot}^2} = 0.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4231}%
$\displaystyle \ensuremath{n_\bot}= \frac{1}{2}\,\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{a}\,\ensuremath{d_\bot}}\,\ensuremath{\displaystyle\left[  \sqrt{1+\frac{4\ensuremath{a}\,\ensuremath{A_\ensuremath{\mathrm{chunk}}}}{\ensuremath{d_\ensuremath{\mathrm{edge}}}^2}}-1 \right] }.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4233}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{edge}}}= \frac{1}{1+\frac{2}{\sqrt{1+\frac{4\ensuremath{a}\,\ensuremath{A_\ensuremath{\mathrm{chunk}}}}{\ensuremath{d_\ensuremath{\mathrm{edge}}}^2}}-1}}
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4235}%
$\displaystyle \quad \mbox{with} \quad
  \frac{\ensuremath{a}\,\ensuremath{A_\ensuremath{\mathrm{chunk}}}}{\ensuremath{d_\ensuremath{\mathrm{edge}}}^2} =
  \frac{\ensuremath{\theta}}{4\ensuremath{\delta}}\,
  \frac{\ensuremath{a}\,\ensuremath{f_\ensuremath{\mathrm{dump}}}\ensuremath{t_\ensuremath{\mathrm{chunk}}}}
       {\ensuremath{\displaystyle\left[  \ensuremath{\displaystyle\left(  \sqrt{\ensuremath{n_\ensuremath{\mathrm{subscan}}}\,\ensuremath{n_\ensuremath{\mathrm{pix}}}}-\frac{1}{\sqrt{\ensuremath{n_\ensuremath{\mathrm{subscan}}}\,\ensuremath{n_\ensuremath{\mathrm{pix}}}}} \right) }
                -\ensuremath{\displaystyle\left(  \sqrt{\ensuremath{n_\ensuremath{\mathrm{subscan}}}}-\frac{1}{\sqrt{\ensuremath{n_\ensuremath{\mathrm{subscan}}}}} \right) } \right] }^2}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3736}%
$(\ensuremath{a}\,\ensuremath{A_\ensuremath{\mathrm{chunk}}})/\ensuremath{d_\ensuremath{\mathrm{edge}}}^2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3330}%
\ensuremath{f_\ensuremath{\mathrm{dump}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3738}%
$\ensuremath{f_\ensuremath{\mathrm{dump}}}= 2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3340}%
\ensuremath{a}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3740}%
$\ensuremath{a}> 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3742}%
$\ensuremath{a}=
1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4279}%
$\displaystyle \ensuremath{n_\bot}= \ensuremath{\mathrm{floor}}(\ensuremath{n_\bot}),
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4281}%
$\displaystyle \ensuremath{a}= \frac{\ensuremath{A_\ensuremath{\mathrm{chunk}}}}{(\ensuremath{n_\bot}\,\ensuremath{d_\bot})^2}-\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{n_\bot}\,\ensuremath{d_\bot}}.
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4295}%
$\displaystyle \ensuremath{d_\bot}= \ensuremath{n_\ensuremath{\mathrm{subscan}}}\,\ensuremath{n_\ensuremath{\mathrm{pix}}}\,\delta,
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4297}%
$\displaystyle \ensuremath{d_\ensuremath{\mathrm{edge}}}= (\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}}-1)\,(1+\ensuremath{n_\ensuremath{\mathrm{subscan}}}\,\ensuremath{\sqrt{n_\ensuremath{\mathrm{pix}}}})\ensuremath{\delta},
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4299}%
$\displaystyle \ensuremath{t_\ensuremath{\mathrm{chunk}}}^\ensuremath{\mathrm{psw}} = 2~\mbox{minutes}
    \quad \mbox{and} \quad
    \ensuremath{t_\ensuremath{\mathrm{chunk}}}^\ensuremath{\mathrm{fsw}} = 10~\mbox{minutes}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4301}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{chunk}}}= \frac{\ensuremath{\theta}}{4}\,\ensuremath{f_\ensuremath{\mathrm{dump}}}\,\frac{\ensuremath{d_\bot}}{\ensuremath{n_\ensuremath{\mathrm{subscan}}}}\,\ensuremath{t_\ensuremath{\mathrm{chunk}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3744}%
$\ensuremath{A_\ensuremath{\mathrm{target}}}<   \ensuremath{\eta_\ensuremath{\mathrm{edge}}^\ensuremath{\mathrm{min}}}\, \ensuremath{A_\ensuremath{\mathrm{chunk}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3746}%
$\ensuremath{\eta_\ensuremath{\mathrm{edge}}^\ensuremath{\mathrm{min}}}= 0.8$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4309}%
$\displaystyle 1.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4310}%
$\displaystyle \ensuremath{n_\bot}= \ensuremath{\mathrm{floor}}\ensuremath{\displaystyle\left[  \frac{\sqrt{\ensuremath{A_\ensuremath{\mathrm{target}}}}}{\ensuremath{d_\bot}} \right] },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4311}%
$\displaystyle 2.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4312}%
$\displaystyle \mbox{if $\ensuremath{n_\bot}= 0$, then send an error message: ``Area too small, use raster mapping.''},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4313}%
$\displaystyle 3.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4314}%
$\displaystyle \ensuremath{a}= \frac{\ensuremath{A_\ensuremath{\mathrm{target}}}}{(\ensuremath{n_\bot}\,\ensuremath{d_\bot})^2}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3750}%
$\ensuremath{A_\ensuremath{\mathrm{target}}}\ge \ensuremath{\eta_\ensuremath{\mathrm{edge}}^\ensuremath{\mathrm{min}}}\, \ensuremath{A_\ensuremath{\mathrm{chunk}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4318}%
$\displaystyle \ensuremath{n_\bot}= \ensuremath{\mathrm{floor}}\ensuremath{\displaystyle\left\{ \frac{1}{2}\,\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{d_\bot}}\,\ensuremath{\displaystyle\left[  \sqrt{1+\frac{4\ensuremath{A_\ensuremath{\mathrm{chunk}}}}{\ensuremath{d_\ensuremath{\mathrm{edge}}}^2}}-1 \right] } \right\}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4322}%
$\displaystyle \ensuremath{a}= \frac{\ensuremath{A_\ensuremath{\mathrm{chunk}}}}{(\ensuremath{n_\bot}\,\ensuremath{d_\bot})^2}-\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{n_\bot}\,\ensuremath{d_\bot}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4325}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{edge}}}= \frac{1}{1+\frac{\ensuremath{d_\ensuremath{\mathrm{edge}}}}{\ensuremath{a}\,\ensuremath{n_\bot}\,\ensuremath{d_\bot}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3754}%
$\ensuremath{A_\ensuremath{\mathrm{target}}}<
  \ensuremath{\eta_\ensuremath{\mathrm{edge}}^\ensuremath{\mathrm{min}}}\, \ensuremath{A_\ensuremath{\mathrm{chunk}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4331}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{chunk}}^\ensuremath{\mathrm{new}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{target}}}}{\ensuremath{\eta_\ensuremath{\mathrm{edge}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4333}%
$\displaystyle \ensuremath{t_\ensuremath{\mathrm{chunk}}^\ensuremath{\mathrm{new}}}= \ensuremath{t_\ensuremath{\mathrm{chunk}}}\,\frac{\ensuremath{A_\ensuremath{\mathrm{chunk}}^\ensuremath{\mathrm{new}}}}{\ensuremath{A_\ensuremath{\mathrm{chunk}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4335}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{chunk}}}= \ensuremath{A_\ensuremath{\mathrm{chunk}}^\ensuremath{\mathrm{new}}}\quad \mbox{and} \quad \ensuremath{t_\ensuremath{\mathrm{chunk}}}= \ensuremath{t_\ensuremath{\mathrm{chunk}}^\ensuremath{\mathrm{new}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3756}%
$\ensuremath{t_\ensuremath{\mathrm{chunk}}}< 1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3758}%
$\ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{}}}+\ensuremath{A_\ensuremath{\mathrm{edge}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4341}%
$\displaystyle \ensuremath{\eta_\ensuremath{\mathrm{edge}}}\,(\ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{}}}+\ensuremath{A_\ensuremath{\mathrm{edge}}}) = \ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3760}%
$\ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{}}}/\ensuremath{\eta_\ensuremath{\mathrm{edge}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3550}%
\ensuremath{n_\ensuremath{\mathrm{pix}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3762}%
$\ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4350}%
$\displaystyle \ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{pix}}} = \frac{\ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{}}}/\ensuremath{\eta_\ensuremath{\mathrm{edge}}}}{\ensuremath{n_\ensuremath{\mathrm{pix}}}}.
  $%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4352}%
$\displaystyle \ensuremath{\sigma_\ensuremath{\mathrm{psw}}}^\ensuremath{\mathrm{otf}} = \frac{\ensuremath{\displaystyle\left(  \sqrt{\ensuremath{n_\ensuremath{\mathrm{beam}}^\ensuremath{\mathrm{pix}}}}+\sqrt{\ensuremath{n_\ensuremath{\mathrm{submap}}^\ensuremath{\mathrm{pix}}}} \right) }\,\ensuremath{\overline{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}}}}},  
  \quad \mbox{and} \quad
  \ensuremath{\sigma_\ensuremath{\mathrm{fsw}}}^\ensuremath{\mathrm{otf}} = \frac{\sqrt{2\,\ensuremath{n_\ensuremath{\mathrm{beam}}^\ensuremath{\mathrm{pix}}}}\,\ensuremath{\overline{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_inline3602}%
\ensuremath{n_\ensuremath{\mathrm{beam}}^\ensuremath{\mathrm{pix}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3604}%
\ensuremath{n_\ensuremath{\mathrm{submap}}^\ensuremath{\mathrm{pix}}}%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4356}%
$\displaystyle \ensuremath{n_\ensuremath{\mathrm{beam}}^\ensuremath{\mathrm{pix}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{}}}}{\ensuremath{\eta_\ensuremath{\mathrm{edge}}}\,\ensuremath{n_\ensuremath{\mathrm{pix}}}\,\ensuremath{A_\ensuremath{\mathrm{beam}}}}
  \quad \mbox{and} \quad
  \ensuremath{n_\ensuremath{\mathrm{submap}}^\ensuremath{\mathrm{pix}}}= \frac{\ensuremath{A_\ensuremath{\mathrm{map}}^\ensuremath{\mathrm{}}}}{\ensuremath{\eta_\ensuremath{\mathrm{edge}}}\,\ensuremath{n_\ensuremath{\mathrm{pix}}}\,\ensuremath{A_\ensuremath{\mathrm{submap}}^\ensuremath{\mathrm{pix}}}}
$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4358}%
$\displaystyle \quad \mbox{with} \quad
  \ensuremath{A_\ensuremath{\mathrm{submap}}^\ensuremath{\mathrm{pix}}}= \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{pix}}}\,\ensuremath{t_\ensuremath{\mathrm{stable}}}\quad \mbox{and} \quad
  \ensuremath{v_\ensuremath{\mathrm{area}}^\ensuremath{\mathrm{pix}}} = \ensuremath{\delta}\,\ensuremath{v_\ensuremath{\mathrm{linear}}^\ensuremath{\mathrm{}}}.
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$\displaystyle \ensuremath{\mathrm{\ensuremath{t_\ensuremath{\mathrm{onoff}}}^{pix}}}= \ensuremath{\eta_\ensuremath{\mathrm{edge}}}\,\ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}\quad \mbox{and} \quad
  \ensuremath{t_\ensuremath{\mathrm{edge}}^\ensuremath{\mathrm{pix}}}= (1-\ensuremath{\eta_\ensuremath{\mathrm{edge}}})\,\ensuremath{\eta_\ensuremath{\mathrm{tel}}}\,\ensuremath{t_\ensuremath{\mathrm{tel}}}.
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\end{document}
