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\pagestyle{fancy}
\fancyhf{} % Clears all fields.
\lhead{\scshape Pety \& Bardeau, 2011: \texttt{CLASS}{} spectral axis}
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{
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   \fancyhead[C]{Original version at \url{www.iram-institute.org/medias/uploads/class-spectral-axis-v12.pdf}}
   \fancyfoot[C]{\bfseries\thepage {}}
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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{\dmeas}[1][]{\ensuremath{d_{\ensuremath{\mathrm{#1}}}^{\ensuremath{\mathrm{meas}}}}}%
\providecommand{\dobs}[1][]{\ensuremath{d_{\ensuremath{\mathrm{#1}}}^{\ensuremath{\mathrm{obs}}}}}%
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\providecommand{\clight}{\ensuremath{c}} 

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\providecommand{\class}{\texttt{CLASS}}%
\providecommand{\mira}{\texttt{MIRA}}%
\providecommand{\mrtcal}{\texttt{MRTCAL}} 

%
\providecommand{\TabHeader}{%
  \begin{table}
    \centering
    \caption{\texttt{CLASS}{} header parameters used to describe the
      frequency/velocity axes and their translation in this document.}
    \begin{tabular}{cccc}
      \hline
      \hline
      \texttt{CLASS}{} name & Unit & Translation & Notation \\
      \hline
      \texttt{nchan}   &    --- & Number of channel           & ---               \\
      \texttt{rchan}   &    --- & Reference channel           & \ensuremath{i_{\ensuremath{\mathrm{0}}}}            \\
      \texttt{restf}   &    MHz & Tuned signal rest frequency & \ensuremath{f_\ensuremath{\mathrm{tuned,sig}}^{\ensuremath{\mathrm{rest}}}} \\
      \texttt{image}   &    MHz & Tuned image rest frequency  & \ensuremath{f_\ensuremath{\mathrm{tuned,ima}}^{\ensuremath{\mathrm{rest}}}} \\
      \texttt{fres}    &    MHz & Observatory channel spacing & \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{meas}}}}}{}         \\
      \texttt{vres}    & \ensuremath{\, \ensuremath{\mathrm{km\,s^{-1}}}}{} & Velocity channel spacing    & \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{meas}}}}}{}         \\
      \texttt{voff}    & \ensuremath{\, \ensuremath{\mathrm{km\,s^{-1}}}}{} & source systemic velocity    & \ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{meas}}}}       \\
      \texttt{doppler} &    --- & Doppler factor              & \ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{meas}}}}       \\
      \hline
    \end{tabular}
    \label{tab:header}
  \end{table}} 




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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5926}%
\ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath275}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\, \ensuremath{\left[ \ensuremath{f_\ensuremath{\mathrm{RF}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}})-\ensuremath{f_\ensuremath{\mathrm{LO}}^{\ensuremath{\mathrm{obs}}}} \right] }
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7064}%
$\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}=-1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7066}%
$\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}=+1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath279}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}},
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath282}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}} \ensuremath{\equiv}\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\, (\ensuremath{f_\ensuremath{\mathrm{RFtuned}}^{\ensuremath{\mathrm{obs}}}} -\ensuremath{f_\ensuremath{\mathrm{LO}}^{\ensuremath{\mathrm{obs}}}})
                 \ensuremath{\equiv}\ensuremath{\mathrm{cste}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5968}%
\ensuremath{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath285}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{RF}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = (\ensuremath{f_\ensuremath{\mathrm{LO}}^{\ensuremath{\mathrm{obs}}}}+\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\,\ensuremath{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}}) 
                 + \ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\, (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5988}%
\ensuremath{f_\ensuremath{\mathrm{RFtuned}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5990}%
\ensuremath{f_\ensuremath{\mathrm{sig}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline5992}%
\ensuremath{f_\ensuremath{\mathrm{ima}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath288}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{sig}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{obs}}}} + \ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\, (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}}
  \quad \mbox{with} \quad
  \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{obs}}}} \ensuremath{\equiv}\ensuremath{f_\ensuremath{\mathrm{LO}}^{\ensuremath{\mathrm{obs}}}}+\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\,\ensuremath{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}},
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath292}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{ima}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{obs}}}} - \ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\, (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}}
  \quad \mbox{with} \quad
  \ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{obs}}}} \ensuremath{\equiv}\ensuremath{f_\ensuremath{\mathrm{LO}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\,\ensuremath{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}}.
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7068}%
$\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\,\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6056}%
\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6062}%
\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7074}%
$\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}} > 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath310}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}} > 0.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath315}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{sig}}^{\ensuremath{\mathrm{rest}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath317}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{ima}}^{\ensuremath{\mathrm{rest}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{rest}}}} - (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath319}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}}= \frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{obs}}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{obs}}}}}
  \quad \mbox{and} \quad
  \ensuremath{d_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{obs}}}} = -\frac{\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}.  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6148}%
\ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6150}%
\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{rest}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath327}%
\begin{displaymath}
  \ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\mathrm{obs}}}}\ensuremath{\equiv}\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\ensuremath{\left[ \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{obs}}}} \right] }.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath330}%
\begin{displaymath}
  \ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{\mathrm{cste}} = 2\,\ensuremath{f_\ensuremath{\mathrm{IFtuned}}^{\ensuremath{\mathrm{obs}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath333}%
\begin{displaymath}
  \frac{\ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}}} = 1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}{}
  \quad \mbox{} \quad
  \frac{\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{rest}}}}} = 1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}{}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath342}%
\begin{displaymath}
  \ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\mathrm{rest}}}}\ensuremath{\equiv}\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\ensuremath{\left[ \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}}-\ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{rest}}}} \right] }.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath345}%
\begin{displaymath}
  \ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\mathrm{rest}}}}\,\ensuremath{\left[ 1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} \right] },
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath348}%
\begin{displaymath}
  
  \ensuremath{f_\ensuremath{\mathrm{ima,tuned}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}}-\frac{\ensuremath{SB_{\ensuremath{\mathrm{sep}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\,\ensuremath{\left[ 1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}} \right] }}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath357}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}= \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}+ \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath361}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \ensuremath{\left(  1-\frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}} \right) }
  \quad \mbox{and} \quad
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}= \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \ensuremath{\left(  1-\frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}} \right) }.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7076}%
$\ensuremath{\left[ \ensuremath{SB_\ensuremath{\mathrm{sign}}^{\ensuremath{\mathrm{}}}}\, \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\,
  (\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}})/\ensuremath{c} \right] }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath370}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{lsr}}}} = \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{obs}}}} + \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}} \, \frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath374}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) + \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}} \, \frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath378}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) + \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) \, \frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath382}%
\begin{displaymath}
  \Delta\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}})\,\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}}\, \frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7078}%
$\ensuremath{i_{\ensuremath{\mathrm{}}}}= \ensuremath{i_{\ensuremath{\mathrm{0}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6296}%
\ensuremath{f_\ensuremath{\mathrm{tuned,sig}}^{\ensuremath{\mathrm{rest}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6298}%
\ensuremath{f_\ensuremath{\mathrm{tuned,ima}}^{\ensuremath{\mathrm{rest}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6300}%
\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{meas}}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6302}%
\ensuremath{\, \ensuremath{\mathrm{km\,s^{-1}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6304}%
\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{meas}}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6308}%
\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{meas}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6310}%
\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{meas}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath399}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}}= \frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{meas}}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}}}
  \quad \mbox{and} \quad
  \ensuremath{d_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}} = -\frac{\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}}}{\ensuremath{c}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6348}%
\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{meas}}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6350}%
\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath409}%
\begin{displaymath}
  \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{meas}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{meas}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{meas}}}}}
  \quad \mbox{with} \quad
  \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{meas}}}}}= -\ensuremath{c}\frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{meas}}}}}}{\ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath416}%
\begin{displaymath}
  \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}
  \quad \mbox{with} \quad
  \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}= -\ensuremath{c}\frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}}}{\ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath426}%
\begin{displaymath}
  \frac{\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}}-\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}}{\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}} = \frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}}}{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}}}-1 = \frac{1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}}-1.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7080}%
$v/\ensuremath{c}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath434}%
\begin{displaymath}
  \frac{\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}}-\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}}{\ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}} = \frac{\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}} \sim 10^{-4}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7082}%
$\sim250\ensuremath{\, \ensuremath{\mathrm{km\,s^{-1}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6442}%
\ensuremath{\, \ensuremath{\mathrm{mm}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6444}%
\ensuremath{\, \ensuremath{\mathrm{kHz}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath443}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}}= \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}}\, \frac{1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{obs}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}},
  \quad
  \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}= -\ensuremath{c}\frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{lsr}}}}}}{\ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}},
  \quad \mbox{and} \quad
  \ensuremath{d_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}= 1-\frac{\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7701}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig}}^{\ensuremath{\mathrm{rest}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7702}%
$\textstyle =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7703}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig,old}}^{\ensuremath{\mathrm{rest}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,old}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7705}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,new}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath459}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}}= \frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{meas}}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath463}%
\begin{displaymath}
    \ensuremath{i_{\ensuremath{\mathrm{0,new}}}}
  = \ensuremath{i_{\ensuremath{\mathrm{0,old}}}}
  + \frac{\ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}}-\ensuremath{f_\ensuremath{\mathrm{sig,old}}^{\ensuremath{\mathrm{rest}}}}}{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{IF}}^{\ensuremath{\mathrm{meas}}}}}} \, \ensuremath{\left(  1+\ensuremath{d_{\ensuremath{\mathrm{\ensuremath{\mathrm{sys}}}}}^{\ensuremath{\mathrm{meas}}}} \right) }
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7710}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{ima}}^{\ensuremath{\mathrm{rest}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7712}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{ima,old}}^{\ensuremath{\mathrm{rest}}}} - (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,old}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7714}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}} - (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,new}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7716}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7719}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7721}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{ima,old}}^{\ensuremath{\mathrm{rest}}}} - (\ensuremath{i_{\ensuremath{\mathrm{0,new}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,old}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath473}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}} + \ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{sig,old}}^{\ensuremath{\mathrm{rest}}}}+\ensuremath{f_\ensuremath{\mathrm{ima,old}}^{\ensuremath{\mathrm{rest}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath476}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}} =  - \ensuremath{c}\frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{meas}}}}}}{\ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath484}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{meas}}}}= (1+\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}}) \, \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{rest}}}} = (1+\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}) \, \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{rest}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath486}%
\begin{displaymath}
  \ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}} = -\frac{\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{meas}}}}}{\ensuremath{c}}
  \quad \mbox{and} \quad
  \ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}} = -\frac{\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{meas}}}}}{\ensuremath{c}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath493}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{rest}}}} \, \frac{1+\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7732}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}}(i)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7734}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,new}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{rest}}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7736}%
$\displaystyle \ensuremath{\left[ \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}} +  (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,old}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{rest}}}}} \right] }
      \, \frac{1+\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath504}%
\begin{displaymath}
  \ensuremath{i_{\ensuremath{\mathrm{0,new}}}} = \ensuremath{i_{\ensuremath{\mathrm{0,old}}}} 
             + \frac{\ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}}}{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{meas}}}}}} \, \ensuremath{\left[ \ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}-\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}} \right] },
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath509}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{rest}}}}} = \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{rest}}}}} \, \frac{1+\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}},
  \quad \mbox{{\em i.e.}{},} \quad
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{meas}}}}} = \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{meas}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7742}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}}(i)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7744}%
$\displaystyle \ensuremath{f_\ensuremath{\mathrm{ima,tuned,new}}^{\ensuremath{\mathrm{rest}}}} - (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,new}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{rest}}}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay7746}%
$\displaystyle \ensuremath{\left[ \ensuremath{f_\ensuremath{\mathrm{ima,tuned,old}}^{\ensuremath{\mathrm{rest}}}} -  (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0,old}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{rest}}}}} \right] }
      \, \frac{1+\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath521}%
\begin{displaymath}
    \ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}}
  = \ensuremath{f_\ensuremath{\mathrm{ima,old}}^{\ensuremath{\mathrm{rest}}}} \, \frac{1+\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}}
  - \ensuremath{f_\ensuremath{\mathrm{sig,tuned}}^{\ensuremath{\mathrm{rest}}}} \, \frac{\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}-\ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}}}{1+\ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath528}%
\begin{displaymath}
  \ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}} = -\frac{\ensuremath{v_{\ensuremath{\mathrm{lsr}}}^{\ensuremath{\mathrm{meas}}}}+\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}}
  \quad \mbox{and} \quad
  \ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}} = -\frac{\ensuremath{v_{\ensuremath{\mathrm{lsr}}}^{\ensuremath{\mathrm{meas}}}}+\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}}.  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath535}%
\begin{displaymath}
  \ensuremath{d_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}} = \ensuremath{d_{\ensuremath{\mathrm{old}}}^{\ensuremath{\mathrm{meas}}}} + \frac{\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{lsr}}}}-\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{lsr}}}}}{\ensuremath{c}}.  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}

%
\providecommand{\vpara}{\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}%


%
\providecommand{\vperp}{\ensuremath{v_{\ensuremath{\mathrm{\perp}}}^{\ensuremath{\mathrm{obs}}}}}%

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath550}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \frac{\sqrt{\ensuremath{c}^2-{\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}}^2}}{\ensuremath{c}+\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}},
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7084}%
${\ensuremath{v_{\ensuremath{\mathrm{}}}^{\ensuremath{\mathrm{obs}}}}}^2 = {\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}^2+{\ensuremath{v_{\ensuremath{\mathrm{\perp}}}^{\ensuremath{\mathrm{obs}}}}}^2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6722}%
\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6724}%
\ensuremath{v_{\ensuremath{\mathrm{\perp}}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7086}%
$\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}\gg \ensuremath{v_{\ensuremath{\mathrm{\perp}}}^{\ensuremath{\mathrm{obs}}}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath565}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \sqrt{\frac{\ensuremath{c}-\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}+\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}}.
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath572}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \ensuremath{\left(  1-\frac{\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}} \right) }.
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath587}%
\begin{displaymath}
  \ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \sqrt{\frac{\ensuremath{c}+\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}-\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath591}%
\begin{displaymath}
  \ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}= \ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}\, \ensuremath{\left(  1+\frac{\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}} \right) }.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath595}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}= \frac{\ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}}{1+\frac{\ensuremath{v_{\ensuremath{\mathrm{\parallel}}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{c}}}.
  
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath602}%
\begin{displaymath}
  \ensuremath{v_{\ensuremath{\mathrm{opt}}}^{\ensuremath{\mathrm{obs}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{v_{\ensuremath{\mathrm{sys,opt}}}^{\ensuremath{\mathrm{obs}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{opt}}}^{\ensuremath{\mathrm{obs}}}}}
  \quad \mbox{with} \quad
  \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{opt}}}^{\ensuremath{\mathrm{obs}}}}} = +\ensuremath{c}\, \frac{\delta\ensuremath{\lambda_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{obs}}}}}{\ensuremath{\lambda_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
\stepcounter{subsubsection}

%
\providecommand{\vconv}[1]{\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{#1}}}}}^{\ensuremath{\mathrm{}}}}}%


%
\providecommand{\Doppler}[2]{\ensuremath{D_{\ensuremath{\mathrm{#1}}}(#2)}}%

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6832}%
\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{1}}}}}^{\ensuremath{\mathrm{}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath617}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{tuned,conv1}}^{\ensuremath{\mathrm{obs}}}} = \ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}\,\ensuremath{D_{\ensuremath{\mathrm{1}}}(\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{1}}}}}^{\ensuremath{\mathrm{}}}})},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6840}%
\ensuremath{D_{\ensuremath{\mathrm{1}}}()}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath626}%
\begin{displaymath}
  D_\ensuremath{\mathrm{opt}}(\ensuremath{v_{\ensuremath{\mathrm{opt}}}^{\ensuremath{\mathrm{}}}}) = \frac{1}{1+\frac{\ensuremath{v_{\ensuremath{\mathrm{opt}}}^{\ensuremath{\mathrm{}}}}}{\ensuremath{c}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6850}%
\ensuremath{f_\ensuremath{\mathrm{tuned,1}}^{\ensuremath{\mathrm{obs}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6854}%
\ensuremath{D_{\ensuremath{\mathrm{2}}}()}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath636}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{}}^{\ensuremath{\mathrm{rest}}}}(\ensuremath{i_{\ensuremath{\mathrm{}}}}) = \ensuremath{f_\ensuremath{\mathrm{apparent}}^{\ensuremath{\mathrm{rest}}}} + (\ensuremath{i_{\ensuremath{\mathrm{}}}}-\ensuremath{i_{\ensuremath{\mathrm{0}}}}) \, \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{apparent}}^{\ensuremath{\mathrm{rest}}}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath638}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{apparent}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}\,\frac{\ensuremath{D_{\ensuremath{\mathrm{1}}}(\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{1}}}}}^{\ensuremath{\mathrm{}}}})}}{\ensuremath{D_{\ensuremath{\mathrm{2}}}(\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{1}}}}}^{\ensuremath{\mathrm{}}}})}},
  \quad \mbox{and} \quad
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{apparent}}^{\ensuremath{\mathrm{rest}}}}} = \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{tuned}}^{\ensuremath{\mathrm{rest}}}}}\,\frac{\ensuremath{D_{\ensuremath{\mathrm{1}}}(\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{1}}}}}^{\ensuremath{\mathrm{}}}})}}{\ensuremath{D_{\ensuremath{\mathrm{2}}}(\ensuremath{v_{\ensuremath{\mathrm{\ensuremath{\mathrm{1}}}}}^{\ensuremath{\mathrm{}}}})}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlpictureA{tex2html_wrap7794}%
\includegraphics[width=\linewidth]{class-spectral-axis-v12-optic-vs-radio}%
\lthtmlpictureZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7092}%
$10^{-5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath669}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{sig,old}}^{\ensuremath{\mathrm{rest}}}}\,\frac{D_\ensuremath{\mathrm{optic}}(\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{obs}}}})}{D_\ensuremath{\mathrm{radio}}(\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{obs}}}})},
  \quad
  \ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{ima,old}}^{\ensuremath{\mathrm{rest}}}}\,\frac{D_\ensuremath{\mathrm{optic}}(\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{obs}}}})}{D_\ensuremath{\mathrm{radio}}(\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{obs}}}})},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath675}%
\begin{displaymath}
  \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{meas}}}}} = \ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{old}}^{\ensuremath{\mathrm{meas}}}}}\,\frac{D_\ensuremath{\mathrm{optic}}(\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{obs}}}})}{D_\ensuremath{\mathrm{radio}}(\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{obs}}}})},
  \quad \mbox{and} \quad
  \ensuremath{\delta \ensuremath{v_{\ensuremath{\mathrm{new}}}^{\ensuremath{\mathrm{meas}}}}} = -\ensuremath{c}\frac{\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{meas}}}}}}{\ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6934}%
\ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6936}%
\ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline6938}%
\ensuremath{\delta \ensuremath{f_\ensuremath{\mathrm{new}}^{\ensuremath{\mathrm{meas}}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath717}%
\begin{displaymath}
    \frac{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{obs}}}})}{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{obs}}}})}
  = \frac{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{lsr}}}})}{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{lsr}}}})}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath723}%
\begin{displaymath}
  \ensuremath{f_\ensuremath{\mathrm{sig,new}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{sig,old}}^{\ensuremath{\mathrm{rest}}}}\,\frac{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{lsr}}}})}{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{lsr}}}})},
  \quad
  \ensuremath{f_\ensuremath{\mathrm{ima,new}}^{\ensuremath{\mathrm{rest}}}} = \ensuremath{f_\ensuremath{\mathrm{ima,old}}^{\ensuremath{\mathrm{rest}}}}\,\frac{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,old}}}^{\ensuremath{\mathrm{lsr}}}})}{D_\ensuremath{\mathrm{relat}}(\ensuremath{v_{\ensuremath{\mathrm{sys,new}}}^{\ensuremath{\mathrm{lsr}}}})},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline7044}%
\ensuremath{v_{\ensuremath{\mathrm{sys}}}^{\ensuremath{\mathrm{lsr}}}}%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
