Index: trunk/MagicSoft/Simulation/Detector/ReflectorII/doc/Tdas0211.tex =================================================================== --- trunk/MagicSoft/Simulation/Detector/ReflectorII/doc/Tdas0211.tex (revision 1672) +++ trunk/MagicSoft/Simulation/Detector/ReflectorII/doc/Tdas0211.tex (revision 1722) @@ -33,4 +33,5 @@ \usepackage{magic-tdas} +\usepackage{amssymb} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -46,6 +47,6 @@ \author{A.Moralejo\\ \texttt{}} -\date{December 6, 2002\\} -\TDAScode{MAGIC-TDAS 02-11\\ 021206/AMoralejo} +\date{January 20, 2003\\} +\TDAScode{MAGIC-TDAS 02-11\\ 030120/AMoralejo} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -61,6 +62,17 @@ been included here for clarity. Two important bugs regarding the ray-tracing routine have been corrected in this new version. +\par +NOTE: In December 2002, a first release of Reflector 0.6 was made, +together with a first version of the present TDAS note. Immediately +after that (too short a time to justify a new version number), some +other changes were implemented in the program to improve the +atmospheric absorption routines, and the dependence of mirror +reflectivity with wavelength was introduced. This document is the +manual of the final 0.6 version of the reflector, including +explanations of these last modifications. + \end{abstract} +\newpage %% contents %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \thetableofcontents @@ -161,5 +173,5 @@ 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. +spot that a f/1 16.97 m $\varnothing$ tesellated paraboloid should produce. % \begin{figure}[h] @@ -182,6 +194,6 @@ 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. +simulations shown in the MAGIC proposal). In this way we can check +just the ray tracing. % \begin{figure}[h!] @@ -242,6 +254,8 @@ 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 +magic.def file was created with {\it all} the mirror parameters +(positions, orientations and radii of curvature) +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 @@ -288,5 +302,5 @@ 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, +direction cosine as $w = -\sqrt{1-u^2-v^2}$, with a minus sign. However, in {\it ph2cph.c} we found exactly the opposite (lines 116 to 118 in v.05): @@ -341,5 +355,5 @@ 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 +origins always coincide. As we have said, 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, @@ -383,6 +397,6 @@ 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 +for the simulation shown in the MAGIC design report 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 @@ -395,7 +409,7 @@ 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. +surprising if the Cherenkov output was modified at some point in the +MAGIC version of Corsika (MMCS). 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\\} @@ -413,5 +427,43 @@ dramatic effect than the defocusing which the bug was producing. % +\subsection {Performance of ray-tracing in 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. +% +\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 {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 @@ -438,41 +490,34 @@ from scratch!). % -\begin{figure}[h] +\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 new reflectivity.dat file} +Up to version 0.5 of the program, the reflectivity of the mirrors +(which the program reads in from the file reflectivity.dat) was +considered to be equal to $90\%$ for all wavelengths. Following +measurements performed in Padua of a mirror sample, the reflectivity +has been found to be between 80 and 90$\%$ in the range from 280 to 650 nm, +with a dependence on wavelength which is shown in figure \ref{reflec}. +% +\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}} + \epsfig{file=eps/reflec.eps,width=0.7\textwidth,height=0.4\textwidth} + \caption{Reflectivity of the MAGIC telescope mirrors as a +function of the wavelength of the incident light. The dip around 350 +nm is due to destructive interference of the light reflected on the +aluminum plate with that reflected on the protective coating of the +mirror. \label{reflec}} \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 +\end{figure} % \begin{figure}[p] @@ -515,16 +560,4 @@ \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) @@ -539,4 +572,52 @@ file is called {\it cer000001}, and can be read by the reflector program. % +\subsection{Changes in the atmospheric absorption routines} +% +In the present version of the program, the simulation of atmospheric +absorption has undergone major changes with respect to the original +implementation by J.C. Gonz\'alez and Aitor Ibarra. Three options are +available in the simulation: ATM\_NOATMOSPHERE, ATM\_90PERCENT and +ATM\_CORSIKA (see section \ref{commands}). In the +first two, 100$\%$ and 90$\%$ of the emitted light respectively +reaches the telescope mirror, regardless of the emission height. The +changes in the present version affect only the third option, which is +the recommended one for running reflector in the standard MAGIC MC +production. In this case, a detailed estimate of the atmospheric +transmission is done. +\par +Three contributions to the atmospheric opacity +are considered: Rayleigh scattering, Mie scattering by aerosols, and +absorption by ozone. Details on how the effect of these three +components is calculated are given in appendix A. In reflector +versions older than 0.6, +due to a bug, the contribution of Mie scattering and Ozone absorption +was slightly overestimated because the vertical height of the emission +point above sea level was interpreted as height above the +telescope. The difference is small, since the density of the aerosols +responsible for Mie scattering decreases very fast with height and +therefore the absorption is hardly increased by going up 2.2 km in the +region were most of the Cherenkov light is produced. In the case of +ozone, its contribution is only important in the very low end of the +Cherenkov light spectrum, and so the effect of the bug in the total +amount of light reaching the telescope is negligible. Another change +is that now the observation level is read in from the cer file, instead +of being a fixed parameter in the routines. In this way the reflector +program has become more flexible, and can now be used to process cer +files produced for a detector at a different observation level. +\par +Another problem in the old implementation of absorption was that the +variation of the optical depth of the atmosphere with the zenith angle +$\theta$ was assumed to be the same for Mie scattering, ozone +absorption and Rayleigh scattering: the so called {\it air +mass} (see appendix A for details) was therefore calculated only once, +using the overall density profile of air molecules (which does not +match that of aerosols or ozone), and used to account for the +variation of all three effects with $\theta$, while rigorously +speaking it is only valid for Rayleigh scattering. Now, the simulation +of Mie scattering and ozone absorption has been moved from {\it +attenu.f} to {\it atm.c} and is done in a more accurate way which +takes into account the vertical profile of aerosols and ozone (see +appendix A for details). +% \subsection{Other changes in Reflector 0.6} @@ -557,7 +638,11 @@ 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 +\item New output format (see sect. \ref{out}): we have removed a null +byte that was written immediately after the ascii label containing the +reflector program version number at the begining of the file. This +byte was there for historical reasons and had no function +whatsoever. Then we have 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 @@ -634,7 +719,8 @@ \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. +All these files (included in the reflector package) are usually kept +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. %------------------------------------------------------------ @@ -676,19 +762,22 @@ Wobble-observation mode (see TDAS 01-05 by W. Wittek). -\item[ct\_file ../Data/magic.def] +\item[ct\_file /path/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. + telescope characteristics. Usually, the magic.def file is kept in + MagicProgs/Simulation/Detector/Data \item[atm\_model ATM\_CORSIKA] - The atm\_model statement says to the program what kind of + + The atm\_model statement tells 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. - + ATM\_NOATMOSPHERE,\\ ATM\_90PERCENT and ATM\_CORSIKA, + corresponding respectively to no absorption, a 10$\%$ + absorption and a model using the US Standard atmosphere (see + Corsika manual, appendix C) for the Rayleigh scattering and a + model by L. Elterman \cite{elterman64,elterman65} for the Mie + scattering and ozone absorption (see appendix A). The third + model should be chosen for the standard MC MAGIC production. + \item[cer\_files] @@ -755,5 +844,5 @@ File containing mirror reflectivity as a function of wavelength (see section \ref{neededfiles}). If this option is - not supplied, the program will look for + not supplied, the program will look for \\ ``../Data/reflectivity.dat'' as previous versions of Reflector did. @@ -796,53 +885,50 @@ %------------------------------------------------------------ -\newpage \section{Output file \label{out}} -The output file begins with two ascii lines:\\ +The reflector output file begins with two ascii lines, the first of +which informs us of the program version with which it has been +produced (NOTE: in the following, the dollar symbol \verb"$" stands +for a carriage return):\\ \\ -\verb"reflector 0.6" \\ -\verb"START---RUN" \\ -After the \verb"START---RUN" flag there is a carriage return, and then -the run header which is basically the one from Corsika with two added -variables, {\it wobble\_mode} and {\it atmospheric\_model}. Check the -Corsika manual for the meaning and units of the rest of them. All of the -variables 4-byte real numbers except the first, which is a 4 character -string containing the run header ascii label from Corsika: +\verb"reflector 0.6$START---RUN$" \\ +\\ +Then there is 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 are 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 \\ +\begin{tabular}{lll} +\multicolumn{2}{c}{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 +&& \\ +1 & ASCII Label & 'RUNH' \\ +2 & RunNumber & \\ +3 & date & \\ +4 & Corsika\_version & \\ +5 & NumObsLev & \\ +6 to 15 & HeightLev[10] & \\ +16 & SlopeSpec & \\ +17 & ELowLim & \\ +18 & EUppLim & \\ +19 & EGS4\_flag & \\ +20 & NKG\_flag & \\ +21 & Ecutoffh & \\ +22 & Ecutoffm & \\ +23 & Ecutoffe & \\ +24 & Ecutoffg & \\ +25 to 74 & C[50] & \\ +75 & wobble\_mode & Wobble mode with which the reflector was run (TDAS 01-05) \\ -atmospheric\_model & Atmospheric model used for the absorption +76 & 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] & \\ +&& 0 = no atmosphere; 1 = atm\_90percent; \\ +&& 2 = atm\_corsika. \\ +77 to 94 & dummy1[18] & not used \\ +95 to 134 & CKA[40] & \\ +135 to 139 & CETA[5] & \\ &\\ \hline @@ -851,6 +937,26 @@ \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 +\begin{tabular}{lll} +\multicolumn{2}{c}{Variable} & \parbox{11cm}{Description} \\ +\hline +&& \\ +140 to 140 & CSTRBA[11] & \\ +151 to 254 & dummy2[104] & not used \\ +255 to 259 & AATM[5] & \\ +260 to 264 & BATM[5] & \\ +265 to 269 & CATM[5] & \\ +270 to 273 & NFL[4] & \\ +&\\ +\hline +\end{tabular} +\vspace*{0.5cm} +\\ +% +Then there comes a carriage return followed by the ascii flag which +indicates the start of an event, and again a carriage return:\\ +\\ +\verb"$START-EVENT$"\\ +\\ +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 @@ -858,51 +964,38 @@ \vspace*{0.5cm} \\ -\begin{tabular}{ll} -\parbox{5cm}{Variable} & Description \\ +\begin{tabular}{lll} +\multicolumn{2}{c}{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 +&& \\ +1 & ASCII label & 'EVTH' \\ +2 & EvtNumber & Event Number \\ +3 & PrimaryID & Primary particle identification code \\ +4 & Etotal & Primary particle total energy (GeV) \\ +5 & Thick0 & CORSIKA's starting altitude in g/cm2 \\ +6 & FirstTarget & CORSIKA's number of first target if fixed \\ +7 & zFirstInt & Height of first interaction in cm \\ +8 to 10 & p[3] & Primary particle momentum in x,y,-z directions (GeV) \\ +11 & Theta & Primary particle zenith angle (rad) \\ +12 & Phi & Primary particle azimuth angle (rad) \\ + +13 & NumRndSeq & Number of different CORSIKA random sequences (max. 10) \\ +14 to 43 & 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. \\ + +44 & RunNumber & Run number \\ +45 & DateRun & Date of run yymmdd \\ +46 & Corsika\_version & Version of {\it CORSIKA} \\ + +47 & 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 & \\ +48 to 57 & HeightLev[10] & Height of observation levels in cm \\ + +58 & SlopeSpec & Energy spectrum slope \\ +59 & ELowLim & Energy lower limit (GeV) \\ +60 & EUppLim & Energy upper limit (GeV) \\ +61 & Ecutoffh & \\ +62 & Ecutoffm & \\ +63 & Ecutoffe & \\ & \\ \hline @@ -912,58 +1005,53 @@ % -\begin{tabular}{ll} - -\parbox{5cm}{Variable} & Description \\ +\begin{tabular}{lll} + +\multicolumn{2}{c}{Variable} & \parbox{11cm}{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\\ +&& \\ +64 & Ecutoffg & \\ +65 & NFLAIN & \\ +66 & NFLDIF & \\ +67 & NFLPI0 & \\ +68 & NFLPIF & \\ +69 & NFLCHE & \\ +70 & NFRAGM & \\ +71 & Bx & \\ +72 & By & \\ +73 & EGS4yn & \\ +74 & NKGyn & \\ +75 & GHEISHAyn & \\ +76 & VENUSyn & \\ +77 & CERENKOVyn & \\ +78 & NEUTRINOyn & \\ +79 & HORIZONTyn & \\ +80 & COMPUTER & \\ +81 & ThetaMin & Minimum Theta of primaries (deg) \\ +82 & ThetaMax & Maximum Theta of primaries (deg) \\ +83 & PhiMin & Minimum Phi of primaries (deg) \\ +84 & PhiMax & Maximum Phi of primaries (deg) \\ +85 & CBunchSize & \\ +86 & CDetInX & \\ +87 & CDetInY & \\ +88 & CSpacInX & \\ +89 & CSpacInY & \\ +90 & CLenInX & \\ +91 & CLenInY & \\ +92 & COutput & \\ +93 & AngleNorthX& \\ +94 & MuonInfo & \\ +95 & StepLength & \\ +96 & CWaveLower & Wavelength lower limit (nm) \\ +97 & CWaveUpper & Wavelength upper limit (nm) \\ +98 & Multipl & \\ +99 to 138 & CorePos[2][20] & Core positions of randomized shower \\ +139 to 140 & SIBYLL[2] & \\ +141 to 142 & QGSJET[2] & \\ +143 to 144 & DPMJET[2] & \\ +145 & VENUS\_cross & \\ +146 & mu\_mult\_scat & \\ +147 & NKG\_range & \\ +148 to 149 & EFRCTHN[2] & \\ +150 to 151 & WMAX[2] & \\ & \\ \hline @@ -972,27 +1060,46 @@ \newpage -\begin{tabular}{ll} -\parbox{5cm}{Variable} & Description \\ +\begin{tabular}{lll} +\multicolumn{2}{c}{Variable} & \parbox{11cm}{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 \\ +&& \\ +152 & rthin\_rmax & \\ +153 to 154 & viewcone\_angles[2] & Inner and outer angles of Corsika's VIEWCONE +option. \\ +155 & telescopePhi & Telescope azimuth (rad). Measured from South, counter-clockwise \\ +156 & telescopeTheta & Telescope zenith angle (rad) \\ +157 & TimeFirst & Arrival time on camera of first photon (ns) \\ +158 & 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)\\ +159 & longi\_Nmax & Numer of charged particles at maximum \\ +160 & longi\_t0 & Atmospheric depth of shower starting point (N=0) \\ +161 & longi\_tmax & Atmospheric depth of shower maximum (g/cm$^2$) \\ +162 & longi\_a & \\ +163 & longi\_b & For {\bf longi\_a}, {\bf longi\_b}, {\bf longi\_c}, see CORSIKA manual \\ +164 & longi\_c & \\ +165 & longi\_chi2 & $\chi^2/dof$ of the fit\\ +166 & CORSIKAPhs & Original photons written by {\it CORSIKA} \\ +167 & AtmAbsPhs & Photons absorbed by the atmosphere \\ +168 & MirrAbsPhs & Photons absorbed by the mirror \\ +169 & OutOfMirrPhs & Photons outside the mirror \\ +170 & BlackSpotPhs & Photons lost in the "black spot" \\ +171 & OutOfChamPhs & Photons outside the camera \\ +172 & CPhotons & Photons reaching the camera \\ + +173 & elec\_cph\_fraction & Fraction of C-photons produced by electrons \\ +174 & muon\_cph\_fraction & Fraction of C-photons produced by muons \\ +175 & other\_cph\_fraction & Fraction of C-photons produced by electrons \\ +176 to 182 & dummy[7] & not used \\ & \\ \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} +\\ +The event header is followed by 8-word blocks, one for each Cherenkov +photon that reaches the camera. A photon block contains the following +variables (as 4-byte float numbers): \vspace*{0.5cm} \\ @@ -1006,9 +1113,12 @@ & 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) \\ +t & Arrival time on camera (ns), measured from the time of first +interaction of the primary \\ +h & Production height (cm), measured above sea level on the +vertical of the telescope location \\ + & (it is not the {\it true} height which would be measured on +the vertical of the emitting particle!) \\ phi & Incidence angle with respect to camera plane (rad) \\ & \\ @@ -1017,17 +1127,343 @@ \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 +After the last photon block of an event there is a carriage return +followed by the ascii flag indicating the event end, and then two more +carriage returns before the ascii flag of the beginning of the next +event, and so on:\\ +\\ +\verb"$END---EVENT$$START-EVENT$Event_header....$END---EVENT$$END-----RUN$$START---RUN$..."\\ +\\ +The flag ``\verb$END-----RUN$'' appears after the last event in a run +(that is, the last event processed of each of the input cer +files). After the last processed run, an end of file flag is +written:\\ +\\ +\verb"...$END---EVENT$$END-----RUN$$END----FILE$"\\ +\\ +Finally, after this flag an ``ascii tail'' has been attached to the file: +it consists of the ascii files {\it magic.def}, {\it axisdev.dat} and +{\it reflectivity.dat} one after the other, separated by carriage returns: +\\ +\\ +\verb"$magic.def$axisdev.dat$reflectivity.dat"\\ +\\ +In this way all the relevant parameters used to produce the output are kept together with the reflected events. - %------------------------------------------------------------ - -\section{Appendix A} +\newpage +\renewcommand{\thesubsection}{A.\arabic{subsection}} +\section*{Appendix A : atmospheric absorption} +\addcontentsline{toc}{section}{Appendix A : atmospheric absorption} +% +The simulation of the absorption of Cherenkov light in the atmosphere +has been included in the {\it Reflector} program because this feature +was not yet available in the first versions of CORSIKA used within the +MAGIC collaboration. In the latest CORSIKA versions, the atmospheric +absorption has been included as an option, but it is not +compatible with the simulation of a curved atmosphere \cite{cor02}, +and hence we have kept this step as a part of our reflector +simulation. This appendix describes how the atmospheric absorption is +implemented in the program when the option ATM\_CORSIKA (see section +\ref{commands}) is chosen. +\par +The geometry of the problem is sketched in figure +\ref{fig:atmoscheme}. A Cherenkov photon is emitted in point A and +travels towards the telescope placed at B. At any moment, the height +$h$ of the photon above sea level is related to the distance $L$ +between the photon and the telescope through +% +\begin{equation} +(R+h)^2 = (R+h_1)^2 + L^2 + 2 L \; (R+h_1) \; \cos \theta +\label{eq:height} +\end{equation} +% +, where $R$ is the Earth radius, $h_1$ the height (a.s.l.) of the +observation level and $\theta$ is the zenith angle of the photon +trajectory measured at the telescope site. The Cherenkov output of +CORSIKA contains for each photon the height $h_C$ of the emission +point A, measured along the vertical of the observer. The {\it true +vertical height} $h_2$ of the emission point can be obtained by +replacing $L$ by $(h_C-h_1)/\cos \theta$ in equation +(\ref{eq:height}). +% +\begin{figure}[ht] +\begin{center} +\mbox{ \epsfig{file=eps/atmoscheme.eps,width=0.8\textwidth} } +\end{center} +\caption[] +{Calculation of the true vertical height $h_2$ of the emission point +of a Cherenkov photon (point A), and the optical path traversed down to the +telescope (point B).} +\label{fig:atmoscheme} +\end{figure} +% +\par +The optical path $I(\theta, h_1, h_2)$ traversed by the photon can be +calculated integrating the air density along the trajectory +$\overline{\text{AB}}$. For the case $h/R \ll 1$, we can drop in +(\ref{eq:height}) the terms in $(h/R)^2$ and smaller, and then solve +for L. Deriving now with respect to $h$, we have: +% +\begin{equation} +\frac{dL}{dh} \simeq \sqrt{\frac{R}{2\;(h-h_1)+R\;\cos^2 \theta}} +\qquad \text{for} \qquad \frac{h}{R} \ll 1 +\label{eq:dldh} +\end{equation} +% +\subsection{Rayleigh scattering} +Rayleigh scattering is the scattering of light by particles smaller +than its wavelength. These are in our case the air molecules. The +transmission coefficient due to Rayleigh scattering is a strong +function of the wavelength $\lambda$: +% +\begin{equation} +T_{\text{Rayl}} (\lambda) = \exp \Biggl[ - \frac{I(\theta, h_1, h_2)}{x_R} \; \Biggl(\frac{400 \; +\text{nm}}{\lambda}\Biggl)^4 \; \Biggl] +\label{eq:rayleigh} +\end{equation} +% +Here $I(\theta, h_1, h_2)$ is the optical path (in g/cm$^2$) traversed +between points A and B, and $x_R = 2970$ g/cm$^2$ is the mean free path of +the Rayleigh scattering at $\lambda = 400$ nm. +\par +A convenient way of expressing the optical path is the following: +% +\begin{equation} +I\;(\theta, h_1, h_2) = (x_1 - x_2) \cdot \mathcal{AM}\;(\theta, h_1, h_2) +\end{equation} +Here $x_{i=1,2}$ is the mass overburden of the atmosphere above a +height $h_i$ (in the +vertical direction) and $\mathcal{AM}$ is the so called {\it air +mass}\footnote{If we set $h_2 = \infty$, we have the usual definition +of {\it air mass} in optical astronomy.}, defined as +% +\begin{equation} +\mathcal{AM} \equiv \frac{I\;(\theta,h_1,h_2)}{I\;(0^\circ,h_1,h_2)} +\label{eq:airmass} +\end{equation} +% +, which is a function mainly of the zenith angle $\theta$ (see +fig. \ref{fig:airmass}). In our simulation, for the calculation of the +mass overburden $x_i$ we have used the U.S. standard atmosphere +parametrized by J. Linsley \cite{cor02}, the same we used in Corsika +for the shower development simulation. It consists of five layers: in +the lower four the density decreases exponentially with height, and in +the upper one the mass overburden cecreases linearly until it vanishes +at $h = 112.8$ km. +% +\begin{figure}[ht] +\begin{center} +\mbox{ \epsfig{file=eps/airmass.eps,width=0.8\textwidth} } +\end{center} +\caption[] +{Dependence with zenith angle of the air mass as defined in the +text. The air mass has been calculated for an exponential atmosphere +with scale height $H = 7.4$ km, for the observation level of MAGIC +(2.2 km a.s.l.), and for light coming from $h_2 = 10$ and at 100 km a.s.l. As +we can see the dependence with the emission height $h_2$ is very small.} +\label{fig:airmass} +\end{figure} +% +\par +For the estimate of $\mathcal{AM}$, a simpler atmospheric model has +been used, in which the vertical density profile is described by a +single exponential: $\rho = \rho_0 \; e^{-h/H}$ with scale height $H += 7.4$ km. This simplifies the calculations, and is accurate enough +for our purposes. Using (\ref{eq:dldh}) the optical path $I(\theta, +h_1, h_2)$ can then be obtained approximately as: +% +\begin{equation} +I(\theta, h_1, h_2) = \int_A^B \rho\;(h)\; \frac{dL}{dh} \; dh \simeq +\sqrt{\frac{R}{2}} \; +\int_{h_1}^{h_2} \frac{\rho_0 +\;e^{-h/H}}{\sqrt{h-h_1+\frac{1}{2}\;R\;\cos^2 \theta}} \; dh +\label{eq:optpath} +\end{equation} +% +and finally: +% +\begin{equation} +\mathcal{AM} \simeq e^{-\frac{R \sin^2 \theta}{2H}} +\cdot +\frac{ +\text{erfc}\;(\sqrt{\frac{R \cos^2 \theta}{2H}}) +\;-\; +\text{erfc}\;(\sqrt{\frac{2 (h_2 - h_1) + R \cos^2 \theta}{2H}}) +} +{ +\text{erfc}\;(\sqrt{\frac{R}{2H}}) +\;-\; +\text{erfc}\;(\sqrt{\frac{2(h_2 - h_1) + R}{2 H}}) +} +\label{eq:airmass2} +\end{equation} +% +where we have used the complementary error function $\text{erfc}\;(x) += \frac{2}{\sqrt{\pi}}\int_x^\infty e^{-t^2} dt$. From +(\ref{eq:airmass2}), $\mathcal{AM}$ can be readily evaluated for any +value of $\theta$, $h_1$ and $h_2$. In fig. \ref{fig:rayleigh} the +resulting Rayleigh transmission coefficient $T_{\text{Rayl}}$ finally +obtained from (\ref{eq:rayleigh}) is plotted versus the zenith angle +for three wavelengths. +% +\begin{figure}[ht] +\begin{center} +\mbox{ \epsfig{file=eps/rayleigh.eps,width=\textwidth} } +\end{center} +\caption[] +{Rayleigh transmission coefficient as a function of zenith angle for three +different wavelengths. The solid, dashed and dotted lines correspond +respectively to light coming from 5, 10 and 20 km distance from the +telescope.} +\label{fig:rayleigh} +\end{figure} +% +\subsection{Mie scattering} +Cherenkov light also suffers Mie scattering through interaction with +small dust particles suspended in the air (aerosols), whose size is +comparable to the wavelength of the light. In our simulation of the +attenuation due to aerosols we have used the model proposed by +Elterman \cite{elterman64,elterman65}, which considers an aerosol +number density $N_p$ which (roughly) decreases exponentially up to 10 +km a.s.l. with scale height $H \simeq 1.2$ km, followed by a more +tenuous layer between 10 and 30 km (see fig. \ref{fig:aerosol}a). In +this model, the aerosol size distribution is considered to be +unchanged with altitude. +% +\begin{figure}[ht] +\begin{center} +\mbox{ \epsfig{file=eps/aerosol.eps,width=0.9\textwidth} } +\end{center} +\caption[] +{Aerosol model by Elterman: in (a), number density of +aerosols as a function of height above sea level; in (b), aerosol +attenuation coefficient at sea level as a function of wavelength.} +\label{fig:aerosol} +\end{figure} +% +\par +Measured values of the aerosol attenuation coefficients at sea level +$\beta_p(0)$ for different wavelengths \cite{elterman65} are shown in +figure \ref{fig:aerosol}b. To obtain the attenuation coefficient at a +given height $h$, we simply do $\beta_p(h, \lambda) = \beta_p(0, +\lambda) \cdot N_p(h)/N_p(0)$. In the Elterman model the aerosol +transmission coefficient for the trajectory from A to B depicted in +figure \ref{fig:atmoscheme} would then be: +% +\begin{equation} +T_{\text{Mie}}(\lambda) = e^{-\tau_{mie}} \quad \text{, with}\quad +\tau_{mie}(h_1, h_2, \theta, \lambda) = \frac{\beta_p(0, \lambda)}{N_p(0)} \; +\int_{h_1}^{h_2} +\; N_p(h) \;\; \frac{dL}{dh}\; dh +\label{eq:aerosoltau} +\end{equation} +% +Here $\tau_{mie}$ is the aerosol optical depth of the path from A to +B. Given that the aerosol density distribution is not a simple +exponential, we have to do the integral in (\ref{eq:aerosoltau}) +numerically. The integral depends on $h_2$ and on $\theta$, through +$dL/dh$ (it also +depends on $h_1$, but this is the observation level and therefore +fixed). In this case we use the exact expression for $\;dL/dh\;$ which can be +obtained from (\ref{eq:height}). At the beginning of each simulation +run we calculate and store the results of the integral for values of +$\theta$ between 0 and 90$^\circ$ (in steps of $1^\circ$), and of +$h_2$ from $h_1$ up to 30 km (in steps of 100 m). To do the integral a +linear interpolation has been used to obtain the value of $N_p$ for +any height. During the simulation of each Cherenkov photon, we get the +corresponding precalculated value of the integral and deduce +$T_{\text{Mie}}$ from expression (\ref{eq:aerosoltau}). +% +\begin{figure}[ht] +\begin{center} +\mbox{ \epsfig{file=eps/mie.eps,width=\textwidth} } +\end{center} +\caption[] +{Aerosol transmission coefficient for three different wavelengths as a +function of the distance between the photon emission point and the +telescope. Plots for four different zenith angles between 0 and 80 +degrees are shown.} +\label{fig:mie} +\end{figure} +% +\par +Since in this model the aerosols are concentrated mainly at very low +altitude, the transmission coefficient is more or less constant above +a certain height (which depends on $\theta$), as can be seen in +fig. \ref{fig:mie}. For instance, for vertically incident 300 nm light +emitted higher than 4 km above the telescope, the Mie transmission is +about 0.95. +% +\subsection{Absorption by Ozone} +% +The absorption of Cherenkov light by Ozone has been implemented +following also the Elterman standard atmosphere \cite{elterman65}. The +coefficient for ozone absorption is given by +% +\begin{equation} +\beta_3(h,\lambda) = A_v(\lambda) \cdot D_3(h) +\end{equation} +% +, where $A_v(\lambda)$ is the Vigroux \cite{vigroux53} ozone +absorption coefficient (cm$^{-1}$) and $D_3(h)$ is the ozone +concentration (cm km$^{-1}$) according to Elterman. The transmission +coefficient of Ozone in the path $\overline{\text{AB}}$ is then: +% +\begin{equation} +T_{\text{Ozone}}(\lambda) = e^{-\tau_{oz}} \quad \text{, with}\quad +\tau_{oz}(h_1, h_2, \theta, \lambda) = A_v(\lambda) \; \int_{h_1}^{h_2} +\; D_3(h) \;\; \frac{dL}{dh}\; dh +\label{eq:ozonetau} +\end{equation} +% +\begin{figure}[ht] +\begin{center} +\mbox{ \epsfig{file=eps/ozone.eps,width=\textwidth} } +\end{center} +\caption[] +{Ozone concentration vertical profile (a) and Vigroux coefficients for +Ozone absorption (b). The Vigroux coefficients for $\lambda =$ 380 and +400 nm are zero.} +\label{fig:ozone} +\end{figure} +% +\par +Once again, like in the case of Mie scattering, the optical depth +$\tau_{oz}$ is the product of a factor which depends on $\lambda$ and +an integral which depends on $h_1$, $h_2$ and $\theta$. We proceed in +the same way as before, precalculating the values of the integral in +steps of $\Delta\theta = 1^\circ$ and $\Delta h = 100$ m, up to a +height of 50 km a.s.l. (where the ozone concentration becomes +negligible), and then reading the appropriate values for every +simulated photon. +\par +Finally, the overall atmospheric transmission coefficient is +calculated as +% +\begin{equation} +T_{total} = T_{Ray} \cdot T_{Mie} \cdot T_{Ozone} +\end{equation} +% +In figure \ref{fig:absorplot} the atmospheric transmission as a +function of the distance to the telescope for $\theta = 0^\circ$ is +shown. Ozone absorption turns out to be dominant below 320 nm, while +Rayleigh scattering is the main cause of the loss of photons at longer +wavelengths. +% +\begin{figure}[ht] +\begin{center} +\mbox{ \epsfig{file=eps/absorplot.eps,width=\textwidth} } +\end{center} +\caption[] +{Total transmission coefficient for vertically incident light as a +function of the distance between the emission point and the +telescope. The contributions of absorption by ozone and of Rayleigh +and Mie scattering are also shown for comparison.} +\label{fig:absorplot} +\end{figure} +% +\newpage +\section*{Appendix B : files in the reflector package} +\addcontentsline{toc}{section}{Appendix B : files in the reflector package} The list of all Reflector files follows. @@ -1060,20 +1496,28 @@ 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.ps 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/doc/eps/absorplot.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/aerosol.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/airmass.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/atmoscheme.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/colimation.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/coma.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/coma_star.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/coorsystems.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/evcompare.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/mie.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/ozone.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/parabola.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/rayleigh.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/refl06images.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/reflec.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/spot10kmf1694.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/spot10kmf1700.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/spot_inf_f1697.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/telecoor.eps +MagicProgs/Simulation/Detector/Reflector_0.6/doc/eps/timing.eps MagicProgs/Simulation/Detector/Reflector_0.6/tester/Makefile @@ -1096,4 +1540,22 @@ %%>>>> Or the following if you include here by hand your %%>>>> bibliographic entries + +\begin{thebibliography}{00} + +\bibitem{elterman64} +L. Elterman, Applied Optics Vol. 3, No. 6 (1964) 745. + +\bibitem{elterman65} +L. Elterman, R.B. Toolin, S.L. Valley (editor), Handbook of +geophysics and space environments, McGraw-Hill, N.Y. (1965). + +\bibitem{cor02}D. Heck and J. Knapp, EAS Simulation with CORSIKA: A User's +Manual, 2002. + +\bibitem{vigroux53} +E. Vigroux, Contributions \`a l'étude expérimentale de l'absorption +de l'ozone, Annales de Physique, v. 8 (1953) 709. + +\end{thebibliography} \end{document}