HMPID/AliHMPIDRecon.cxx

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  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
  72   ph+=TMath::Pi();                         // right XYZ local orientation
  73   SetTrack(xRa,yRa,th,ph);
  74
  75   fRadNmean=nmean;
  76
  77   Float_t dMin=999,mipX=-1,mipY=-1;Int_t chId=-1,mipId=-1,mipQ=-1;
  78   fPhotCnt=0;
  79   for (Int_t iClu=0; iClu<pCluLst->GetEntriesFast();iClu++){//clusters loop
  80     AliHMPIDCluster *pClu=(AliHMPIDCluster*)pCluLst->UncheckedAt(iClu);                       //get pointer to current cluster
  81     chId=pClu->Ch();
  82     if(pClu->Q()>pParam->QCut()){                                                             //charge compartible with MIP clusters
  83       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
  84       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
  85     }else{                                                                                    //charge compatible with photon cluster
  86       Double_t thetaCer,phiCer;
  87       if(FindPhotCkov(pClu->X(),pClu->Y(),thetaCer,phiCer)){                                  //find ckov angle for this  photon candidate
  88         fPhotCkov[fPhotCnt]=thetaCer;                                                         //actual theta Cerenkov (in TRS)
  89         fPhotPhi [fPhotCnt]=phiCer-TMath::Pi();                                               //actual phi   Cerenkov (in TRS): -pi to come back to "unusual" ref system (X,Y,-Z)
  90         fPhotCnt++;                                                                           //increment counter of photon candidates
  91       }
  92     }
  93   }//clusters loop
  94   Int_t iNacc=FlagPhot(HoughResponse());                                                      //flag photons according to individual theta ckov with respect to most probable
  95   pTrk->SetHMPIDmip(mipX,mipY,mipQ,iNacc);                                                    //store mip info
  96
  97   if(mipId==-1)              {pTrk->SetHMPIDsignal(kMipQdcCut);  return;}                     //no clusters with QDC more the threshold at all
  98   if(dMin>pParam->DistCut()) {pTrk->SetHMPIDsignal(kMipDistCut); return;}                     //closest cluster with enough charge is still too far from intersection
  99   pTrk->SetHMPIDcluIdx(chId,mipId);                                                           //set index of cluster
 100   if(iNacc<1)    pTrk->SetHMPIDsignal(kNoPhotAccept);                                         //no photon candidates is accepted
 101   else           pTrk->SetHMPIDsignal(FindRingCkov(pCluLst->GetEntries()));                   //find best Theta ckov for ring i.e. track
 102
 103   pTrk->SetHMPIDchi2(fCkovSigma2);                                                            //errors squared
 104
 105 }//ThetaCerenkov()
 106 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 107 Bool_t AliHMPIDRecon::FindPhotCkov(Double_t cluX,Double_t cluY,Double_t &thetaCer,Double_t &phiCer)
 108 {
 109 // Finds Cerenkov angle  for this photon candidate
 110 // Arguments: cluX,cluY - position of cadidate's cluster
 111 // Returns: Cerenkov angle
 112
 113   TVector3 dirCkov;
 114
 115   Double_t zRad=-0.5*AliHMPIDRecon::fgkRadThick
 116                     -AliHMPIDRecon::fgkWinThick
 117                     -AliHMPIDRecon::fgkGapThick;                    //z position of middle of RAD
 118
 119   TVector3 rad(fTrkPos.X(),fTrkPos.Y(),zRad);                       //impact point at middle of RAD
 120   TVector3  pc(cluX,cluY,0);                                        //mip at PC: z=0 @ PC
 121   Double_t cluR = TMath::Sqrt((cluX-fTrkPos.X())*(cluX-fTrkPos.X())+
 122                               (cluY-fTrkPos.Y())*(cluY-fTrkPos.Y()));//ref. distance impact RAD-CLUSTER
 123   Double_t phi=(pc-rad).Phi();                                      //phi of photon
 124
 125   Double_t ckov1=0,ckov2=0.75+fTrkDir.Theta();                      //start to find theta cerenkov in DRS
 126   const Double_t kTol=0.01;
 127   Int_t iIterCnt = 0;
 128   while(1){
 129     if(iIterCnt>=50) return kFALSE;
 130     Double_t ckov=0.5*(ckov1+ckov2);
 131     dirCkov.SetMagThetaPhi(1,ckov,phi);
 132     TVector2 posC=TraceForward(dirCkov);                      //trace photon with actual angles
 133     Double_t dist=cluR-(posC-fTrkPos).Mod();                  //get distance between trial point and cluster position
 134     if(posC.X()==-999) dist = - 999;                          //total reflection problem
 135     iIterCnt++;                                               //counter step
 136     if     (dist> kTol) ckov1=ckov;                           //cluster @ larger ckov
 137     else if(dist<-kTol) ckov2=ckov;                           //cluster @ smaller ckov
 138     else{                                                     //precision achived: ckov in DRS found
 139       dirCkov.SetMagThetaPhi(1,ckov,phi);                     //
 140       RecPhot(dirCkov,thetaCer,phiCer);                       //find ckov (in TRS:the effective Cherenkov angle!)
 141       return kTRUE;
 142     }
 143   }
 144 }//FindPhotTheta()
 145 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 146 TVector2 AliHMPIDRecon::TraceForward(TVector3 dirCkov)const
 147 {
 148   //Trace forward a photon from (x,y) up to PC
 149   // Arguments: dirCkov photon vector in LORS
 150   //   Returns: pos of traced photon at PC
 151   TVector2 pos(-999,-999);
 152   if(dirCkov.Theta() > TMath::ASin(1./fRadNmean))  return pos;      //total refraction on WIN-GAP boundary
 153   Double_t zRad=-0.5*AliHMPIDRecon::fgkRadThick
 154                     -AliHMPIDRecon::fgkWinThick
 155                     -AliHMPIDRecon::fgkGapThick;                    //z position of middle of RAD
 156   TVector3  posCkov(fTrkPos.X(),fTrkPos.Y(),zRad);                  //RAD: photon position is track position @ middle of RAD
 157   Propagate(dirCkov,posCkov,-fgkWinThick-fgkGapThick);              //go to RAD-WIN boundary
 158   Refract  (dirCkov,         fRadNmean,fgkWinIdx    );              //RAD-WIN refraction
 159   Propagate(dirCkov,posCkov,            -fgkGapThick);              //go to WIN-GAP boundary
 160   Refract  (dirCkov,         fgkWinIdx,fgkGapIdx    );              //WIN-GAP refraction
 161   Propagate(dirCkov,posCkov,                       0);              //go to PC
 162   pos.Set(posCkov.X(),posCkov.Y());
 163   return pos;
 164 }//TraceForward()
 165 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 166 void AliHMPIDRecon::RecPhot(TVector3 dirCkov,Double_t &thetaCer,Double_t &phiCer)
 167 {
 168   //Theta Cerenkov reconstruction
 169   // Arguments: (x,y) of initial point in LORS, dirCkov photon vector in LORS
 170   //   Returns: thetaCer theta cerenkov reconstructed
 171 //  TVector3 dirTrk;
 172 //  dirTrk.SetMagThetaPhi(1,fTrkDir.Theta(),fTrkDir.Phi());
 173 //  Double_t thetaCer = TMath::ACos(dirCkov*dirTrk);
 174   TRotation mtheta;   mtheta.RotateY(- fTrkDir.Theta());
 175   TRotation mphi;       mphi.RotateZ(- fTrkDir.Phi());
 176   TRotation mrot=mtheta*mphi;
 177   TVector3 dirCkovTRS;
 178   dirCkovTRS=mrot*dirCkov;
 179   phiCer  = dirCkovTRS.Phi();                                          //actual value of the phi of the photon
 180   thetaCer= dirCkovTRS.Theta();                                        //actual value of thetaCerenkov of the photon
 181 }
 182 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 183 Double_t AliHMPIDRecon::FindRingArea(Double_t ckovAng)const
 184 {
 185 // Find area inside the cerenkov ring which lays inside PCs
 186 // Arguments: ckovAng - cerenkov angle
 187 //   Returns: area of the ring in cm^2 for given theta ckov
 188
 189   const Int_t kN=100;
 190   Double_t area=0;
 191   for(Int_t i=0;i<kN;i++){
 192     TVector2 pos1=TracePhot(ckovAng,Double_t(TMath::TwoPi()*i    /kN));//trace this photon
 193     TVector2 pos2=TracePhot(ckovAng,Double_t(TMath::TwoPi()*(i+1)/kN));//trace the next photon
 194     area+=(pos1-fTrkPos)*(pos2-fTrkPos);                               //add area of the triangle...
 195   }
 196   return area;
 197 }//FindRingArea()
 198 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 199 Double_t AliHMPIDRecon::FindRingCkov(Int_t)
 200 {
 201 // 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
 202 // collecting errors for all single Ckov candidates thetas. (Assuming they are independent)
 203 // Arguments: iNclus- total number of clusters in chamber for background estimation
 204 //    Return: best estimation of track Theta ckov
 205
 206   Double_t wei = 0.;
 207   Double_t weightThetaCerenkov = 0.;
 208
 209   Double_t ckovMin=9999.,ckovMax=0.;
 210   Double_t sigma2 = 0;   //to collect error squared for this ring
 211
 212   for(Int_t i=0;i<fPhotCnt;i++){//candidates loop
 213     if(fPhotFlag[i] == 2){
 214       if(fPhotCkov[i]<ckovMin) ckovMin=fPhotCkov[i];                         //find max and min Theta ckov from all candidates within probable window
 215       if(fPhotCkov[i]>ckovMax) ckovMax=fPhotCkov[i];
 216       weightThetaCerenkov += fPhotCkov[i]*fPhotWei[i];
 217       wei += fPhotWei[i];                                                    //collect weight as sum of all candidate weghts
 218
 219       sigma2 += 1./Sigma2(fPhotCkov[i],fPhotPhi[i]);
 220     }
 221   }//candidates loop
 222
 223   if(sigma2>0) fCkovSigma2=1./sigma2;
 224   else         fCkovSigma2=1e10;
 225
 226   if(wei != 0.) weightThetaCerenkov /= wei; else weightThetaCerenkov = 0.;
 227   return weightThetaCerenkov;
 228 }//FindCkovRing()
 229 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 230 Int_t AliHMPIDRecon::FlagPhot(Double_t ckov)
 231 {
 232 // Flag photon candidates if their individual ckov angle is inside the window around ckov angle returned by  HoughResponse()
 233 // Arguments: ckov- value of most probable ckov angle for track as returned by HoughResponse()
 234 //   Returns: number of photon candidates happened to be inside the window
 235
 236 // Photon Flag:  Flag = 0 initial set;
 237 //               Flag = 1 good candidate (charge compatible with photon);
 238 //               Flag = 2 photon used for the ring;
 239
 240   Int_t steps = (Int_t)((ckov )/ fDTheta); //how many times we need to have fDTheta to fill the distance between 0  and thetaCkovHough
 241
 242   Double_t tmin = (Double_t)(steps - 1)*fDTheta;
 243   Double_t tmax = (Double_t)(steps)*fDTheta;
 244   Double_t tavg = 0.5*(tmin+tmax);
 245
 246   tmin = tavg - 0.5*fWindowWidth;  tmax = tavg + 0.5*fWindowWidth;
 247
 248   Int_t iInsideCnt = 0; //count photons which Theta ckov inside the window
 249   for(Int_t i=0;i<fPhotCnt;i++){//photon candidates loop
 250     if(fPhotCkov[i] >= tmin && fPhotCkov[i] <= tmax)    {
 251       fPhotFlag[i]=2;
 252       iInsideCnt++;
 253     }
 254   }
 255   return iInsideCnt;
 256 }//FlagPhot()
 257 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 258 TVector2 AliHMPIDRecon::TracePhot(Double_t ckovThe,Double_t ckovPhi)const
 259 {
 260 // Trace a single Ckov photon from emission point somewhere in radiator up to photocathode taking into account ref indexes of materials it travereses
 261 // Arguments: ckovThe,ckovPhi- photon ckov angles in DRS, [rad]
 262 //   Returns: distance between photon point on PC and track projection
 263   TRotation mtheta;   mtheta.RotateY(fTrkDir.Theta());
 264   TRotation mphi;       mphi.RotateZ(fTrkDir.Phi());
 265   TRotation mrot=mphi*mtheta;
 266   TVector3  dirCkov,dirCkovTors;
 267
 268   dirCkovTors.SetMagThetaPhi(1,ckovThe,ckovPhi);                    //initially photon is directed according to requested ckov angle
 269   dirCkov=mrot*dirCkovTors;                                         //now we know photon direction in LORS
 270   return TraceForward(dirCkov);
 271 }//TracePhot()
 272 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 273 void AliHMPIDRecon::Propagate(const TVector3 dir,TVector3 &pos,Double_t z)const
 274 {
 275 // Finds an intersection point between a line and XY plane shifted along Z.
 276 // Arguments:  dir,pos   - vector along the line and any point of the line
 277 //             z         - z coordinate of plain
 278 //   Returns:  none
 279 //   On exit:  pos is the position if this intesection if any
 280   static TVector3 nrm(0,0,1);
 281          TVector3 pnt(0,0,z);
 282
 283   TVector3 diff=pnt-pos;
 284   Double_t sint=(nrm*diff)/(nrm*dir);
 285   pos+=sint*dir;
 286 }//Propagate()
 287 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 288 void AliHMPIDRecon::Refract(TVector3 &dir,Double_t n1,Double_t n2)const
 289 {
 290 // Refract direction vector according to Snell law
 291 // Arguments:
 292 //            n1 - ref idx of first substance
 293 //            n2 - ref idx of second substance
 294 //   Returns: none
 295 //   On exit: dir is new direction
 296   Double_t sinref=(n1/n2)*TMath::Sin(dir.Theta());
 297   if(sinref>1.)    dir.SetXYZ(-999,-999,-999);
 298   else             dir.SetTheta(TMath::ASin(sinref));
 299 }//Refract()
 300 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 301 Double_t AliHMPIDRecon::HoughResponse()
 302 {
 303 //
 304 //
 305 //
 306   Double_t kThetaMax=0.75;
 307   Int_t nChannels = (Int_t)(kThetaMax/fDTheta+0.5);
 308   TH1D *phots   = new TH1D("Rphot"  ,"phots"         ,nChannels,0,kThetaMax);
 309   TH1D *photsw  = new TH1D("RphotWeighted" ,"photsw" ,nChannels,0,kThetaMax);
 310   TH1D *resultw = new TH1D("resultw","resultw"       ,nChannels,0,kThetaMax);
 311   Int_t nBin = (Int_t)(kThetaMax/fDTheta);
 312   Int_t nCorrBand = (Int_t)(fWindowWidth/(2*fDTheta));
 313
 314   for (Int_t i=0; i< fPhotCnt; i++){//photon cadidates loop
 315     Double_t angle = fPhotCkov[i];  if(angle<0||angle>kThetaMax) continue;
 316     phots->Fill(angle);
 317     Int_t bin = (Int_t)(0.5+angle/(fDTheta));
 318     Double_t weight=1.;
 319     if(fIsWEIGHT){
 320       Double_t lowerlimit = ((Double_t)bin)*fDTheta - 0.5*fDTheta;  Double_t upperlimit = ((Double_t)bin)*fDTheta + 0.5*fDTheta;
 321       Double_t diffArea = FindRingArea(upperlimit)-FindRingArea(lowerlimit);
 322       if(diffArea>0) weight = 1./diffArea;
 323     }
 324     photsw->Fill(angle,weight);
 325     fPhotWei[i]=weight;
 326   }//photon candidates loop
 327
 328   for (Int_t i=1; i<=nBin;i++){
 329     Int_t bin1= i-nCorrBand;
 330     Int_t bin2= i+nCorrBand;
 331     if(bin1<1) bin1=1;
 332     if(bin2>nBin)bin2=nBin;
 333     Double_t sumPhots=phots->Integral(bin1,bin2);
 334     if(sumPhots<3) continue;                            // if less then 3 photons don't trust to this ring
 335     Double_t sumPhotsw=photsw->Integral(bin1,bin2);
 336     resultw->Fill((Double_t)((i+0.5)*fDTheta),sumPhotsw);
 337   }
 338 // evaluate the "BEST" theta ckov as the maximum value of histogramm
 339   Double_t *pVec = resultw->GetArray();
 340   Int_t locMax = TMath::LocMax(nBin,pVec);
 341   phots->Delete();photsw->Delete();resultw->Delete(); // Reset and delete objects
 342
 343   return (Double_t)(locMax*fDTheta+0.5*fDTheta); //final most probable track theta ckov
 344 }//HoughResponse()
 345 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 346 Double_t AliHMPIDRecon::Sigma2(Double_t ckovTh, Double_t ckovPh)const
 347 {
 348 // Analithical calculation of total error (as a sum of localization, geometrical and chromatic errors) on Cerenkov angle for a given Cerenkov photon
 349 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 350 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 351 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 352 //            MIP beta
 353 //   Returns: absolute error on Cerenkov angle, [radians]
 354
 355   TVector3 v(-999,-999,-999);
 356   Double_t trkBeta = 1./(TMath::Cos(ckovTh)*fRadNmean);
 357
 358   v.SetX(SigLoc (ckovTh,ckovPh,trkBeta));
 359   v.SetY(SigGeom(ckovTh,ckovPh,trkBeta));
 360   v.SetZ(SigCrom(ckovTh,ckovPh,trkBeta));
 361
 362   return v.Mag2();
 363 }
 364 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 365 Double_t AliHMPIDRecon::SigLoc(Double_t thetaC, Double_t phiC,Double_t betaM)const
 366 {
 367 // Analithical calculation of localization error (due to finite segmentation of PC) on Cerenkov angle for a given Cerenkov photon
 368 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 369 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 370 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 371 //            MIP beta
 372 //   Returns: absolute error on Cerenkov angle, [radians]
 373   Double_t phiDelta = phiC - fTrkDir.Phi();
 374
 375   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 376   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 377   if (k<0) return 1e10;
 378
 379   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()));
 380   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()));
 381
 382   Double_t kk = betaM*TMath::Sqrt(k)/(8*alpha);
 383   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));
 384   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));
 385
 386   return  TMath::Sqrt(0.2*0.2*dtdxc*dtdxc + 0.25*0.25*dtdyc*dtdyc);
 387 }
 388 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 389 Double_t AliHMPIDRecon::SigCrom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 390 {
 391 // Analithical calculation of chromatic error (due to lack of knowledge of Cerenkov photon energy) on Cerenkov angle for a given Cerenkov photon
 392 // created by a given MIP. Fromulae according to CERN-EP-2000-058
 393 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 394 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 395 //            MIP beta
 396 //   Returns: absolute error on Cerenkov angle, [radians]
 397   Double_t phiDelta = phiC - fTrkDir.Phi();
 398   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 399
 400   Double_t dtdn = TMath::Cos(fTrkDir.Theta())*fRadNmean*betaM*betaM/(alpha*TMath::Tan(thetaC));
 401
 402   Double_t f = 0.00928*(7.75-5.635)/TMath::Sqrt(12.);
 403
 404   return f*dtdn;
 405 }//SigCrom()
 406 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 407 Double_t AliHMPIDRecon::SigGeom(Double_t thetaC, Double_t phiC,Double_t betaM)const
 408 {
 409 // Analithical calculation of geometric error (due to lack of knowledge of creation point in radiator) on Cerenkov angle for a given Cerenkov photon
 410 // created by a given MIP. Formulae according to CERN-EP-2000-058
 411 // Arguments: Cerenkov and azimuthal angles for Cerenkov photon, [radians]
 412 //            dip and azimuthal angles for MIP taken at the entrance to radiator, [radians]
 413 //            MIP beta
 414 //   Returns: absolute error on Cerenkov angle, [radians]
 415
 416   Double_t phiDelta = phiC - fTrkDir.Phi();
 417   Double_t alpha =TMath::Cos(fTrkDir.Theta())-TMath::Tan(thetaC)*TMath::Cos(phiDelta)*TMath::Sin(fTrkDir.Theta());
 418
 419   Double_t k = 1.-fRadNmean*fRadNmean+alpha*alpha/(betaM*betaM);
 420   if (k<0) return 1e10;
 421
 422   Double_t eTr = 0.5*1.5*betaM*TMath::Sqrt(k)/(8*alpha);
 423   Double_t lambda = 1.-TMath::Sin(fTrkDir.Theta())*TMath::Sin(fTrkDir.Theta())*TMath::Sin(phiC)*TMath::Sin(phiC);
 424
 425   Double_t c = 1./(1.+ eTr*k/(alpha*alpha*TMath::Cos(thetaC)*TMath::Cos(thetaC)));
 426   Double_t i = betaM*TMath::Tan(thetaC)*lambda*TMath::Power(k,1.5);
 427   Double_t ii = 1.+eTr*betaM*i;
 428
 429   Double_t err = c * (i/(alpha*alpha*8) +  ii*(1.-lambda) / ( alpha*alpha*8*betaM*(1.+eTr)) );
 430   Double_t trErr = 1.5/(TMath::Sqrt(12.)*TMath::Cos(fTrkDir.Theta()));
 431
 432   return trErr*err;
 433 }//SigGeom()
 434 //++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++