\documentclass[11pt]{article}
%\usepackage[utf8]{inputenc}
\usepackage[titles]{tocloft}
\usepackage{natbib}
\usepackage{color}
\include{gildas-def} % GILDAS ( + at some point IMAGER) specific definitions
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\pdfminorversion=7

% \newcommand{\lang}[1]{\texttt{\MakeUppercase{#1}$\backslash$}}

\newcommand{\lmv}{\texttt{lmv}}
\newcommand{\clean}{\texttt{CLEAN}}
\newcommand{\uv}{\textit{uv}}
\newcommand{\emm}[1]{\ensuremath{#1}}   % Ensures math mode.
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\newcommand{\paren}[1]  {\nds{\left(  #1 \right) }} % Parenthesis. 
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\newcommand{\imager} {\mbox{{{\sc imager}}}}

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\begin{document}

% \frontmatter{} % For BOOKS only

\begin{center}
  \huge{
  \textbf{IMAGER} 
  } \\[2\bigskipamount]
  \Large{}
  A \gildas{} software\\[\bigskipamount]
  June 27th, 2019\\[\bigskipamount]
  Version 2.1 \\[\bigskipamount]
  corresponding to code language versions:
\begin{verbatim}
I-IMAGER,  CLEAN\     Version 5.1-03 25-Jun-2019  S.Guilloteau
I-IMAGER,  ADVANCED\  Version 1.7-02 24-May-2019  S.Guilloteau
I-IMAGER,  CALIBRATE\ Version 1.2-01 20-Mar-2019  S.Guilloteau
\end{verbatim}
  \vspace{0.5cm}
  \large{}
  Questions? Comments? Bug reports? Mail to: \texttt{gildas@iram.fr}\\[2\bigskipamount]
  The \gildas{} team welcomes an acknowledgment in publications\\
  using \gildas{} software to reduce and/or analyze data.\\
  Please use the following reference in your publications:\\
  \texttt{http://www.iram.fr/IRAMFR/GILDAS}\\[2\bigskipamount]
\end{center}

\begin{description}
\item[Documentation] \mbox{}\\
  \credit{E.~Di~Folco$^{1}$}{S.~Guilloteau$^{1}$}{J.~Pety$^{2,3}$} 
\item[Software] \mbox{}\\
  \credit{S.~Guilloteau$^{1}$}{S.~Guilloteau$^{1}$}{S.~Bardeau$^{2}$,J.~Pety$^{2,3}$}
\end{description}
1. Laboratoire d'Astrophysique de Bordeaux
2. IRAM\\
3. Observatoire de Paris\\

\begin{rawhtml}
  Note: this is the on-line version of the IMAGER Manual.
  A <A HREF="../../pdf/imager.pdf"> PDF version</A>
  is also available.
\end{rawhtml}

\bigskip{} %

Related information is available in:
\begin{latexonly}
  \begin{itemize}
  \item{IRAM Plateau de Bure Interferometer: Introduction}
  \item{IRAM Plateau de Bure Interferometer: OBS Users Guide}
  \item{IRAM Plateau de Bure Interferometer: Atmospheric Calibration}
  \item{IRAM Plateau de Bure Interferometer: Calibration Cookbook}
  \item{CLIC: Continuum and Line Interferometric Calibration}
  % \item{MIS:  Millimeter Interferometry Simulation Tools}
  \item{GREG: Graphical Possibilities}
  \item{SIC:  Command Line Interpretor}
  \end{itemize}
\end{latexonly}
%
\begin{rawhtml}
  <UL>
  <LI> IRAM Plateau de Bure Interferometer: <A HREF="../noema-intro-html/noema-intro.html">
  Introduction</A>
  <LI> IRAM Plateau de Bure Interferometer: <A HREF="../obs-html/obs.html"> 
  OBS Users Guide</A>
  <LI> IRAM Plateau de Bure Interferometer: <A HREF="../pdbi-cookbook-html/pdbi-cookbook.html"> 
  Calibration CookBook</A>
  <LI> <A HREF="../clic-html/clic.html"> CLIC:</A>  
  Continuum and Line Interferometric Calibration 
  <LI> <A HREF="../mis-html/mis.html"> MIS:</A>
  Tools for Millimeter Interferometry Simulation
  <LI> <A HREF="../greg-html/greg.html"> GREG: Graphical Possibilities</A>
  <LI> <A HREF="../sic-html/sic.html">   SIC:  Command Line Interpretor</A>
  </UL>
\end{rawhtml}

\newpage
\tableofcontents{} %

% \mainmatter{} % for BOOKS only

\newpage
\input{preamble.tex}

\newpage
\input{basic-concepts}

\newpage
\input{uv-table}

\newpage
\input{single-field}

\newpage
\input{wide-field}

\newpage
\input{self-calibration}

\clearpage
\newpage
\input{view-show}

\clearpage
\newpage
\input{all-in-one}

\clearpage
\newpage
\input{polarization}

%\input{in-out-imager}

%% \section{OTF}


%% \chapter{Imaging simulation}

% {Internal Helps}
\clearpage
\newpage

\section{CLEAN Language Internal Help} \label{CLEANH}
\input{imager-help-clean}

\newpage
\section{CALIBRATE Language Internal Help} \label{CLEANC}
\input{imager-help-calib}

\newpage
\section{ADVANCED Language Internal Help} \label{CLEANN}
\input{imager-help-news}

%\section{Description of Associated Tasks}
%\input{mapping-task-summ}
%the file mapping-task-summ.tex was copied from gildas-src-dev/integ/doc/tasks
% see also mapping-tasks-list.tex

\newpage

\appendix{}
\input{app-casa}

\section{Properties of the Fourier Transform}
\label{app:fourier}
Let us name $f(x)$ a function, and $F(X)$ its Fourier transform. We
use here the simple, non-unitary convention
\begin{itemize}
\item Definition: $F(X) = \int_{-\infty}^{+\infty} f(x) e^{-2i\pi x X} dx$
\item Linearity:  $h(x) = a f(x) + b g(x)$, then $H(X) = a F5X) + b G(X)$
\item Translation:  $h(x) = f(x-x_0)$, then $H(X) = e^{-2i\pi x_0 X} F(X)$
\item Shifting: $h(x) = e^{2i\pi x X_0} f(x)$, then $H(X) = F(X-X_0)$
\item Scaling: $h(x) = f(ax)$, then $H(X) = \frac{1}{|a|}F(\frac{X}{a}$
(the so-called \textit{time reversal} property is obtained with $a=1$
\item Conjugation: if $h(x) = \bar{f(x)}$, then $H(X) = \bar{F(-X)}$
\item Integration: With $X=0$ in the definition\\
$F(0) = \int_{-\infty}^{+\infty} f(x) dx$
\item Convolution: $h(x)= f(x) * g(x)$ then $H(X) = F(X) G((X)$. \\
The Fourier Transform of a product of two functions is the convolution of
the Fourier Transforms of the functions.
\item Uncertainty principle:  the more concentrated $f(x)$ is, the 
more spread out its Fourier transform $F(X)$ must be. In particular, 
the scaling property of the Fourier transform may be seen as saying: if 
we squeeze a function in $x$, its Fourier transform stretches out in $X$. 
It is not possible to arbitrarily concentrate both a function and its 
Fourier transform. 
\end{itemize}
The definition, illustrated here with scalars, also holds for $x,X$ 
being 2-D vectors in Euclidean space, the product in the definition 
being a standard dot product of these vectors. 


% \backmatter{} % for BOOKS only

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\bibliographystyle{aa}

\printindex{} %

\end{document}

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