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%%%  Kopyleft (K) 2000 J C Gonzalez
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%%%  E-mail: gonzalez@mppmu.mpg.de
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\documentclass[12pt]{article}

\usepackage{magic-tdas}

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\begin{document}

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\title{ The Reflector simulation program v.0.6 }
\author{A.Moralejo\\ 
	\texttt{<moralejo@pd.infn.it>}} 
\date{December 6, 2002\\}
\TDAScode{MAGIC-TDAS 02-11\\ 021206/AMoralejo}
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%% title %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\maketitle

%% abstract %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{abstract}
In this document we provide a brief description of Reflector program
(version 0.6) and a guide to install and run it. Some of the
information contained in this document is also present in MAGIC-TDAS
02-05 dealing with the previous version of the program, but it has also
been included here for clarity. Two important bugs regarding the
ray-tracing routine have been corrected in this new version.
\end{abstract}

%% contents %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\thetableofcontents

\newpage

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%------------------------------------------------------------
\section{Introduction}

The Reflector program was originally written by Jose Carlos Gonz\'alez 
and then improved by Harald Kornmayer. The Reflector program reads in
MMCS output files (cerxxxxxx files from corsika) and writes an output
file with the information about all the photons which reach the
telescope focal plane (taking into account atmospheric and mirror
absorption) and which are within the camera radius defined in the file 
{\bf magic.def}. In September 2001 D. Bastieri and C. Bigongiari
released a new version (v.0.4) to adapt the program to a format change
in the MMCS output. In June 2002 the version 0.5 was released, with
small changes in the ouput file format and some bug fixing (see TDAS
02-05).
\par
The aim of releasing the present version 0.6 was in principle only to
add some missing information in the output. However, the ray-tracing
routine was checked in detail and some inconsistencies were
found. As a result of this, an important bug was detected which
produced a systematic blurring of all the images. Later another bug
was found in the calculation of the photon arrival time on the
camera.These bugs, fixed in this version, are discussed in detail in
section \ref{notes}. 

%------------------------------------------------------------
\section{Description of simulation \label{descrip}}

The main steps of the simulation are:

\begin{enumerate}

\item Atmospheric absorption. 

\item Checking if the photon hits the dish.

\item Aluminum  absorption.

\item Determination of the mirror hitted.

\item Mirror reflection.

\item Checking if the photon is inside the camera borders. 

\item Calculation of photon arrival time on camera.

\end{enumerate}

The reflection of each mirror element is simulated in a realistic way
by introducing a gaussian spread of the reflected photons positions on
the camera plane. The sigma of this PSF is defined via the
{\bf point\_spread} parameter in the telescope description file {\bf
magic.def}, and has a value of 0.5 cm, which corresponds approximately
to the quality of the MAGIC mirrors produced up to date. Also the
possible misalignment of mirror elements is simulated (see section
\ref{neededfiles}).

\section{Notes on version 0.6 \label{notes}}

\subsection {First bug fixed in the ray tracing}

The previous versions of the reflector were extensively checked and a
strange behaviour was found in them. It is a well known fact (see for
instance the discussions in the MAGIC design report) that, to focus a
telescope on an object placed at a finite distance, one has to shift
the camera plane {\it away} from the mirror dish, with respect to the
position in which an object at infinity (a star) would be
focused (see fig. \ref{colimation}). For instance, with a paraboloid
of focal distance f = 1697 cm, an object placed 10 km above the
telescope would be focused on a plane at $\simeq 1700$ cm from the
dish (a distance measured along the telescope axis).
%
\begin{figure}[h!]
  \begin{center}
    \epsfig{file=eps/colimation.eps,width=0.7\textwidth}
    \caption{To focus an object at a finite distance h, the camera plane
must be moved away from the mirror a distance d, given by the formula
on the right. For MAGIC, the shift is of around 3 cm for a source
located 10 km above the telescope.\label{colimation}}
  \end{center} 
\end{figure}
%
\par
With reflector program up to version 0.5, and using the mirror
parameters in the standard magic.def file, we found out just the
opposite behaviour. We wrote a program to produce files with the same
structure as the Corsika Cherenkov output, but containing photons from
a point source. If we set the source at infinity, we found the best
spot placing the camera at a distance of 1697 cm (this can be changed in
the magic.def file via the {\it focal\_distance} parameter). We can
see the resulting spot in fig. \ref{spot_inf_f1697}. A completely
independent ray-tracing program was used to verify that this is the
spot that our 17 m tesellated paraboloid should produce.
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=eps/spot_inf_f1697.eps,width=0.85\textwidth}
    \caption{Image of a point like source placed at infinity with
Reflector 0.5 (units of x and y are cm). Camera plane placed at 1697 cm
from the mirror. The circle on the left indicates (small) pixel
size. On the right side, projections on x and y of the
spot. \label{spot_inf_f1697}}
  \end{center} 
\end{figure}
%
If we now
place the source 10 km above the telescope, the best spot is achieved
at 1694 cm from the dish, instead of the expected 1700 cm
(figs. \ref{spot10kmf1700} and \ref{spot10kmf1694}). It must be
noted that for these and the following checks we removed all the
gaussian smearing which the program introduces to simulate the
possible mirror misalignments and surface irregularities (by the way,
a feature which somehow optimistically was not included in the
simulations shown in the proposal). In this way we can check just the
ray tracing.
%
\begin{figure}[h!]
  \begin{center}
    \epsfig{file=eps/spot10kmf1700.eps,width=0.85\textwidth}
    \caption{Image of a point like source placed 10 km above the
telescope with Reflector 0.5 (units of x and y are cm). Camera plane
placed at f = 1700 cm from the mirror. The fact that the spot is so large
indicates a problem in the simulation, since with this camera position
the telescope should be focused at 10 km (see
fig. \ref{spot_inf_f1697}) and hence produce a spot similar to the one
shown in fig. \ref{spot_inf_f1697}. The hole in the middle of the spot
corresponds to the hole in the mirror dish, and indicates by itself a
focusing problem.
\label{spot10kmf1700}}
  \end{center} 
\end{figure}
%
\begin{figure}[h!]
  \begin{center}
    \epsfig{file=eps/spot10kmf1694.eps,width=0.85\textwidth}
    \caption{Image of a point like source placed 10 km above the
telescope with Reflector 0.5 (units of x and y are cm). Camera plane
placed at f = 1694 cm from the mirror. Now the spot is small, but the
camera plane is not at the expected position (see text).
\label{spot10kmf1694}}
  \end{center} 
\end{figure}
%
\par
In order to rule out a possible mistake in the generation of the
``false'' Cherenkov files, we repeated the check using real Corsika
files, and directly looking at shower images ($\Theta = 10^\circ$
incident gammas with a Crab-like spectrum). We must bear in mind that
the shower maximum for gammas of 100 GeV lies around 10 km above the MAGIC
level. From the result we can clearly see that the images are best
focused at 1694 cm (fig. \ref{evcompare}), therefore confirming the
existence of a real problem in the reflector simulation.
%
\begin{figure}[p]
  \begin{center}
    \epsfig{file=eps/evcompare.eps,width=0.85\textwidth}
    \caption{Gamma shower images obtained with Reflector 0.5 placing
the camera at 1700 cm (left) and 1694 cm (right) from the mirror
dish. Primary gammas at $\theta = 10^\circ$, E = 16, 46 and 232 GeV.
\label{evcompare}}
  \end{center} 
\end{figure}
%
\paragraph {Check of the mirror parameters in the magic.def file\\}
In the standard magic.def file we have been using up to now, the
spherical mirrors centers were found to be distributed on the surface
of a f = 1700 cm paraboloid. Their curvature radii, though discretized
in 8 ``zones'' as explained in the design report, corresponded in
average to the local mean curvature radius of the same parabolic
surface. However, their orientations were those corresponding to a f =
1697 cm paraboloid. Personally I do not think this is something
intended, and looks more like an error, but anyway we checked that this
was not the reason for the problems in the ray tracing: a test
magic.def file was created with all parameters calculated as for a f =
1697 cm paraboloid, and no significant difference could be seen. That
is: i) the individual mirror orientations are the dominant factor, and
the overall dish in the old reflector behaved indeed like a f = 1697
cm parabolic 
mirror, and ii) the bug must be somewhere else. Even though the error
was not there, a new magic.def file has been produced containing the
parameters for the 956 mirrors of the final MAGIC design (instead of
the 920 mirrors foreseen in the beginning).
%
\paragraph {Solution of the problem\\}
Finally, a check of the routines in {\it ph2cph.c} revealed that the
reflector program was actually misinterpreting the information read
from the Cherenkov file written by Corsika. In figure \ref{coorsystems}
we can see the definition of Corsika's coordinate system (see also the
Corsika manual). In it, the x axis points north and the z axis points
up. The zenith angle $\Theta$ of a particle trajectory is measured
between the particle momentum and the negative z-axis, and the
azimuthal angle $\Phi$ between the positive x-axis and the x-y
component of the particle momentum, counterclockwise (0 -
2$\pi$). When the direction cosines of a particle's trajectory are
given, they refer also to its momentum vector (a downgoing
vector)\footnote{In Corsika the third component of the momentum is
measured along the negative z-axis and this is probably the origin of
the confusion which resulted in the bug}. The same is true for the
Cherenkov photons.
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=eps/coorsystems.eps,width=\textwidth}
    \caption{Coordinate systems of Corsika and MAGIC.\label{coorsystems}}
  \end{center} 
\end{figure}
%
\begin{figure}[h!]
  \begin{center}
    \epsfig{file=eps/parabola.eps,width=0.6\textwidth}
    \caption{Misunderstanding of photon direction cosines from Corsika
by Reflector v 0.5 and older versions.\label{parabola}}
  \end{center} 
\end{figure}
%
Unfortunately, in the output of Corsika, only the direction cosines
(u, v) with respect to the x and y axis are given. These completely
determine the particle's trajectory as long as one knows that they
refer to a downgoing versor, in which case one gets the third
direction cosine as $w = -\sqrt{u^2+v^2}$, with a minus sign. However,
in {\it ph2cph.c} we found exactly the opposite (lines 116 to 118 in
v.05):

\begin{verbatim}
  r[0] = ph->u; 
  r[1] = ph->v; 
  r[2] = (float) sqrt(1.0 - r[0]*r[0] - r[1]*r[1]);
\end{verbatim}

This means that the program was interpreting u and v as the direction
cosines of the {\it upgoing} versor towards which one should ``look''
to see the incoming photon. The situation is depicted in figure
\ref{parabola}. The two vectors at the bottom left of the plot are the
two possible interpretations of the direction cosines u and v. These
vectors have the same u and v, and differ only in the sign of their
third components w. As the figure illustrates, the reflector
simulation, by taking the wrong (positive) sign of w, was transforming
the light coming from a point source 10 km away, into a convergent
light beam which was then focused at a distance (1694 cm),
shorter than the focal length of the paraboloid, and produced a 
blurred image at the theoretically optimal distance (1700 cm). Of
course a paralel beam of light was focused at the right distance (1697
cm) since in that case u = v = 0, and both the upgoing and downgoing
versors have the same direction. 
\par
The example in figure \ref{parabola} shows the case in which the
telescope is pointing at zenith. It is easy to see that if the
telescope was pointing in an arbitrary direction a few degrees away
from zenith, the fact of taking the wrong sign in the third direction
cosine would spoil the reflection completely, to the point that the
spot would lie outside the camera limits. However, this is not what we
observed: when using the older reflector versions for different zenith
angles the images were still contained in the camera. The explanation
is that the transformation between Corsika's coordinates system and
the telescope system was also wrong, since the angles $\Phi$ and
$\Theta$ which indicate the telescope orientation (see fixed\_target
option in section \ref{commands}) follow the same convention taken
from Corsika: for instance, for pointing the telescope towards North
we should set $\Phi = 180^\circ$, because that would be the $\Phi$
value for a particle or photon coming from North (see again
fig. \ref{coorsystems}, left). This wrong transformation of coordinates
oriented the telescope in a way that the situation was always like the
one shown in fig. \ref{parabola}, and the image was formed in the
camera also for $\Theta > 0$, though also defocused.
\par
The telescope coordinate system shown in figure \ref{coorsystems}
(right) has its z-axis along the telescope axis, and the origin in the
center of the mirror dish. This system is used in the ray tracing
routine of the reflector simulation. When the telescope points up 
($\Theta = \Phi = 0$) this system matches exactly the one in Corsika. 
The general transformation between both is a simple rotation,
since for the sake of simplicity we assume in the simulation that the
origins always coincide. In Reflector v.05 or older the rotation
matrix was wrong: it had been written assuming that ($\Phi$, $\Theta$)
indicated the direction towards which the telescope pointed. Actually,
for the reasons already exposed, the telescope must point to 
($\Phi +\pi$, $\Theta$). The function in charge of building the rotation
matrix is {\it makeOmega} (a part of {\it ph2cph.c}), which is called
from {\it reflector.c}. For the present version we have simply
replaced $\Phi$ by $\Phi + \pi$ in the function call. The transformation of
coordinates is shown in figure \ref{telecoor}, and can be seen as a
rotation of angle $\Phi +\pi$ around the z axis of Corsika plus a
rotation of angle $\Theta$ around the y'' axis of the telescope (the
same way in which the real MAGIC points).
%
\paragraph {New coordinate system of the camera \label{newcoordi}}
We have introduced another change in Reflector 0.6 regarding the
coordinates. In versions up to 0.5 the coordinates ($x_{camera}$,
$y_{camera}$) of the photon impact point on the camera plane were
given in the telescope system (x'', y'', z'') described in
fig. \ref{coorsystems}. This was a bit confusing (a rotation of the
telescope in the zenith axis resulted in a displacement in x'' of the
images), in particular it would have been messy when working in wobble
mode. We have now adopted the camera coordinate system proposed in
TDAS 01-05: when the observer is looking from the center of the
reflector in the direction of the telescope axis (towards the camera)
the $x_{camera}$ axis points horizontally to the right, and the
$y_{camera}$ axis points upwards. It is trivial from figure
\ref{telecoor} to see that the transformation needed to obtain these
coordinates is: $x_{camera} = -y''$, $\:y_{camera} = -x''$. This has been
added at the end of {\it ph2cph.c}.
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=eps/telecoor.eps,width=\textwidth}
    \caption{Transformation of coordinates between the Corsika and
MAGIC coordinate systems.\label{telecoor}}
  \end{center} 
\end{figure}
%
\paragraph {How old was the ray-tracing bug?\\}
%
The bug was certainly present in versions 0.4 and 0.5, but may be even
older. Nevertheless, there is no doubt that the reflector program used
for the simulation shown in the MAGIC design report (which must have been
an early version of the present one) was working fine. Extensive proof
of this is provided in an appendix of the design report. A plausible
explanation could be that, up to some date, the data being read in by
the reflector program (the Corsika output) contained direction cosines
which really referred to the upgoing versors of the photon directions,
and until then the program worked well. Then may be the output of
Corsika was changed to its present form, and the change went unnoticed.
The Corsika version used then was 4.52, whereas all further work has
been done with Corsika 5.20 or later versions. The Corsika history
file shows no record of any change in this respect, but given that we
have always used a slightly modified Corsika, it would not be
surprising if the Cherenkov output was modified at some point. There
is no documentation on this, so if anyone has any relevant information,
please make it public.
%
\paragraph {Influence of the bug on image analysis\\}
The fixing of the bug (resulting in sharper images) will for sure
improve the results of the image analysis, in particular with regard
to gamma / hadron separation. This could in part explain the
differences we have been observing in the expected performance of
MAGIC with respect to what was foreseen in the design report. However,
we note here again that in the simulation used there, not only was the
reflector working well, but also no noise was introduced in the
reflecting process. This was surely too optimistic, and it implies
that it will be hard to reproduce those results using a more realistic
approach which accounts for mirror imperfections. However, the
introduction of the noise (fig. \ref{refl06images}) has a less
dramatic effect than the defocusing which the bug was producing.
%
\subsection {Second bug: photon timing}
After a first release of Reflector 0.6 had been made public, another
important bug was found. We tried to check whether the simulated
reflecting dish was really ``isochronous''. A paralel beam of photons,
all sharing the same arrival time on the ground, were processed by the
simulation program and their arrival times on the camera plane were
histogrammed. The result can be seen in fig. \ref{timing} (dashed
histograms). This time the bug was quite evident: since Corsika gives
us the arrival time of photons on ground, the path from the point
where the photon hits the dish to the ground has to be subtracted (or
added, because since the center of the dish in the MC is at $z = 0$,
the mirror reflecting the photon may have $z < 0$ when the dish is
inclined). The sign in this subtraction (in {\it ph2cph.c}) was
wrong. This bug was present in both versions 0.5 and 0.4, and might
be related to the other one (a change of orientation of the z axis
at some point may have produced it). Since in the simulation made for
the design report the timing played little or no role (the camera
simulation did not consider the arrival times of photons) it is not
possible to know whether the bug was already in the code by then.
\par
This bug means that all the studies made up to now regarding photon
arrival times on the camera are completely useless (for instance, the
optimization of the time parameters in the L1 trigger has to be redone
from scratch!).
%
\begin{figure}[h]
  \begin{center}
    \epsfig{file=eps/timing.eps,width=\textwidth}
    \caption{Test of reflector isochrony. The arrival time
distributions of photons in the camera are shown for (buggy) Reflector
0.5 and for Reflector 0.6. The sketch in the center shows the test for
the case in which the light beam is paralel to the telescope axis
(left plot). On the right, the same test has been made with light
arriving 1 degree off axis.
 \label{timing}}
  \end{center} 
\vspace*{-1cm}
\end{figure}

\subsection {Performance of the new version}
In figure \ref{coma} we show the images of a point-like source at 10
km from the telescope, produced with the Reflector version 0.6,
and using the new version of the magic.def file (see see next
section). No noise has been introduced in the reflection, the observed
spots are just the result of optical aberrations. The light source has
been put at slightly different viewing angles
from the telescope. The results are comparable to those in the design
report, actually these are a bit better, the difference probably being
that the focal lengths of the mirror tiles in the older magic.def file
were discretized in only eight values, while now they change rather
continuously. Some images of a point source at infinity (a star) can be
seen in fig. \ref{coma_star}. We can see that for any incidence angle,
the area within which 50$\%$ of the light is concentrated is smaller
than that of a small pixel.
\par
In figure \ref{refl06images} the images of three gamma events ($\theta
= 10^\circ$, E = 16, 46, 232 GeV), the same of fig. \ref{evcompare}
are shown. They have been produced with Reflector 0.6 assuming perfect
spherical mirrors (left) and realistic ones (right). The images look
reasonable, much sharper than with the older versions, even when the
mirror imperfections are taken into account.
\par
%
\begin{figure}[p]
  \begin{center}
    \epsfig{file=eps/coma.eps,width=0.85\textwidth}
    \caption{Reflector 0.6. Images of a point-like source at
10 km from the telescope for different incident angles (from on-axis
to 2 degrees off-axis). The quantity d50 indicates the diameter of a
circle (plotted) containing 50$\%$ of the reflected light. Note that
the z-axis scale is logarithmic, and the same in the first five
plots. The last plot shows the x-axis projections in linear scale.
 \label{coma}}
  \end{center} 
\vspace*{-1cm}
\end{figure}
%
\begin{figure}[p]
  \begin{center}
    \epsfig{file=eps/refl06images.eps,width=0.85\textwidth}
    \caption{Reflector 0.6. Images of the three gamma showers shown in
fig. \ref{evcompare}, without noise added in the reflection (left) and
with the standard noise (right) as described in section
\ref{descrip}. Note that the orientation of the images has changed as a
result of the introduction of a new camera coordinate system (see page
\pageref{newcoordi}).
 \label{refl06images}}
  \end{center} 
\vspace*{-1cm}
\end{figure}
%
\begin{figure}[p]
  \begin{center}
    \epsfig{file=eps/coma_star.eps,width=0.85\textwidth}
    \caption{Reflector 0.6. Images of a star. The quantity d50
indicates the diameter of a circle (plotted) containing 50$\%$ of the
reflected light.
 \label{coma_star}}
  \end{center} 
\vspace*{-1cm}
\end{figure}
%
\subsection{The new magic.def file}
A new magic.def file (see sect. \ref{neededfiles}) has been created
and included in the Reflector 0.6 package. Now the number of
individual mirror tiles is 956, matching 
the number and distribution of the final MAGIC design. The mirror
centers and orientations are those corresponding to a paraboloid of
1697 cm focal (hence the camera plane is placed at 1700 cm from the
dish). The focal lengths have been calculated by R. Mirzoyan taking
into account the so called ``shortening effect'' (see design report).
A new axisdev.dat file (se again \ref{neededfiles}) with data for the
956 mirrors is also included.
%
\subsection{The {\itshape cermaker} program}
A test program to produce cer files (input for the reflector)
containing photons from a point-light source of light placed in any
position has been added to the Reflector package {\it
(tester/cermaker.c)}. This is the same program used to produce the
plots shown in this report. The usage is as follows:
\begin{verbatim}
cermaker source_x(cm) source_y(cm) source_z(cm) [events]
\end{verbatim}
The source position is given with respect to the telescope. The output
file is called {\it cer000001}, and can be read by the reflector program.
%
\subsection{Other changes in Reflector 0.6}

Some other minor improvements have been introduced in Reflector 0.6:

\begin{enumerate}

\item reflector.c: Introduced NaN (Not a Number) check in the photon
loop. If NaNs are found in a photon data block (there are some in the
Corsika output from time to time, for unkown reason), it is not processed.

\item ph2cph.c: Introduced "check of positiveness" before taking a
square root in the calculation of the photon trajectory intersection
with the paraboloid (resulted sometimes in NaNs when the photon did
not intersect the paraboloid).

\item Added an option for the wobble mode in the input card (see
section \ref{opt}).

\item New output format (see sect. \ref{out}): added a Run header,
which is like that of Corsika, plus a couple of variables concerning
the reflector parameters: the wobble mode and the atmospheric model
used for the simulation. The event header has also been changed to
include all the information present in the Corsika event
header. We also added in the event header three new variables which
tell us for each event what fraction of the Cherenkov photons on the
camera plane has been produced by electrons, muons, or other
particles.
\par
Finally, the ascii files {\it magic.def}, {\it 
axisdev.dat} and {\it reflectivity.dat} which the program has used as
input are now attached at the end of the output file, so that each
output file contains all the relevant information on how it was
produced.

\end{enumerate}

%------------------------------------------------------------
\section{How to Install Reflector Program \label{installation}}

You can get the current version of the Reflector Program from the
MAGIC web page: \\
{\bf http://hegra1.mppmu.mpg.de/MAGICWeb/ }\\ 
You can find
the latest public version of this program as tarred gzipped file in
the Monte Carlo Download area (you need the usual password). You have to
download the file reflector\_0.6.tar.gz and then follow the
instructions below: 
  
\begin{description}  
\item[Decompress the file using:]
	gunzip reflector*.tar.gz   
\item[Unpack the tar file with:] 
	tar xvf reflector*.tar   
\item[Go to the directory where the source files are:]
	cd MagicProgs/Simulation/Detector/Reflector\_0.6/
\item[Make symbolic links running the script:] 	
	refl-install    
\item[Check if all dependencies are fulfilled:] 
	make depend   
\item[Compile the program:] 
	make 
\end{description}

If everything goes right you should have an executable file called
{\bf reflector}. 

%------------------------------------------------------------
\section{How to Run Reflector Program \label{running}}

You need a steering card to run the Reflector program. You can find an 
example in the {\bf MagicProgs/Simulation/Detector/Reflector\_0.6/input.card}
file. You have to modify this file according to your needs (see below
for instructions about steering card) and then run the program with the 
following statement:\\

\hspace{1cm}{\bf reflector $<$ input.card}

%------------------------------------------------------------
\section{Needed Files \label{neededfiles}}

The Reflector program needs some other files to run. These files are
the following:
\begin{itemize}
\item {\bf magic.def}: contains the description of MAGIC telescope
geometry, together with some other parameters needed by the Reflector
program.
\item {\bf axisdev.dat}: contains data to simulate the possible
deviation of the spot of each single mirror on the camera plane due
to its non perfect alignment. The values are x, y coordinates
distributed at random (according to a gaussian with $\sigma =
0.5$ cm).
\item {\bf reflectivity.dat}: contains the mirror reflectivity index as
a function of the wavelength. 
\end{itemize}

All these files are usually in the {\bf
MagicProgs/Simulation/Detector/Data/} directory and {\it in principle} you
should {\bf not} make any change in them to run the program.

%------------------------------------------------------------
\section{Steering Card}

The steering card sets all the parameters and options 
to steer the reflection simulation. Each line of the steering card is
a statement with its parameters, if it is the case. Lines beginning
with \# are considered comments. The Reflector program parses all the
lines sequentially. Then if you repeat a statement with different
options only the last one will be considered.  

\subsection{Mandatory Commands \label{commands}} 

\begin{description}

\item[reflector 0.6]

	This statement must be the first line of the steering card
	file. The Reflector program checks it to verify if it is reading 
	a steering card. 

\item[output\_file /disk99/reflex/Gamma\_0\_7\_1001to1010\_w0.rfl]

	The output\_file command specifies the name and the 
	path of the output file. The path can be absolute, like in the 
	example above, or relative. Although any name can be used,
        conventionally the Reflector program 
	output file name has the .rfl extension, and starts with
	the primary particle name. The first number indicates the
	zenith angle of the incident primaries, the second one
	indicates the production site (7 is for Padua) and is related
        to the random number generator seed used by CORSIKA. Then the run
	number range is shown (10 runs in this case, from 1001 to
	1010). Each run corresponds to 10000 showers. Finally, the
        label "w0" means no wobble mode was used (telescope pointing
        at the source). Alternatively,  the "w+" or  "w-" labels (only 
        in gamma files) refer to the two pointings in the
	Wobble-observation mode (see TDAS 01-05 by W. Wittek).

\item[ct\_file ../Data/magic.def]

	The ct\_file statement defines where the program can find the 
	telescope characteristics. The path in the example above is
	correct to run reflector in
	MagicProgs/Simu\-la\-tion/De\-tector/Reflector\_0.6/ directory. 
	If you want to run it in a different directory you have to modify the 
	path accordingly. 

\item[atm\_model ATM\_CORSIKA]
	The atm\_model statement says to the program what kind of
	atmospheric absorption model to use. Possible choices are: 
	ATM\_CORSIKA, ATM\_ISO\-THERMAL, ATM\_90\-PER\-CENT and
	ATM\_NO\-ATMO\-SPHE\-RE.
	
\item[cer\_files] 

	All the lines following this statement are considered files to
	be processed by the Reflector program, one for each line,
	eventually with their paths (see the example below). Therefore this
	command must be the last one.\\
	\\
	cer\_files\\
	/disk99/cer001001\\
	/disk99/cer001002\\
	/disk99/cer001003\\
	........ \\
	/disk99/cer001009\\
	/disk99/cer001010\\
	\\
	The cer file name can be followed by two numbers, for example:
	\\
	/disk99/cer001001 376 5723\\
	\\	
	In this case the program processes only the events between and
      including the numbers given.
	
\end{description}

\subsection{Optional Commands \label{opt}}

\begin{description}
	
\item[verbose\_level 1]

	Sets the quantity of information printed out by Reflector
	when running. Possible values are 0 to 4

\item[max\_events 50000] 

	Fixes the maximum number of events to process. 

\item[energy\_cuts 100 1000]

	This statement forces the Reflector to process only showers
	with primary energy between the given values (GeV).
	
\item[seeds n1 n2]

	Seeds for the random number generators to used by the program
	for the simulation of the absorption (both in the atmosphere
	and on the mirror). Default values are 3141592 and
	2718182.

\item[telescope\_position x y]

	Option included in version 0.5 of Reflector. Usually it is
	not needed, since for normal MC production for MAGIC the
	telescope is placed at the origin of coordinates (0,0). But,
	if for some reason, we produce cerxxxxxx files with the
	telescope in a different position, we must inform the
	Reflector program in the input card using this option
	(otherwise Reflector will fail to {\it find} the photons
	in the cer file).

\item[reflectivity\_file /path/reflectivity.dat]

	File containing mirror reflectivity as a function of
	wavelength (see section \ref{neededfiles}). If this option is
	not supplied, the program will look for
	``../Data/reflectivity.dat'' as previous versions of
	Reflector did.

\item[axisdev\_file /path/axisdev.dat]

	File containing single mirror spot deviation in {\bf x} and
	{\bf y} on the camera in cm (see section
	\ref{neededfiles}) for each mirror. If this option is not
	supplied, the  program will look for ``../Data/axisdev.dat''
	as previous versions of Reflector did.

\item[fixed\_target $\Theta$ $\Phi$] 
	
	This statement fixes the telescope axis position. The first
	number is the zenith angle $\Theta$ (deg) while the second is
	the azimuthal angle $\Phi$ (deg). This corresponds to {\it
	CORSIKA}'s definition of primary particle incident direction
	(see fig. \ref{coorsystems}, left). For instance, $\phi = 90^\circ$
        means that the telescope is pointing towards East. If this
	option is omitted the telescope will always point in the
	direction of the Corsika primary (whatever it is), or a
        slightly modified direction if the wobble\_mode option is used
	(see next point). When running the reflector over gamma data
        generated in a range of zenith angles, one should therefore
	ommit the fixed\_target option.

\item[wobble\_mode w]

	Indicates whether the reflection should be done in the wobble
        mode, that is, with shifted pointing with respect to the
        nominal telescope orientation (given by fixed\_target or
	otherwise, see above). The wobble mode is described in TDAS
	01-05. Possible values for w are 0 (no wobble mode), 1, -1
	(image shift along $x_{camera}$ axis) and 3 (image shift along
	$y_{camera}$ axis).

\end{description}  

%------------------------------------------------------------

\newpage
\section{Output file \label{out}} 
The output file begins with two ascii lines:\\
\\
\verb"reflector 0.6" \\
\verb"START---RUN" \\ 
After the \verb"START---RUN" flag there is a carriage return, and then
the run header which is basically the one from Corsika with two added
variables, {\it wobble\_mode} and {\it atmospheric\_model}. Check the
Corsika manual for the meaning and units of the rest of them. All of the
variables 4-byte real numbers except the first, which is a 4 character
string containing the run header ascii label from Corsika:
\vspace*{0.5cm}
\\
%
\begin{tabular}{ll}
\parbox{5cm}{Variable} & Description \\
\hline 
& \\
ASCII Label & 'RUNH' \\
RunNumber & \\
date & \\
Corsika\_version & \\
NumObsLev & \\
HeightLev[10] & \\
SlopeSpec & \\
ELowLim & \\
EUppLim & \\
EGS4\_flag & \\
NKG\_flag & \\
Ecutoffh & \\
Ecutoffe & \\
Ecutoffg & \\
C[50] & \\
wobble\_mode & Wobble mode with which the reflector was run (TDAS
01-05) \\
atmospheric\_model & Atmospheric model used for the absorption
simulation \\
& 0 = no atmosphere;  1 = atm\_90percent;  \\
& 2 = atm\_isothermal;  3 = atm\_corsika. \\
dummy1[18] & not used \\
CKA[40] & \\
CETA[5] & \\
CSTRBA[11] & \\
dummy2[104] & not used \\
AATM[5] & \\
BATM[5] & \\
CATM[5] & \\
NFL[4] & \\
&\\
\hline 
\end{tabular}

\newpage

Then there comes a ``\verb"START-EVENT"'' flag, followed by a carriage
return and then the binary event header. Each variable is a 4-byte
float number except for the first one which is the event header label
from Corsika (a string of 4 characters). Some of of the variables from
Corsika are not explained here (see Corsika manual instead).
\vspace*{0.5cm}
\\
\begin{tabular}{ll}
\parbox{5cm}{Variable} & Description \\
\hline
& \\ 
ASCII label     & 'EVTH' \\
EvtNumber       & Event Number \\
PrimaryID 	& Primary particle identification code \\
Etotal 		& Primary particle total energy (GeV) \\
Thick0 		& CORSIKA's starting altitude in g/cm2 \\
FirstTarget 	& CORSIKA's number of first target if fixed \\
zFirstInt 	& Height of first interaction in cm \\
p[3] 		& Primary particle momentum in x,y,-z directions (GeV) \\
Theta 		& Primary particle zenith angle (rad) \\
Phi 		& Primary particle azimuth angle (rad) \\	

NumRndSeq 	& Number of different CORSIKA random sequences (max. 10) \\
RndData[10][3] 	& RndData[i][0]: integer seed of sequence i \\
		& RndData[i][1]: number of offset random calls (mod $10^6$) of sequence i. \\ 
		& RndData[i][2]: number of offset random calls ($/10^6$) of sequence i. \\ 

RunNumber 	& Run number \\
DateRun 	& Date of run yymmdd \\
Corsika\_version & Version of {\it CORSIKA} \\

NumObsLev 	& Number of observation levels (should be always 1 for
us) \\
HeightLev[10]	& Height of observation levels in cm \\

SlopeSpec 	& Energy spectrum slope \\
ELowLim 	& Energy lower limit (GeV) \\
EUppLim 	& Energy upper limit (GeV) \\
Ecutoffh        & \\
Ecutoffm        & \\
Ecutoffe        & \\
Ecutoffg        & \\
NFLAIN		& \\
NFLDIF		& \\
NFLPI0		& \\
NFLPIF		& \\
NFLCHE		& \\
NFRAGM		& \\
Bx		& \\
By		& \\
EGS4yn		& \\
NKGyn		& \\
GHEISHAyn	& \\
VENUSyn		& \\
& \\
\hline 
\end{tabular}
%
\newpage
%

\begin{tabular}{ll}

\parbox{5cm}{Variable} & Description \\
\hline 
& \\
CERENKOVyn	& \\
NEUTRINOyn	& \\
HORIZONTyn	& \\
COMPUTER	& \\

ThetaMin 	& Minimum Theta of primaries (deg) \\
ThetaMax 	& Maximum Theta of primaries (deg) \\
PhiMin 		& Minimum Phi of primaries (deg) \\
PhiMax 		& Maximum Phi of primaries (deg) \\
CBunchSize	& \\
CDetInX		& \\
CDetInY		& \\
CSpacInX	& \\
CSpacInY	& \\
CLenInX		& \\
CLenInY		& \\
COutput		& \\
AngleNorthX	& \\
MuonInfo	& \\
StepLength	& \\
CWaveLower 	& Wavelength lower limit (nm) \\
CWaveUpper 	& Wavelength upper limit (nm) \\
Multipl		& \\
CorePos[2][20] 	& Core positions of randomized shower \\
SIBYLL[2]	& \\
QGSJET[2]	& \\
DPMJET[2]	& \\
VENUS\_cross	& \\
mu\_mult\_scat	& \\
NKG\_range	& \\
EFRCTHN[2]	& \\
WMAX[2]		& \\
rthin\_rmax	& \\
viewcone\_angles[2] & Inner and outer angles of Corsika's VIEWCONE
option. \\
telescopePhi	& Telescope azimuth (rad). Measured from South, counter-clockwise \\
telescopeTheta 	& Telescope zenith angle (rad) \\
TimeFirst 	& Arrival time on camera of first photon (ns) \\
TimeLast 	& Arrival time on camera of last photon (ns) \\

& 6 next variables: CORSIKA longitudinal particle fit parameters \\
& \hspace{0.5cm} (see CORSIKA manual for precise meaning and units)\\
longi\_Nmax        & Numer of charged particles at maximum \\
longi\_t0          & Atmospheric depth of shower starting point (N=0) \\
longi\_tmax        & Atmospheric depth of shower maximum (g/cm$^2$) \\
longi\_a           & \\
longi\_b           & For {\bf longi\_a}, {\bf longi\_b}, {\bf longi\_c}, see CORSIKA manual  \\
longi\_c           &  \\
longi\_chi2        & $\chi^2/dof$ of the fit\\
& \\
\hline 
\end{tabular}

\newpage

\begin{tabular}{ll}
\parbox{5cm}{Variable} & Description \\
\hline 
& \\
CORSIKAPhs      & Original photons written by {\it CORSIKA} \\ 
AtmAbsPhs       & Photons absorbed by the atmosphere  \\
MirrAbsPhs      & Photons absorbed by the mirror      \\ 
OutOfMirrPhs    & Photons outside the mirror          \\ 
BlackSpotPhs    & Photons lost in the "black spot"    \\ 
OutOfChamPhs    & Photons outside the camera         \\ 
CPhotons        & Photons reaching the camera        \\ 

elec\_cph\_fraction & Fraction of C-photons produced by electrons \\
muon\_cph\_fraction & Fraction of C-photons produced by muons \\
other\_cph\_fraction & Fraction of C-photons produced by electrons \\
& \\
\hline 
\end{tabular}

\vspace*{1cm}
The event header is followed by 8-word blocks, one for each photon
that reaches the camera. A photon block contains the following
variables:
\vspace*{0.5cm}
\\
\begin{tabular}{ll}
Variable & Description \\
\hline
& \\
w 	& 100000 $\times$ Particle\_type + 1000 $\times$ n + Wavelength (nm) \\
	& Particle\_type indicates what particle produced the C-photon. Its value is 2 for electrons \\
	& and positrons, and the standard codes of Corsika for the rest. \\
	& n is the index from 1 to ICERML (see Corsika manual) for the case in which each Corsika \\
	& shower is used more than once (normally, in MMCS will be just 1). \\
	& \\
x, y	& Impact point in camera coordinates (cm) \\
u, v 	& Director cosines of down-going versor indicating the photon direction \\
t	& Arrival time on camera (ns) \\
h	& Production height (cm) \\
phi 	& Incidence angle with respect to camera plane (rad) \\
& \\
\hline
\end{tabular}
\vspace*{0.5cm}
\\
After the last event photon block there is a blank line, an \verb$END---EVENT$
flag, another blank line and then the following event. After the last
event in a run it appears the flag ``\verb$END-----RUN$'', while after all
the processed runs, a ``\verb$END----FILE$'' flag is written. Finally,
after this flag an ``ascii tail'' has been added to the file: it
consists of the ascii files {\it magic.def}, {\it axisdev.dat} and {\it
reflectivity.dat} one after the other separated by blank lines. In
this way all the relevant parameters used to produce the output are
kept together with the reflected events.

%------------------------------------------------------------

\section{Appendix A}

The list of all Reflector files follows.
\begin{verbatim}

MagicProgs/Simulation/Detector/Reflector_0.6/Changelog
MagicProgs/Simulation/Detector/Reflector_0.6/Makefile
MagicProgs/Simulation/Detector/Reflector_0.6/atm.c
MagicProgs/Simulation/Detector/Reflector_0.6/atm.h
MagicProgs/Simulation/Detector/Reflector_0.6/attach.c
MagicProgs/Simulation/Detector/Reflector_0.6/attenu.f
MagicProgs/Simulation/Detector/Reflector_0.6/config.mk.linux
MagicProgs/Simulation/Detector/Reflector_0.6/config.mk.linux-gnu
MagicProgs/Simulation/Detector/Reflector_0.6/config.mk.osf1
MagicProgs/Simulation/Detector/Reflector_0.6/diag.c
MagicProgs/Simulation/Detector/Reflector_0.6/diag.h
MagicProgs/Simulation/Detector/Reflector_0.6/geometry.c
MagicProgs/Simulation/Detector/Reflector_0.6/geometry.h
MagicProgs/Simulation/Detector/Reflector_0.6/header.c
MagicProgs/Simulation/Detector/Reflector_0.6/header.h
MagicProgs/Simulation/Detector/Reflector_0.6/init.c
MagicProgs/Simulation/Detector/Reflector_0.6/init.h
MagicProgs/Simulation/Detector/Reflector_0.6/input.card
MagicProgs/Simulation/Detector/Reflector_0.6/lagrange.h
MagicProgs/Simulation/Detector/Reflector_0.6/parms.c
MagicProgs/Simulation/Detector/Reflector_0.6/parms.h
MagicProgs/Simulation/Detector/Reflector_0.6/ph2cph.c
MagicProgs/Simulation/Detector/Reflector_0.6/refl-install
MagicProgs/Simulation/Detector/Reflector_0.6/reflector.c
MagicProgs/Simulation/Detector/Reflector_0.6/version.h

MagicProgs/Simulation/Detector/Reflector_0.6/doc/Tdas0211.ps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/Tdas0211.tex
MagicProgs/Simulation/Detector/Reflector_0.6/doc/magic-tdas.sty
MagicProgs/Simulation/Detector/Reflector_0.6/doc/magiclogo.eps
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/colimation.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/coma.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/coma_star.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/coorsystems.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/evcompare.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/parabola.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/refl06images.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/spot10kmf1694.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/spot10kmf1700.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/spot_inf_f1697.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/telecoor.eps.gz
MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/timing.eps.gz

MagicProgs/Simulation/Detector/Reflector_0.6/tester/Makefile
MagicProgs/Simulation/Detector/Reflector_0.6/tester/cermaker.c

MagicProgs/Simulation/Detector/Data/axisdev.dat
MagicProgs/Simulation/Detector/Data/magic.def
MagicProgs/Simulation/Detector/Data/reflectivity.dat

MagicProgs/Simulation/Detector/lib/libranlib.a.osf1
MagicProgs/Simulation/Detector/lib/libranlib.a.linux

\end{verbatim}

%%% BIBLIOGRAPHY %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

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%%>>>> bibliographic entries

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