HMPID/AliHMPIDRecon.cxx

   1 /**************************************************************************
   2  * Copyright(c) 1998-1999, ALICE Experiment at CERN, All rights reserved. *
   3  *                                                                        *
   4  * Author: The ALICE Off-line Project.                                    *
   5  * Contributors are mentioned in the code where appropriate.              *
   6  *                                                                        *
   7  * Permission to use, copy, modify and distribute this software and its   *
   8  * documentation strictly for non-commercial purposes is hereby granted   *
   9  * without fee, provided that the above copyright notice appears in all   *
  10  * copies and that both the copyright notice and this permission notice   *
  11  * appear in the supporting documentation. The authors make no claims     *
  12  * about the suitability of this software for any purpose. It is          *
  13  * provided "as is" without express or implied warranty.                  *
  14  **************************************************************************/
  15
  16 //////////////////////////////////////////////////////////////////////////
  17 //                                                                      //
  18 // AliHMPIDRecon                                                         //
  19 //                                                                      //
  20 // HMPID class to perfom pattern recognition based on Hough transfrom    //
  21 // for single chamber                                                   //
  22 //////////////////////////////////////////////////////////////////////////
  23
  24 #include "AliHMPIDRecon.h"   //class header
  25 #include "AliHMPIDParam.h"   //CkovAngle()
  26 #include "AliHMPIDCluster.h" //CkovAngle()
  27 #include <TRotation.h>       //TracePhot()
  28 #include <TH1D.h>            //HoughResponse()
  29 #include <TClonesArray.h>    //CkovAngle()
  30 #include <AliESDtrack.h>     //CkovAngle()
  31
  32 const Double_t AliHMPIDRecon::fgkRadThick=1.5;
  33 const Double_t AliHMPIDRecon::fgkWinThick=0.5;
  34 const Double_t AliHMPIDRecon::fgkGapThick=8.0;
  35 const Double_t AliHMPIDRecon::fgkWinIdx  =1.5787;
  36 const Double_t AliHMPIDRecon::fgkGapIdx  =1.0005;
  37
  38 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  39 AliHMPIDRecon::AliHMPIDRecon():TTask("RichRec","RichPat"),
  40   fRadNmean(1.292),
  41   fPhotCnt(-1),
  42   fCkovSigma2(0),
  43   fIsWEIGHT(kFALSE),
  44   fDTheta(0.001),
  45   fWindowWidth(0.045),
  46   fTrkDir(TVector3(0,0,1)),fTrkPos(TVector2(30,40))
  47 {
  48 // main ctor
  49   for (Int_t i=0; i<3000; i++) {
  50     fPhotFlag[i] =  0;
  51     fPhotCkov[i] = -1;
  52     fPhotPhi [i] = -1;
  53     fPhotWei [i] =  0;
  54   }
  55 }
  56 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  57 void AliHMPIDRecon::CkovAngle(AliESDtrack *pTrk,TClonesArray *pCluLst,Double_t nmean)
  58 {
  59 // Pattern recognition method based on Hough transform
  60 // Arguments:   pTrk     - track for which Ckov angle is to be found
  61 //              pCluLst  - list of clusters for this chamber
  62 //   Returns:            - track ckov angle, [rad],
  63
  64   AliHMPIDParam *pParam=AliHMPIDParam::Instance();
  65
  66   if(pCluLst->GetEntries()>pParam->MultCut()) fIsWEIGHT = kTRUE; // offset to take into account bkg in reconstruction
  67   else                                        fIsWEIGHT = kFALSE;
  68
  69   Float_t xRa,yRa,th,ph;
  70   pTrk->GetHMPIDtrk(xRa,yRa,th,ph);        //initialize this track: th and ph angles at middle of RAD
  71   SetTrack(xRa,yRa,th,ph);
  72
  73   fRadNmean=nmean;
  74
  75   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
  76   fPhotCnt=0;
  77   for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
  78     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster
  79     chId=pClu->Ch();
  80     if(pClu->Q()>pParam->QCut()){                                                             //charge compartible with MIP clusters
  81       Float_t dX=fPc.X()-pClu->X(),dY=fPc.Y()-pClu->Y(),d =TMath::Sqrt(dX*dX+dY*dY);          //distance between current cluster and intersection point
  82       if( d < dMin) {mipId=iClu; dMin=d;mipX=pClu->X();mipY=pClu->Y();mipQ=(Int_t)pClu->Q();} //current cluster is closer, overwrite data for min cluster
  83     }else{                                                                                    //charge compatible with photon cluster
  84       Double_t thetaCer,phiCer;
  85       if(FindPhotCkov(pClu->X(),pClu->Y(),thetaCer,phiCer)){                                  //find ckov angle for this  photon candidate
  86         fPhotCkov[fPhotCnt]=thetaCer;                                                         //actual theta Cerenkov (in TRS)
  87         fPhotPhi [fPhotCnt]=phiCer;                                                           //actual phi   Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
  88         fPhotCnt++;                                                                           //increment counter of photon candidates
  89       }
  90     }
  91   }//clusters loop
  92   Int_t iNacc=FlagPhot(HoughResponse());                                                      //flag photons according to individual theta ckov with respect to most probable
  93   pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc);                                                    //store mip info
  94
  95   if(mipId==-1)              {pTrk->SetHMPIDsignal(kMipQdcCut);  return;}                     //no clusters with QDC more the threshold at all
  96   if(dMin>pParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;}                     //closest cluster with enough charge is still too far from intersection
  97   pTrk->SetHMPIDcluIdx(chId,mipId);                                                           //set index of cluster
  98   if(iNacc<1)    pTrk->SetHMPIDsignal(kNoPhotAccept);                                         //no photon candidates is accepted
  99   else           pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries()));                   //find best Theta ckov for ring i.e. track
 100
 101   pTrk->SetHMPIDchi2(fCkovSigma2);                                                            //errors squared
 102
 103 }//ThetaCerenkov()
 104 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 105 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
 106 {
 107 // Finds Cerenkov angle  for this photon candidate
 108 // Arguments: cluX,cluY - position of cadidate's cluster
 109 // Returns: Cerenkov angle
 110
 111   TVector3 dirCkov;
 112
 113   Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick;                   //z position of middle of RAD
 114   TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad);                        //impact point at middle of RAD
 115   TVector3  pc(cluX,cluY,0.5*fgkWinThick+fgkGapIdx);                 //mip at PC
 116   Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
 117                               (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
 118   Double_t phi=(pc-rad).Phi();                                       //phi of photon
 119
 120   Double_t ckov1=0;
 121   Double_t ckov2=0.75+fTrkDir.Theta();                        //start to find theta cerenkov in DRS
 122   const Double_t kTol=0.01;
 123   Int_t iIterCnt = 0;
 124   while(1){
 125     if(iIterCnt>=50) return kFALSE;
 126     Double_t ckov=0.5*(ckov1+ckov2);
 127     dirCkov.SetMagThetaPhi(1,ckov,phi);
 128     TVector2 posC=TraceForward(dirCkov);                      //trace photon with actual angles
 129     Double_t dist=cluR-(posC-fTrkPos).Mod();                  //get distance between trial point and cluster position
 130     if(posC.X()==-999) dist = - 999;                          //total reflection problem
 131     iIterCnt++;                                               //counter step
 132     if     (dist> kTol) ckov1=ckov;                           //cluster @ larger ckov
 133     else if(dist<-kTol) ckov2=ckov;                           //cluster @ smaller ckov
 134     else{                                                     //precision achived: ckov in DRS found
 135       dirCkov.SetMagThetaPhi(1,ckov,phi);                     //
 136       RecPhot(dirCkov,thetaCer,phiCer);                       //find ckov (in TRS:the effective Cherenkov angle!)
 137       return kTRUE;
 138     }
 139   }
 140 }//FindPhotTheta()
 141 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 142 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
 143 {
 144   //Trace forward a photon from (x,y) up to PC
 145   // Arguments: dirCkov photon vector in LORS
 146   //   Returns: pos of traced photon at PC
 147   TVector2 pos(-999,-999);
 148   Double_t thetaCer = dirCkov.Theta();
 149   if(thetaCer > TMath::ASin(1./fRadNmean))  return pos;         //total refraction on WIN-GAP boundary
 150   Double_t zRad= -0.5*fgkRadThick-0.5*fgkWinThick;              //z position of middle of RAD
 151   TVector3  posCkov(fTrkPos.X(),fTrkPos.Y(),zRad);              //RAD: photon position is track position @ middle of RAD
 152   Propagate(dirCkov,posCkov,           -0.5*fgkWinThick);       //go to RAD-WIN boundary
 153   Refract  (dirCkov,         fRadNmean,fgkWinIdx);              //RAD-WIN refraction
 154   Propagate(dirCkov,posCkov,            0.5*fgkWinThick);       //go to WIN-GAP boundary
 155   Refract  (dirCkov,         fgkWinIdx,fgkGapIdx);              //WIN-GAP refraction
 156   Propagate(dirCkov,posCkov,0.5*fgkWinThick+fgkGapThick);       //go to PC
 157   pos.Set(posCkov.X(),posCkov.Y());
 158   return pos;
 159 }//TraceForward()
 160 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 161 void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
 162 {
 163   //Theta Cerenkov reconstruction
 164   // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
 165   //   Returns: thetaCer theta cerenkov reconstructed
 166 //  TVector3 dirTrk;
 167 //  dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
 168 //  Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
 169   TRotation mtheta;   mtheta.RotateY(- fTrkDir.Theta());
 170   TRotation mphi;       mphi.RotateZ(- fTrkDir.Phi());
 171   TRotation mrot=mtheta*mphi;
 172   TVector3 dirCkovTRS;
 173   dirCkovTRS=mrot*dirCkov;
 174   phiCer  = dirCkovTRS.Phi();                                          //actual value of the phi of the photon
 175   thetaCer= dirCkovTRS.Theta();                                        //actual value of thetaCerenkov of the photon
 176 }
 177 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 178 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
 179 {
 180 // Find area inside the cerenkov ring which lays inside PCs
 181 // Arguments: ckovAng - cerenkov angle
 182 //   Returns: area of the ring in cm^2 for given theta ckov
 183
 184   const Int_t kN=100;
 185   Double_t area=0;
 186   for(Int_t i=0;i<kN;i++){
 187     TVector2 pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*i    /kN));//trace this photon
 188     TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));//trace the next photon
 189     area+=(pos1-fTrkPos)*(pos2-fTrkPos);                               //add area of the triangle...
 190   }
 191   return area;
 192 }//FindRingArea()
 193 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 194 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
 195 {
 196 // Loops on all Ckov candidates and estimates the best Theta Ckov for a ring formed by those candidates. Also estimates an error for that Theat Ckov
 197 // collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
 198 // Arguments: iNclus- total number of clusters in chamber for background estimation
 199 //    Return: best estimation of track Theta ckov
 200
 201   Double_t wei = 0.;
 202   Double_t weightThetaCerenkov = 0.;
 203
 204   Double_t ckovMin=9999.,ckovMax=0.;
 205   Double_t sigma2 = 0;   //to collect error squared for this ring
 206
 207   for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
 208     if(fPhotFlag[i] == 2){
 209       if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i];                         //find max and min Theta ckov from all candidates within probable window
 210       if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
 211       weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
 212       wei += fPhotWei[i];                                                    //collect weight as sum of all candidate weghts
 213
 214       sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
 215     }
 216   }//candidates loop
 217
 218   if(sigma2>0) fCkovSigma2=1./sigma2;
 219   else         fCkovSigma2=1e10;
 220
 221   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
 222   return weightThetaCerenkov;
 223 }//FindCkovRing()
 224 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 225 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
 226 {
 227 // Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by  HoughResponse()
 228 // Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
 229 //   Returns: number of photon candidates happened to be inside the window
 230
 231 // Photon Flag:  Flag = 0 initial set;
 232 //               Flag = 1 good candidate (charge compatible with photon);
 233 //               Flag = 2 photon used for the ring;
 234
 235   Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0  and thetaCkovHough
 236
 237   Double_t tmin = (Double_t)(steps - 1)*fDTheta;
 238   Double_t tmax = (Double_t)(steps)*fDTheta;
 239   Double_t tavg = 0.5*(tmin+tmax);
 240
 241   tmin = tavg - 0.5*fWindowWidth;  tmax = tavg + 0.5*fWindowWidth;
 242
 243   Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
 244   for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
 245     if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax)    {
 246       fPhotFlag[i]=2;
 247       iInsideCnt++;
 248     }
 249   }
 250   return iInsideCnt;
 251 }//FlagPhot()
 252 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 253 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
 254 {
 255 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
 256 // Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]
 257 //   Returns: distance between photon point on PC and track projection
 258   TRotation mtheta;   mtheta.RotateY(fTrkDir.Theta());
 259   TRotation mphi;       mphi.RotateZ(fTrkDir.Phi());
 260   TRotation mrot=mphi*mtheta;
 261   TVector3  dirCkov,dirCkovTors;
 262
 263   dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi);                    //initially photon is directed according to requested ckov angle
 264   dirCkov=mrot*dirCkovTors;                                         //now we know photon direction in LORS
 265   return TraceForward(dirCkov);
 266 }//TracePhot()
 267 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 268 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
 269 {
 270 // Finds an intersection point between a line and XY plane shifted along Z.
 271 // Arguments:  dir,pos   - vector along the line and any point of the line
 272 //             z         - z coordinate of plain
 273 //   Returns:  none
 274 //   On exit:  pos is the position if this intesection if any
 275   static TVector3 nrm(0,0,1);
 276          TVector3 pnt(0,0,z);
 277
 278   TVector3 diff=pnt-pos;
 279   Double_t sint=(nrm*diff)/(nrm*dir);
 280   pos+=sint*dir;
 281 }//Propagate()
 282 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 283 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
 284 {
 285 // Refract direction vector according to Snell law
 286 // Arguments:
 287 //            n1 - ref idx of first substance
 288 //            n2 - ref idx of second substance
 289 //   Returns: none
 290 //   On exit: dir is new direction
 291   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
 292   if(sinref>1.)    dir.SetXYZ(-999,-999,-999);
 293   else             dir.SetTheta(TMath::ASin(sinref));
 294 }//Refract()
 295 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 296 Double_t AliHMPIDRecon::HoughResponse()
 297 {
 298 //
 299 //
 300 //
 301   Double_t kThetaMax=0.75;
 302   Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
 303   TH1D *phots   = new TH1D("Rphot"  ,"phots"         ,nChannels,0,kThetaMax);
 304   TH1D *photsw  = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
 305   TH1D *resultw = new TH1D("resultw","resultw"       ,nChannels,0,kThetaMax);
 306   Int_t nBin = (Int_t)(kThetaMax/fDTheta);
 307   Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
 308
 309   for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
 310     Double_t angle = fPhotCkov[i];  if(angle<0||angle>kThetaMax) continue;
 311     phots->Fill(angle);
 312     Int_t bin = (Int_t)(0.5+angle/(fDTheta));
 313     Double_t weight=1.;
 314     if(fIsWEIGHT){
 315       Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta;  Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
 316       Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
 317       if(diffArea>0) weight = 1./diffArea;
 318     }
 319     photsw->Fill(angle,weight);
 320     fPhotWei[i]=weight;
 321   }//photon candidates loop
 322
 323   for (Int_t i=1; i<=nBin;i++){
 324     Int_t bin1= i-nCorrBand;
 325     Int_t bin2= i+nCorrBand;
 326     if(bin1<1) bin1=1;
 327     if(bin2>nBin)bin2=nBin;
 328     Double_t sumPhots=phots->Integral(bin1,bin2);
 329     if(sumPhots<3) continue;                            // if less then 3 photons don't trust to this ring
 330     Double_t sumPhotsw=photsw->Integral(bin1,bin2);
 331     resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
 332   }
 333 // evaluate the "BEST" theta ckov as the maximum value of histogramm
 334   Double_t *pVec = resultw->GetArray();
 335   Int_t locMax = TMath::LocMax(nBin,pVec);
 336   phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
 337
 338   return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
 339 }//HoughResponse()
 340 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 341 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
 342 {
 343 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
 344 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 345 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 346 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 347 //            MIP beta
 348 //   Returns: absolute error on Cerenkov angle, [radians]
 349
 350   TVector3 v(-999,-999,-999);
 351   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
 352
 353   v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
 354   v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
 355   v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
 356
 357   return v.Mag2();
 358 }
 359 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 360 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
 361 {
 362 // Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
 363 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 364 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 365 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 366 //            MIP beta
 367 //   Returns: absolute error on Cerenkov angle, [radians]
 368   Double_t phiDelta = phiC - fTrkDir.Phi();
 369
 370   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 371   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 372   if (k<0) return 1e10;
 373
 374   Double_t mu =TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()));
 375   Double_t e  =TMath::Sin(fTrkDir.Theta())*TMath::Cos(fTrkDir.Phi())+TMath::Tan(thetaC)*(TMath::Cos(fTrkDir.Theta())*TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()));
 376
 377   Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
 378   Double_t dtdxc = kk*(k*(TMath::Cos(phiDelta)*TMath::Cos(fTrkDir.Phi())-TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Sin(fTrkDir.Phi()))-(alpha*mu/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
 379   Double_t dtdyc = kk*(k*(TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Phi())+TMath::Cos(fTrkDir.Theta())*TMath::Sin(phiDelta)*TMath::Cos(fTrkDir.Phi()))+(alpha* e/(betaM*betaM))*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiDelta));
 380
 381   return  TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
 382 }
 383 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 384 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 385 {
 386 // Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
 387 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 388 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 389 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 390 //            MIP beta
 391 //   Returns: absolute error on Cerenkov angle, [radians]
 392   Double_t phiDelta = phiC - fTrkDir.Phi();
 393   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 394
 395   Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fRadNmean*betaM*betaM/(alpha*TMath::Tan(thetaC));
 396
 397   Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
 398
 399   return f*dtdn;
 400 }//SigCrom()
 401 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 402 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 403 {
 404 // Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
 405 // created by a given MIP. Formulae according to CERN-EP-2000-058
 406 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 407 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 408 //            MIP beta
 409 //   Returns: absolute error on Cerenkov angle, [radians]
 410
 411   Double_t phiDelta = phiC - fTrkDir.Phi();
 412   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 413
 414   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 415   if (k<0) return 1e10;
 416
 417   Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
 418   Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
 419
 420   Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
 421   Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
 422   Double_t ii = 1.+eTr*betaM*i;
 423
 424   Double_t err = c * (i/(alpha*alpha*8) +  ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
 425   Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
 426
 427   return trErr*err;
 428 }//SigGeom()
 429 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++