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