Index: trunk/MagicDoku/strategy_mc_ana.tex
===================================================================
--- trunk/MagicDoku/strategy_mc_ana.tex	(revision 771)
+++ trunk/MagicDoku/strategy_mc_ana.tex	(revision 772)
@@ -13,6 +13,6 @@
 %% elements: title, author, date, plus TDAScode
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\title{The strategy for MC production and analysis
-optimisation}
+\title{Outline of a standard analysis for MAGIC \\
+(including Monte Carlo work)}
 \author{W. Wittek, H. Kornmayer\\ 
 \texttt{wittek@mppu.mpg.de, h.kornmayer@web.de }}
@@ -38,7 +38,173 @@
 
 %------------------------------------------------------------
-\section{teil 1}
-
-\section{teil 2}
+\section{Aim of this paper}
+The aim of this paper is to describe the procedure to obtain the
+absolute energy spectrum of a point source from the data taken with
+MAGIC. This includes work on Mont Carlo (MC) data and the analysis of
+the real data.
+
+Various steps in the procedure will depend on details of the MC
+generation, on the way the real data are taken, etc.. These details
+have therefore to be specified, which is done in Section 2.
+
+In Section 3 some basic definitions and formulas are collected in
+order to avoid any misunderstanding of the meaning of frequently
+used terms.
+
+Section 4 describes the MC work and Section 5 the actual analysis of
+the real data.
+
+One aim of this paper is also to define jobs for those who want to
+join the activities in the software developments. As will be seen, the
+main ingredients both for the MC work and the real data analysis are
+available. However, certain parts have yet to be implemented, others
+have to be changed, modified, improved or extended. Last not least
+extensive tests have to be performed.
+
+
+
+\section{Assumptions}
+The assumptions for a 'standard analysis' listed below are the result of
+discussions in the software group. Some of them are rather arbitrary. 
+They should by no means be
+understood as final or optimal choices. They should be considered as a
+starting point. As our experience with the analysis grows we may
+have to revise some of the assumptions.
+
+The aim in all what follows is to define a strategy that is as simple 
+and robust as possible. Tests that have yet to be performed will tell
+us whether the assumptions are reasonable and realistic.
+
+The assumptions are :
+
+\begin{itemize}
+\item Mode of observation :\\
+Data are taken in the wobble mode. This means that the telescope is
+directed not to the position of the selected source but rather to a
+position which has a certain offset ($\Delta\beta$) from the source
+position. $\Delta\beta$ is taken as  ... degree in right ascension and
+every 20 minutes of observation the sign of $\Delta\beta$ is changed.
+The two wobble positions are called wobble-1 and wobble-2.
+
+There is no compelling reason to do the wobbling in right ascension 
+rather than in any other direction. It also appears that this choice
+has no severe consequences for the analysis.
+
+Note that the sky region projected onto the camera is different for
+wobble positions 1 and 2. For fixed wobble position the sky region
+projected onto the camera remains the same during tracking of a
+source, although the sky image is rotating in the camera.
+
+The wobble mode has to be understood as an alternative to taking on
+and off data in separate runs. Choosing the wobble mode thus implies
+that one is taking on data only, from which also the 'off data' have to be
+obtained by some procedure.
+
+\item Pedestals :\\
+Pedestals and their fluctuations are not determined from triggered
+showers but rather from pedestal events. The pedestal events are taken 
+'continuously' at a constant rate of 5 Hz. In this way the pedestals
+and their fluctuations are always up to date, and the presence of
+stars and their position in the camera can be monitored continuously.
+
+\item Gamma/hadron separation :\\
+It is assumed that it is possible to define a gamma/hadron separation
+which is independent 
+ \begin{itemize}
+ \item[-] of the level of the light of the night sky (LONS)
+ \item[-] of the presence of stars in the field of view (FOV) of the camera
+ \item[-] of the orientation of the sky image in the camera
+ \item[-] of the source being observed
+ \end{itemize}
+
+It has yet to be proven that this is possible. The corresponding
+procedures have to be developed, which includes a proper treatment of the
+pedestal fluctuations in the image analysis. 
+
+The gamma/hadron separation will be given in terms of a set of cuts
+on quantities which are derived from the measurable quantities, which are :
+ \begin{itemize}
+ \item[-] the direction $\Theta$ and $\phi$ the telescope is pointing to
+ \item[-] the image parameters
+ \item[-] the pedestal fluctuations 
+ \end{itemize}
+
+Under the above assumption the only dependence to be considered for
+the collection areas (see Section 3) is the dependence on the energy
+of the cosmic ray particle and on the zenith angle $\Theta$.
+
+It has to be investigated whether also the azimuthal angle $\phi$ has to be
+taken into account, for example because of influences from the earth
+magnetic field.
+
+\item Trigger condition :\\
+
+\item Standard analysis cuts :\\ 
+ 
+\end{itemize}
+
+
+\section{Definitions and formulas}
+\subsection{Definitions}
+
+\begin{itemize} 
+\item Image parameters :\\
+The standard definition of the image parameters is assumed. See for
+example \cite{...}.
+ 
+\item Impact parameter :\\
+The impact parameter $p$ is defined as the vertical distance 
+of the telescope from the shower axis. It is not directly
+measurable. It may be estimated from the image parameters.
+
+\item Energy :\\
+The energy of the shower is not directly measurable either, but may be
+estimated from the image parameters too.
+
+\item The direction $(\Theta,\phi)$ :\\
+$(\Theta,\phi)$ denotes the direction the telescope is pointing to,
+not the position of the source being observed.
+\end{itemize}
+
+
+\subsection{Formulas}
+
+\begin{enumerate}
+\item Differential gamma flux and collection area for a point source
+
+The differential gamma flux from as point sourse $s$ is
+
+\begin{eqnarray}
+\Phi^{\gamma}_s(E)\;=\;\dfrac{dN^{\gamma}_s}{dE \cdot dF \cdot dt} 
+\end{eqnarray} 
+
+where $dN^{\gamma}_s$ is the number of gammas from the source $s$ in
+the bin $dE,\;dF,\;dt$ of energy, area and time respectively. We
+denote the probabiolity for reconstructing a gamma shower with energy
+$E$, zenith angle $\Theta$ and impact parameter $p$ by 
+$R^{\gamma}(E,\;\Theta,\;p)$. The effective collection area is defined as
+
+\begin{eqnarray}{lll}
+F^{\gamma}_{eff}\;  &=  &\int R^{\gamma}(E,\Theta,p)\;dF  \\
+                    &=  &2\pi\;\int R^{\gamma}(E,\Theta,p)\;p\;dp
+\end{eqnarray} 
+
+
+The number of $\gamma$ showers observed in the bin $\Delta \Theta$ of
+the zenith angle $\Theta$ and in the bin $|Delta E$ of the energy is
+then :
+
+\begin{eqnarray}{lll}
+\Delta N^{\gamma,obs}_s  &=         &\Delta T_{on}(\Theta) \cdot
+ \int_{\Delta E}{} \Phi^{\gamma}_s(E)\;F^{\gamma}_{eff}(E,\Theta)\;dE \\
+                         &\approx=  &\Delta T_{on}(\Theta) \cdot 
+  F^{\gamma}_{eff}(E),\Theta) \cdot \int_{\Delta E}{}
+ \Phi^{\gamma}_s(E)\;dE \\
+                         &=         &\Delta T_{on}(\Theta) \cdot 
+  F^{\gamma}_{eff}(E),\Theta) \cdot \Delta E \cdot 
+  \overline{\Phi^{\gamma}_s}(E) \\
+\end{eqnarray} 
+
+\end{enumerate}
 
 \section{MC work}
@@ -148,4 +314,6 @@
   \item rotating star field
 \end{itemize} 
+
+\section{Analysis of the real data}
 
 \end{document}